ImpactX
ImpactX is an s-based beam dynamics code including space charge effects. This is the next generation of the IMPACT-Z code.
Note
ImpactX development is in beta status. Please contact us with any questions on it or if you like to contribute to its development.
Contact us
If you are starting using ImpactX, or if you have a user question, please pop in our discussions page and get in touch with the community.
The ImpactX GitHub repo is the main communication platform. Have a look at the action icons on the top right of the web page: feel free to watch the repo if you want to receive updates, or to star the repo to support the project. For bug reports or to request new features, you can also open a new issue.
We also have a discussion page on which you can find already answered questions, add new questions, get help with installation procedures, discuss ideas or share comments.
Code of Conduct
Our Pledge
In the interest of fostering an open and welcoming environment, we as contributors and maintainers pledge to making participation in our project and our community a harassment-free experience for everyone, regardless of age, body size, disability, ethnicity, sex characteristics, gender identity and expression, level of experience, education, socio-economic status, nationality, personal appearance, race, religion, or sexual identity and orientation.
Our Standards
Examples of behavior that contributes to creating a positive environment include:
Using welcoming and inclusive language
Being respectful of differing viewpoints and experiences
Gracefully accepting constructive criticism
Focusing on what is best for the community
Showing empathy towards other community members
Examples of unacceptable behavior by participants include:
The use of sexualized language or imagery and unwelcome sexual attention or advances
Trolling, insulting/derogatory comments, and personal or political attacks
Public or private harassment
Publishing others’ private information, such as a physical or electronic address, without explicit permission
Other conduct which could reasonably be considered inappropriate in a professional setting
Our Responsibilities
Project maintainers are responsible for clarifying the standards of acceptable behavior and are expected to take appropriate and fair corrective action in response to any instances of unacceptable behavior.
Project maintainers have the right and responsibility to remove, edit, or reject comments, commits, code, wiki edits, issues, and other contributions that are not aligned to this Code of Conduct, or to ban temporarily or permanently any contributor for other behaviors that they deem inappropriate, threatening, offensive, or harmful.
Scope
This Code of Conduct applies both within project spaces and in public spaces when an individual is representing the project or its community. Examples of representing a project or community include using an official project e-mail address, posting via an official social media account, or acting as an appointed representative at an online or offline event. Representation of a project may be further defined and clarified by project maintainers.
Enforcement
Instances of abusive, harassing, or otherwise unacceptable behavior may be reported by contacting the project team at warpx-coc@lbl.gov. All complaints will be reviewed and investigated and will result in a response that is deemed necessary and appropriate to the circumstances. The project team is obligated to maintain confidentiality with regard to the reporter of an incident. Further details of specific enforcement policies may be posted separately.
Project maintainers who do not follow or enforce the Code of Conduct in good faith may face temporary or permanent repercussions as determined by other members of the project’s leadership.
Attribution
This Code of Conduct is adapted from the Contributor Covenant, version 1.4, available at https://www.contributor-covenant.org/version/1/4/code-of-conduct.html
For answers to common questions about this code of conduct, see https://www.contributor-covenant.org/faq
Acknowledge ImpactX
Please acknowledge the role that ImpactX played in your research.
In presentations
Note
TODO :-)
In publications
Please add the following sentence to your publications, it helps contributors keep in touch with the community and promote the project.
Plain text:
This research used the open-source particle-in-cell code ImpactX https://github.com/ECP-WarpX/impactx. We acknowledge all ImpactX contributors.
Latex:
\usepackage{hyperref}
This research used the open-source particle-in-cell code ImpactX \url{https://github.com/ECP-WarpX/impactx}.
We acknowledge all ImpactX contributors.
Main ImpactX Reference
If your project leads to a scientific publication, please consider citing the paper below.
Huebl A, Lehe R, Mitchell C E, Qiang J, Ryne R D, Sandberg R T, Vay JL. Next Generation Computational Tools for the Modeling and Design of Particle Accelerators at Exascale. 2022 North American Particle Accelerator Conference (NAPAC’22), TUYE2, pp. 302-306, 2022. arXiv:2208.02382, DOI:10.18429/JACoW-NAPAC2022-TUYE2
Further ImpactX References
Sandberg R T, Lehe R, Mitchell C E, Garten M, Qiang J, Vay J-L and Huebl A. Hybrid Beamline Element ML-Training for Surrogates in the ImpactX Beam-Dynamics Code. 14th International Particle Accelerator Conference (IPAC’23), WEPA101, 2023. DOI:10.18429/JACoW-IPAC2023-WEPA101
Huebl A, Lehe R, Zoni E, Shapoval O, Sandberg R T, Garten M, Formenti A, Jambunathan R, Kumar P, Gott K, Myers A, Zhang W, Almgren A, Mitchell C E, Qiang J, Sinn A, Diederichs S, Thevenet M, Grote D, Fedeli L, Clark T, Zaim N, Vincenti H, Vay JL. From Compact Plasma Particle Sources to Advanced Accelerators with Modeling at Exascale. Proceedings of the 20th Advanced Accelerator Concepts Workshop (AAC’22), in print, 2023. arXiv:2303.12873
Installation
Users
Our community is here to help. Please report installation problems in case you should get stuck.
Choose one of the installation methods below to get started:
HPC Systems
If want to use ImpactX on a specific high-performance computing (HPC) systems, jump directly to our HPC system-specific documentation.
Using the Conda Package
A package for ImpactX is available via the Conda package manager.
conda create -n impactx -c conda-forge impactx
conda activate impactx
Note: the impactx conda package does not yet provide GPU support.
From Source with CMake
After installing the ImpactX dependencies, you can also install ImpactX from source with CMake:
# get the source code
git clone https://github.com/ECP-WarpX/impactx.git $HOME/src/impactx
cd $HOME/src/impactx
# configure
cmake -S . -B build
# optional: change configuration
ccmake build
# compile
# on Windows: --config Release
cmake --build build -j 4
# executables for ImpactX are now in build/bin/
We document the details in the developer installation.
Tips for macOS Users
Tip
Before getting started with package managers, please check what you manually installed in /usr/local.
If you find entries in bin/, lib/ et al. that look like you manually installed MPI, HDF5 or other software in the past, then remove those files first.
If you find software such as MPI in the same directories that are shown as symbolic links then it is likely you brew installed software before.
If you are trying annother package manager than brew, run brew unlink … on such packages first to avoid software incompatibilities.
See also: A. Huebl, Working With Multiple Package Managers, Collegeville Workshop (CW20), 2020
Developers
CMake is our primary build system. If you are new to CMake, this short tutorial from the HEP Software foundation is the perfect place to get started. If you just want to use CMake to build the project, jump into sections 1. Introduction, 2. Building with CMake and 9. Finding Packages.
Dependencies
Before you start, you will need a copy of the ImpactX source code:
git clone https://github.com/ECP-WarpX/impactx.git $HOME/src/impactx
cd $HOME/src/impact
ImpactX depends on popular third party software.
On your development machine, follow the instructions here.
If you are on an HPC machine, follow the instructions here.
Dependencies
ImpactX depends on the following popular third party software. Please see installation instructions below.
a mature C++17 compiler, e.g., GCC 8.4+, Clang 7, NVCC 11.0, MSVC 19.15 or newer
AMReX: we automatically download and compile a copy
ABLASTR/WarpX: we automatically download and compile a copy
Optional dependencies include:
MPI 3.0+: for multi-node and/or multi-GPU execution
for on-node accelerated compute one of either:
OpenMP 3.1+: for threaded CPU execution or
CUDA Toolkit 11.0+ (11.3+ recommended): for Nvidia GPU support (see matching host-compilers) or
ROCm 5.2+ (5.5+ recommended): for AMD GPU support
openPMD-api 0.15.1+: we automatically download and compile a copy of openPMD-api for openPMD I/O support
CCache: to speed up rebuilds (For CUDA support, needs version 3.7.9+ and 4.2+ is recommended)
Ninja: for faster parallel compiles
-
see our
requirements.txtfile for compatible versions
If you are on a high-performance computing (HPC) system, then please see our separate HPC documentation.
For all other systems, we recommend to use a package dependency manager: Pick one of the installation methods below to install all dependencies for ImpactX development in a consistent manner.
Conda (Linux/macOS/Windows)
Conda/Mamba are cross-compatible, user-level package managers.
Tip
We recommend to configure your conda to use the faster libmamba dependency solver.
conda update -n base conda
conda install -n base conda-libmamba-solver
conda config --set solver libmamba
We recommend to deactivate that conda self-activates its base environment.
This avoids interference with the system and other package managers.
conda config --set auto_activate_base false
conda create -n impactx-cpu-mpich-dev -c conda-forge blaspp boost ccache cmake compilers git lapackpp "openpmd-api=*=mpi_mpich*" python numpy pandas scipy yt pkg-config matplotlib mamba ninja mpich pip virtualenv
conda activate impactx-cpu-mpich-dev
# compile ImpactX with -DImpactX_MPI=ON
# for pip, use: export IMPACTX_MPI=ON
conda create -n impactx-cpu-dev -c conda-forge blaspp boost ccache cmake compilers git lapackpp openpmd-api python numpy pandas scipy yt pkg-config matplotlib mamba ninja pip virtualenv
conda activate impactx-cpu-dev
# compile ImpactX with -DImpactX_MPI=OFF
# for pip, use: export IMPACTX_MPI=OFF
For OpenMP support, you will further need:
conda install -c conda-forge libgomp
conda install -c conda-forge llvm-openmp
Spack (Linux/macOS)
Spack is a user-level package manager. It is primarily written for Linux, with slightly less support for macOS, and future support for Windows.
First, download a WarpX Spack desktop development environment of your choice (which will also work for ImpactX). For most desktop developments, pick the OpenMP environment for CPUs unless you have a supported GPU.
Debian/Ubuntu Linux:
OpenMP:
system=ubuntu; compute=openmp(CPUs)CUDA:
system=ubuntu; compute=cuda(Nvidia GPUs)ROCm:
system=ubuntu; compute=rocm(AMD GPUs)SYCL: todo (Intel GPUs)
macOS: first, prepare with
brew install gpg2; brew install gccOpenMP:
system=macos; compute=openmp
If you already installed Spack, we recommend to activate its binary caches for faster builds:
spack mirror add rolling https://binaries.spack.io/develop
spack buildcache keys --install --trust
Now install the WarpX/ImpactX dependencies in a new development environment:
# download environment file
curl -sLO https://raw.githubusercontent.com/ECP-WarpX/WarpX/development/Tools/machines/desktop/spack-${system}-${compute}.yaml
# create new development environment
spack env create impactx-${compute}-dev spack-${system}-${compute}.yaml
spack env activate impactx-${compute}-dev
# installation
spack install
python3 -m pip install jupyter matplotlib numpy openpmd-api openpmd-viewer pandas scipy virtualenv yt
In new terminal sessions, re-activate the environment with
spack env activate impactx-openmp-dev
again.
Replace openmp with the equivalent you chose.
Compile ImpactX with -DImpactX_MPI=ON.
For pip, use export IMPACTX_MPI=ON.
Brew (macOS/Linux)
Homebrew (Brew) is a user-level package manager primarily for Apple macOS, but also supports Linux.
brew update
brew tap openpmd/openpmd
brew install adios2 # for openPMD
brew install ccache
brew install cmake
brew install git
brew install hdf5-mpi # for openPMD
brew install libomp
brew unlink gcc
brew link --force libomp
brew install open-mpi
brew install openblas # for PSATD in RZ
brew install openpmd-api # for openPMD
If you also want to compile with PSATD in RZ, you need to manually install BLAS++ and LAPACK++:
sudo mkdir -p /usr/local/bin/
sudo curl -L -o /usr/local/bin/cmake-easyinstall https://raw.githubusercontent.com/ax3l/cmake-easyinstall/main/cmake-easyinstall
sudo chmod a+x /usr/local/bin/cmake-easyinstall
cmake-easyinstall --prefix=/usr/local git+https://github.com/icl-utk-edu/blaspp.git \
-Duse_openmp=OFF -Dbuild_tests=OFF -DCMAKE_VERBOSE_MAKEFILE=ON
cmake-easyinstall --prefix=/usr/local git+https://github.com/icl-utk-edu/lapackpp.git \
-Duse_cmake_find_lapack=ON -Dbuild_tests=OFF -DCMAKE_VERBOSE_MAKEFILE=ON
Compile ImpactX with -DImpactX_MPI=ON.
For pip, use export IMPACTX_MPI=ON.
APT (Debian/Ubuntu Linux)
The Advanced Package Tool (APT) is a system-level package manager on Debian-based Linux distributions, including Ubuntu.
sudo apt update
sudo apt install build-essential ccache cmake g++ git libhdf5-openmpi-dev libopenmpi-dev pkg-config python3 python3-matplotlib python3-numpy python3-pandas python3-pip python3-scipy python3-venv
# optional:
# for CUDA, either install
# https://developer.nvidia.com/cuda-downloads (preferred)
# or, if your Debian/Ubuntu is new enough, use the packages
# sudo apt install nvidia-cuda-dev libcub-dev
# compile ImpactX with -DImpactX_MPI=ON
# for pip, use: export IMPACTX_MPI=ON
sudo apt update
sudo apt install build-essential ccache cmake g++ git libhdf5-dev pkg-config python3 python3-matplotlib python3-numpy python3-pandas python3-pip python3-scipy python3-venv
# optional:
# for CUDA, either install
# https://developer.nvidia.com/cuda-downloads (preferred)
# or, if your Debian/Ubuntu is new enough, use the packages
# sudo apt install nvidia-cuda-dev libcub-dev
# compile ImpactX with -DImpactX_MPI=OFF
# for pip, use: export IMPACTX_MPI=OFF
Note
Preparation: make sure you work with up-to-date Python tooling.
python3 -m pip install -U pip
python3 -m pip install -U build packaging setuptools wheel pytest
python3 -m pip install -U -r examples/requirements.txt
Compile
From the base of the ImpactX source directory, execute:
# find dependencies & configure
# see additional options below, e.g.
# -DCMAKE_INSTALL_PREFIX=$HOME/sw/impactX
cmake -S . -B build -DImpactX_PYTHON=ON
# compile, here we use four threads
cmake --build build -j 4
That’s all! ImpactX binaries are now in build/bin/.
Most people execute these binaries directly or copy them out.
If you want to install the executables in a programmatic way, run this:
# for default install paths, you will need administrator rights, e.g. with sudo:
# this installs the application
cmake --build build --target install
# this installs the Python bindings via "python3 -m pip install ..."
cmake --build build --target pip_install -j 4
You can inspect and modify build options after running cmake -S . -B build with either
ccmake build
or by adding arguments with -D<OPTION>=<VALUE> to the first CMake call, e.g.:
cmake -S . -B build -DImpactX_PYTHON=ON -DImpactX_COMPUTE=CUDA
That’s it! You can now run a first example.
Developers could now change the ImpactX source code and then call the install lines again to refresh the installation.
Tip
If you do not develop with a user-level package manager, e.g., because you rely on a HPC system’s environment modules, then consider to set up a virtual environment via Python venv.
Otherwise, without a virtual environment, you likely need to add the CMake option -DPYINSTALLOPTIONS="--user".
Build Options
CMake Option |
Default & Values |
Description |
|---|---|---|
|
ON/OFF |
Build tests |
|
RelWithDebInfo/Release/Debug |
Type of build, symbols & optimizations |
|
system-dependent path |
Install path prefix |
|
ON/OFF |
Print all compiler commands to the terminal during build |
|
ON/OFF |
Build the ImpactX executable application |
|
NOACC/OMP/CUDA/SYCL/HIP |
On-node, accelerated computing backend |
|
ON/OFF |
Compile ImpactX with interprocedural optimization (aka LTO) |
|
ON/OFF |
Multi-node support (message-passing) |
|
ON/OFF |
MPI thread-multiple support, i.e. for |
|
ON/OFF |
openPMD I/O (HDF5, ADIOS) |
|
SINGLE/DOUBLE |
Floating point precision (single/double) |
|
ON/OFF |
Python bindings |
|
(newest found) |
Path to Python executable |
ImpactX can be configured in further detail with options from AMReX, which are documented in the AMReX manual.
Developers might be interested in additional options that control dependencies of ImpactX. By default, the most important dependencies of ImpactX are automatically downloaded for convenience:
CMake Option |
Default & Values |
Description |
|---|---|---|
|
ON/OFF |
Build shared libraries for dependencies |
|
First found |
Set to |
|
None |
Path to ABLASTR source directory (preferred if set) |
|
|
Repository URI to pull and build ABLASTR from |
|
we set and maintain a compatible commit |
Repository branch for |
|
ON/OFF |
Needs a pre-installed ABLASTR library if set to |
|
None |
Path to AMReX source directory (preferred if set) |
|
|
Repository URI to pull and build AMReX from |
|
we set and maintain a compatible commit |
Repository branch for |
|
ON/OFF |
Needs a pre-installed AMReX library if set to |
|
None |
Path to openPMD-api source directory (preferred if set) |
|
|
Repository URI to pull and build openPMD-api from |
|
we set and maintain a compatible commit |
Repository branch for |
|
ON/OFF |
Needs a pre-installed openPMD-api library if set to |
|
None |
Path to AMReX source directory (preferred if set) |
|
|
Repository URI to pull and build pyAMReX from |
|
we set and maintain a compatible commit |
Repository branch for |
|
ON/OFF |
Needs a pre-installed pyAMReX module if set to |
For example, one can also build against a local AMReX copy.
Assuming AMReX’ source is located in $HOME/src/amrex, add the cmake argument -DImpactX_amrex_src=$HOME/src/amrex.
Relative paths are also supported, e.g. -DImpactX_amrex_src=../amrex.
Or build against an AMReX feature branch of a colleague.
Assuming your colleague pushed AMReX to https://github.com/WeiqunZhang/amrex/ in a branch new-feature then pass to cmake the arguments: -DImpactX_amrex_repo=https://github.com/WeiqunZhang/amrex.git -DImpactX_amrex_branch=new-feature.
If you want to develop against local versions of ABLASTR (from WarpX) and AMReX at the same time, pass for instance -DImpactX_ablastr_src=$HOME/src/warpx -DImpactX_amrex_src=$HOME/src/amrex.
You can speed up the install further if you pre-install these dependencies, e.g. with a package manager.
Set -DImpactX_<dependency-name>_internal=OFF and add installation prefix of the dependency to the environment variable CMAKE_PREFIX_PATH.
Please see the introduction to CMake if this sounds new to you.
If you re-compile often, consider installing the Ninja build system.
Pass -G Ninja to the CMake configuration call to speed up parallel compiles.
Configure Your Compiler
If you don’t want to use your default compiler, you can set the following environment variables. For example, using a Clang/LLVM:
export CC=$(which clang)
export CXX=$(which clang++)
If you also want to select a CUDA compiler:
export CUDACXX=$(which nvcc)
export CUDAHOSTCXX=$(which clang++)
Note
Please clean your build directory with rm -rf build/ after changing the compiler.
Now call cmake -S . -B build (+ further options) again to re-initialize the build configuration.
Run
The ImpactX Python bindings, which provide the imports impactx and amrex (from pyAMReX), are automatically packaged and installed when calling the pip_install CMake target.
An executable ImpactX application binary with the current compile-time options encoded in its file name will be created in build/bin/.
Additionally, a symbolic link named impactx can be found in that directory, which points to the last built ImpactX executable.
HPC
On selected high-performance computing (HPC) systems, ImpactX has documented or even pre-build installation routines. Follow the guide here instead of the generic installation routines for optimal stability and best performance.
impactx.profile
Use a impactx.profile file to set up your software environment without colliding with other software.
Ideally, store that file directly in your $HOME/ and source it after connecting to the machine:
source $HOME/impactx.profile
We list example impactx.profile files below, which can be used to set up ImpactX on various HPC systems.
HPC Systems
Perlmutter (NERSC)
The Perlmutter cluster is located at NERSC.
Introduction
If you are new to this system, please see the following resources:
Batch system: Slurm
-
$HOME: per-user directory, use only for inputs, source and scripts; backed up (40GB)${CFS}/m3239/: community file system for users in the projectm3239(or equivalent); moderate performance (20TB default)$PSCRATCH: per-user production directory; very fast for parallel jobs; purged every 8 weeks (20TB default)
Preparation
Use the following commands to download the ImpactX source code:
git clone https://github.com/ECP-WarpX/impactx.git $HOME/src/impactx
On Perlmutter, you can run either on GPU nodes with fast A100 GPUs (recommended) or CPU nodes.
We use system software modules, add environment hints and further dependencies via the file $HOME/perlmutter_gpu_impactx.profile.
Create it now:
cp $HOME/src/impactx/docs/source/install/hpc/perlmutter-nersc/perlmutter_gpu_impactx.profile.example $HOME/perlmutter_gpu_impactx.profile
Edit the 2nd line of this script, which sets the export proj="" variable.
Perlmutter GPU projects must end in ..._g.
For example, if you are member of the project m3239, then run nano $HOME/perlmutter_gpu_impactx.profile and edit line 2 to read:
export proj="m3239_g"
Exit the nano editor with Ctrl + O (save) and then Ctrl + X (exit).
Important
Now, and as the first step on future logins to Perlmutter, activate these environment settings:
source $HOME/perlmutter_gpu_impactx.profile
Finally, since Perlmutter does not yet provide software modules for some of our dependencies, install them once:
bash $HOME/src/impactx/docs/source/install/hpc/perlmutter-nersc/install_gpu_dependencies.sh
source ${CFS}/${proj%_g}/${USER}/sw/perlmutter/gpu/venvs/impactx/bin/activate
We use system software modules, add environment hints and further dependencies via the file $HOME/perlmutter_cpu_impactx.profile.
Create it now:
cp $HOME/src/impactx/docs/source/install/hpc/perlmutter-nersc/perlmutter_cpu_impactx.profile.example $HOME/perlmutter_cpu_impactx.profile
Edit the 2nd line of this script, which sets the export proj="" variable.
For example, if you are member of the project m3239, then run nano $HOME/perlmutter_cpu_impactx.profile and edit line 2 to read:
export proj="m3239"
Exit the nano editor with Ctrl + O (save) and then Ctrl + X (exit).
Important
Now, and as the first step on future logins to Perlmutter, activate these environment settings:
source $HOME/perlmutter_cpu_impactx.profile
Finally, since Perlmutter does not yet provide software modules for some of our dependencies, install them once:
bash $HOME/src/impactx/docs/source/install/hpc/perlmutter-nersc/install_cpu_dependencies.sh
source ${CFS}/${proj}/${USER}/sw/perlmutter/cpu/venvs/impactx/bin/activate
Compilation
Use the following cmake commands to compile the application executable:
cd $HOME/src/impactx
rm -rf build_pm_gpu
cmake -S . -B build_pm_gpu -DImpactX_COMPUTE=CUDA -DImpactX_PSATD=ON -DImpactX_QED_TABLE_GEN=ON -DImpactX_DIMS="1;2;RZ;3"
cmake --build build_pm_gpu -j 16
The ImpactX application executables are now in $HOME/src/impactx/build_pm_gpu/bin/.
Additionally, the following commands will install ImpactX as a Python module:
cd $HOME/src/impactx
rm -rf build_pm_gpu_py
cmake -S . -B build_pm_gpu_py -DImpactX_COMPUTE=CUDA -DImpactX_PSATD=ON -DImpactX_QED_TABLE_GEN=ON -DImpactX_APP=OFF -DImpactX_PYTHON=ON -DImpactX_DIMS="1;2;RZ;3"
cmake --build build_pm_gpu_py -j 16 --target pip_install
cd $HOME/src/impactx
rm -rf build_pm_cpu
cmake -S . -B build_pm_cpu -DImpactX_COMPUTE=OMP -DImpactX_PSATD=ON -DImpactX_QED_TABLE_GEN=ON -DImpactX_DIMS="1;2;RZ;3"
cmake --build build_pm_cpu -j 16
The ImpactX application executables are now in $HOME/src/impactx/build_pm_cpu/bin/.
Additionally, the following commands will install ImpactX as a Python module:
rm -rf build_pm_cpu_py
cmake -S . -B build_pm_cpu_py -DImpactX_COMPUTE=OMP -DImpactX_PSATD=ON -DImpactX_QED_TABLE_GEN=ON -DImpactX_APP=OFF -DImpactX_PYTHON=ON -DImpactX_DIMS="1;2;RZ;3"
cmake --build build_pm_cpu_py -j 16 --target pip_install
Now, you can submit Perlmutter compute jobs for ImpactX Python (PICMI) scripts (example scripts).
Or, you can use the ImpactX executables to submit Perlmutter jobs (example inputs).
For executables, you can reference their location in your job script or copy them to a location in $PSCRATCH.
Update ImpactX & Dependencies
If you already installed ImpactX in the past and want to update it, start by getting the latest source code:
cd $HOME/src/impactx
# read the output of this command - does it look ok?
git status
# get the latest ImpactX source code
git fetch
git pull
# read the output of these commands - do they look ok?
git status
git log # press q to exit
And, if needed,
update the perlmutter_gpu_impactx.profile or perlmutter_cpu_impactx files,
log out and into the system, activate the now updated environment profile as usual,
As a last step, clean the build directory rm -rf $HOME/src/impactx/build_pm_* and rebuild ImpactX.
Running
The batch script below can be used to run a ImpactX simulation on multiple nodes (change -N accordingly) on the supercomputer Perlmutter at NERSC.
This partition as up to 1536 nodes.
Replace descriptions between chevrons <> by relevant values, for instance <input file> could be plasma_mirror_inputs.
Note that we run one MPI rank per GPU.
$HOME/src/impactx/docs/source/install/hpc/perlmutter-nersc/perlmutter_gpu.sbatch.#!/bin/bash -l
# Copyright 2021-2023 Axel Huebl, Kevin Gott
#
# This file is part of ImpactX.
#
# License: BSD-3-Clause-LBNL
#SBATCH -t 00:10:00
#SBATCH -N 2
#SBATCH -J ImpactX
# note: <proj> must end on _g
#SBATCH -A <proj>
#SBATCH -q regular
# A100 40GB (most nodes)
#SBATCH -C gpu
# A100 80GB (256 nodes)
#S BATCH -C gpu&hbm80g
#SBATCH --exclusive
# ideally single:1, but NERSC cgroups issue
#SBATCH --gpu-bind=none
#SBATCH --ntasks-per-node=4
#SBATCH --gpus-per-node=4
#SBATCH -o ImpactX.o%j
#SBATCH -e ImpactX.e%j
# executable & inputs file or python interpreter & PICMI script here
EXE=./impactx
INPUTS=inputs
# pin to closest NIC to GPU
export MPICH_OFI_NIC_POLICY=GPU
# threads for OpenMP and threaded compressors per MPI rank
# note: 16 avoids hyperthreading (32 virtual cores, 16 physical)
export SRUN_CPUS_PER_TASK=16
# GPU-aware MPI optimizations
GPU_AWARE_MPI="amrex.use_gpu_aware_mpi=1"
# CUDA visible devices are ordered inverse to local task IDs
# Reference: nvidia-smi topo -m
srun --cpu-bind=cores bash -c "
export CUDA_VISIBLE_DEVICES=\$((3-SLURM_LOCALID));
${EXE} ${INPUTS} ${GPU_AWARE_MPI}" \
> output.txt
To run a simulation, copy the lines above to a file perlmutter_gpu.sbatch and run
sbatch perlmutter_gpu.sbatch
to submit the job.
Perlmutter has 256 nodes that provide 80 GB HBM per A100 GPU.
In the A100 (40GB) batch script, replace -C gpu with -C gpu&hbm80g to use these large-memory GPUs.
The Perlmutter CPU partition as up to 3072 nodes, each with 2x AMD EPYC 7763 CPUs.
$HOME/src/impactx/docs/source/install/hpc/perlmutter-nersc/perlmutter_cpu.sbatch.#!/bin/bash -l
# Copyright 2021-2023 ImpactX
#
# This file is part of ImpactX.
#
# Authors: Axel Huebl
# License: BSD-3-Clause-LBNL
#SBATCH -t 00:10:00
#SBATCH -N 2
#SBATCH -J ImpactX
#SBATCH -A <proj>
#SBATCH -q regular
#SBATCH -C cpu
#SBATCH --ntasks-per-node=16
#SBATCH --exclusive
#SBATCH -o ImpactX.o%j
#SBATCH -e ImpactX.e%j
# executable & inputs file or python interpreter & PICMI script here
EXE=./impactx
INPUTS=inputs_small
# each CPU node on Perlmutter (NERSC) has 64 hardware cores with
# 2x Hyperthreading/SMP
# https://en.wikichip.org/wiki/amd/epyc/7763
# https://www.amd.com/en/products/cpu/amd-epyc-7763
# Each CPU is made up of 8 chiplets, each sharing 32MB L3 cache.
# This will be our MPI rank assignment (2x8 is 16 ranks/node).
# threads for OpenMP and threaded compressors per MPI rank
export SRUN_CPUS_PER_TASK=16 # 8 cores per chiplet, 2x SMP
export OMP_PLACES=threads
export OMP_PROC_BIND=spread
srun --cpu-bind=cores \
${EXE} ${INPUTS} \
> output.txt
Post-Processing
For post-processing, most users use Python via NERSC’s Jupyter service (documentation).
As a one-time preparatory setup, log into Perlmutter via SSH and do not source the ImpactX profile script above. Create your own Conda environment and Jupyter kernel for post-processing:
module load python
conda config --set auto_activate_base false
# create conda environment
rm -rf $HOME/.conda/envs/impactx-pm-postproc
conda create --yes -n impactx-pm-postproc -c conda-forge mamba conda-libmamba-solver
conda activate impactx-pm-postproc
conda config --set solver libmamba
mamba install --yes -c conda-forge python ipykernel ipympl matplotlib numpy pandas yt openpmd-viewer openpmd-api h5py fast-histogram dask dask-jobqueue pyarrow
# create Jupyter kernel
rm -rf $HOME/.local/share/jupyter/kernels/impactx-pm-postproc/
python -m ipykernel install --user --name impactx-pm-postproc --display-name ImpactX-PM-PostProcessing
echo -e '#!/bin/bash\nmodule load python\nsource activate impactx-pm-postproc\nexec "$@"' > $HOME/.local/share/jupyter/kernels/impactx-pm-postproc/kernel-helper.sh
chmod a+rx $HOME/.local/share/jupyter/kernels/impactx-pm-postproc/kernel-helper.sh
KERNEL_STR=$(jq '.argv |= ["{resource_dir}/kernel-helper.sh"] + .' $HOME/.local/share/jupyter/kernels/impactx-pm-postproc/kernel.json | jq '.argv[1] = "python"')
echo ${KERNEL_STR} | jq > $HOME/.local/share/jupyter/kernels/impactx-pm-postproc/kernel.json
exit
When opening a Jupyter notebook on https://jupyter.nersc.gov, just select ImpactX-PM-PostProcessing from the list of available kernels on the top right of the notebook.
Additional software can be installed later on, e.g., in a Jupyter cell using !mamba install -y -c conda-forge ....
Software that is not available via conda can be installed via !python -m pip install ....
Tip
Your HPC system is not in the list? Our instructions are nearly identical to installing WarpX, documented here.
Also, please do not hesitate to open an issue and together we can document how to run on your preferred system!
Usage
Run ImpactX
In order to run a new simulation:
create a new directory, where the simulation will be run
make sure the ImpactX executable is either copied into this directory or in your
PATHenvironment variableadd an inputs file and on HPC systems a submission script to the directory
run
1. Run Directory
On Linux/macOS, this is as easy as this
mkdir -p <run_directory>
Where <run_directory> by the actual path to the run directory.
2. Executable
If you installed ImpactX with a package manager, a impactx-prefixed executable will be available as a regular system command to you.
Depending on the choosen build options, the name is suffixed with more details.
Try it like this:
impactx<TAB>
Hitting the <TAB> key will suggest available ImpactX executables as found in your PATH environment variable.
If you compiled the code yourself, the ImpactX executable is stored in the source folder under build/bin.
We also create a symbolic link that is just called impactx that points to the last executable you built, which can be copied, too.
Copy the executable to this directory:
cp build/bin/<impactx_executable> <run_directory>/
where <impactx_executable> should be replaced by the actual name of the executable (see above) and <run_directory> by the actual path to the run directory.
3. Inputs
Add an input file in the directory (see examples and parameters). This file contains the numerical and physical parameters that define the situation to be simulated.
On HPC systems, also copy and adjust a submission script that allocated computing nodes for you. Please reach out to us if you need help setting up a template that runs with ideal performance.
4. Run
Run the executable, e.g. with MPI:
cd <run_directory>
# run with an inputs file:
mpirun -np <n_ranks> ./impactx <input_file>
or
# run with a PICMI input script:
mpirun -np <n_ranks> python <python_script>
Here, <n_ranks> is the number of MPI ranks used, and <input_file> is the name of the input file (<python_script> is the name of the PICMI script).
Note that the actual executable might have a longer name, depending on build options.
We used the copied executable in the current directory (./); if you installed with a package manager, skip the ./ because ImpactX is in your PATH.
On an HPC system, you would instead submit the job script at this point, e.g. sbatch <submission_script> (SLURM on Perlmutter/NERSC) or bsub <submission_script> (LSF on Summit/OLCF).
Tip
In the next sections, we will explain parameters of the <input_file>.
You can overwrite all parameters inside this file also from the command line, e.g.:
mpirun -np 4 ./impactx <input_file> max_step=10 amr.n_cell=64 64 128
Parameters: Python
This documents on how to use ImpactX as a Python script (python3 run_script.py).
General
- class impactx.ImpactX
This is the central simulation class.
- property particle_shape
Control the particle B-spline order.
The order of the shape factors (splines) for the macro-particles along all spatial directions: 1 for linear, 2 for quadratic, 3 for cubic. Low-order shape factors result in faster simulations, but may lead to more noisy results. High-order shape factors are computationally more expensive, but may increase the overall accuracy of the results. For production runs it is generally safer to use high-order shape factors, such as cubic order.
- Parameters
order (int) – B-spline order
1,2, or3
- property n_cell
The number of grid points along each direction on the coarsest level.
- property max_level
The maximum mesh-refinement level for the simulation.
- property finest_level
The currently finest level of mesh-refinement used. This is always less or equal to
max_level.
- property domain
The physical extent of the full simulation domain, relative to the reference particle position, in meters. When set, turns
dynamic_sizetoFalse.Note: particles that move outside the simulation domain are removed.
- property prob_relative
By default, we dynamically extract the minimum and maximum of the particle positions in the beam. The field mesh spans, per direction, multiple times the maximum physical extent of beam particles, as given by this factor. The beam minimum and maximum extent are symmetrically padded by the mesh. For instance,
1.2means the mesh will span 10% above and 10% below the beam;1.0means the beam is exactly covered with the mesh.Default:
3.0. When set, turnsdynamic_sizetoTrue.
- property dynamic_size
Use dynamic (
True) resizing of the field mesh or static sizing (False).
- property space_charge
Enable (
True) or disable (False) space charge calculations (default:True).Whether to calculate space charge effects. This is in-development. At the moment, this flag only activates coordinate transformations and charge deposition.
- property mlmg_relative_tolerance
Default:
1.e-7The relative precision with which the electrostatic space-charge fields should be calculated. More specifically, the space-charge fields are computed with an iterative Multi-Level Multi-Grid (MLMG) solver. This solver can fail to reach the default precision within a reasonable time.
- property mlmg_absolute_tolerance
Default:
0, which means: ignoredThe absolute tolerance with which the space-charge fields should be calculated in units of \(V/m^2\). More specifically, the acceptable residual with which the solution can be considered converged. In general this should be left as the default, but in cases where the simulation state changes very little between steps it can occur that the initial guess for the MLMG solver is so close to the converged value that it fails to improve that solution sufficiently to reach the
mlmg_relative_tolerancevalue.
- property mlmg_max_iters
Default:
100Maximum number of iterations used for MLMG solver for space-charge fields calculation. In case if MLMG converges but fails to reach the desired self_fields_required_precision, this parameter may be increased.
- property mlmg_verbosity
Default:
1The verbosity used for MLMG solver for space-charge fields calculation. Currently MLMG solver looks for verbosity levels from 0-5. A higher number results in more verbose output.
- property diagnostics
Enable (
True) or disable (False) diagnostics generally (default:True). Disabling this is mostly used for benchmarking.
- property slice_step_diagnostics
Enable (
True) or disable (False) diagnostics every slice step in elements (default:True).By default, diagnostics is performed at the beginning and end of the simulation. Enabling this flag will write diagnostics every step and slice step.
- property diag_file_min_digits
The minimum number of digits (default:
6) used for the step number appended to the diagnostic file names.
- set_diag_iota_invariants(alpha, beta, tn, cn)
Set the parameters of the IOTA nonlinear lens invariants diagnostics.
- Parameters
alpha (float) – Twiss alpha
beta (float) – Twiss beta (m)
tn (float) – dimensionless strength of the nonlinear insert
cn (float) – scale parameter of the nonlinear insert (m^[1/2])
- property particle_lost_diagnostics_backend
Diagnostics for particles lost in apertures. See the
BeamMonitorelement for backend values.
- init_grids()
Initialize AMReX blocks/grids for domain decomposition & space charge mesh.
This must come first, before particle beams and lattice elements are initialized.
- add_particles(charge_C, distr, npart)
Generate and add n particles to the particle container. Note: Set the reference particle properties (charge, mass, energy) first.
Will also resize the geometry based on the updated particle distribution’s extent and then redistribute particles in according AMReX grid boxes.
- Parameters
charge_C (float) – bunch charge (C)
distr – distribution function to draw from (object from
impactx.distribution)npart (int) – number of particles to draw
- particle_container()
Access the beam particle container (
impactx.ParticleContainer).
- property lattice
Access the elements in the accelerator lattice. See
impactx.elementsfor lattice elements.
- property periods
The number of periods to repeat the lattice.
- property abort_on_warning_threshold
(optional) Set to “low”, “medium” or “high”. Cause the code to abort if a warning is raised that exceeds the warning threshold.
- property abort_on_unused_inputs
Set to
1to cause the simulation to fail after its completion if there were unused parameters. (default:0for false) It is mainly intended for continuous integration and automated testing to check that all tests and inputs are adapted to API changes.
- property always_warn_immediately
If set to
1, ImpactX immediately prints every warning message as soon as it is generated. (default:0for false) It is mainly intended for debug purposes, in case a simulation crashes before a global warning report can be printed.
- evolve()
Run the main simulation loop for a number of steps.
- resize_mesh()
Resize the mesh
domainbased on thedynamic_sizeand related parameters.
- class impactx.Config
Configuration information on ImpactX that were set at compile-time.
- property have_mpi
Indicates multi-process/multi-node support via the message-passing interface (MPI). Possible values:
True/FalseNote
Particle beam particles are not yet dynamically load balanced. Please see the progress in issue 198.
- property have_gpu
Indicates GPU support. Possible values:
True/False
- property gpu_backend
Indicates the available GPU support. Possible values:
None,"CUDA"(for Nvidia GPUs),"HIP"(for AMD GPUs) or"SYCL"(for Intel GPUs).
- property have_omp
Indicates multi-threaded CPU support via OpenMP. Possible values:
True/False`Set the environment variable
OMP_NUM_THREADSto control the number of threads.Warning
By default, OpenMP spawns as many threads as there are available virtual cores on a host. When MPI and OpenMP support are used at the same time, it can easily happen that one over-subscribes the available physical CPU cores. This will lead to a severe slow-down of the simulation.
By setting appropriate environment variables for OpenMP, ensure that the number of MPI processes (ranks) per node multiplied with the number of OpenMP threads is equal to the number of physical (or virtual) CPU cores. Please see our examples in the high-performance computing (HPC) on how to run efficiently in parallel environments such as supercomputers.
Particles
- class impactx.ParticleContainer
Beam Particles in ImpactX.
This class stores particles, distributed over MPI ranks.
- add_n_particles(lev, x, y, t, px, py, pt, qm, bchchg)
Add new particles to the container for fixed s.
- Note: This can only be used after the initialization (grids) have
been created, meaning after the call to
ImpactX.init_grids()has been made in the ImpactX class.
- Parameters
lev – mesh-refinement level
x – positions in x
y – positions in y
t – positions as time-of-flight in c*t
px – momentum in x
py – momentum in y
pt – momentum in t
qm – charge over mass in 1/eV
bchchg – total charge within a bunch in C
- ref_particle()
Access the reference particle (
impactx.RefPart).- Returns
return a data reference to the reference particle
- Return type
- set_ref_particle(refpart)
Set reference particle attributes.
- Parameters
refpart (impactx.RefPart) – a reference particle to copy all attributes from
- reduced_beam_characteristics()
Compute reduced beam characteristics like the position and momentum moments of the particle distribution, as well as emittance and Twiss parameters.
- Returns
beam properties with string keywords
- Return type
dict
- min_and_max_positions()
Compute the min and max of the particle position in each dimension.
- Returns
x_min, y_min, z_min, x_max, y_max, z_max
- Return type
Tuple[float, float, float, float, float, float]
- mean_and_std_positions()
Compute the mean and std of the particle position in each dimension.
- Returns
x_mean, x_std, y_mean, y_std, z_mean, z_std
- Return type
Tuple[float, float, float, float, float, float]
- redistribute()
Redistribute particles in the current mesh in x, y, z.
- class impactx.RefPart
This struct stores the reference particle attributes stored in
impactx.ParticleContainer.- property s
integrated orbit path length, in meters
- property x
horizontal position x, in meters
- property y
vertical position y, in meters
- property z
longitudinal position y, in meters
- property t
clock time * c in meters
- property px
momentum in x, normalized to mass*c, \(p_x = \gamma \beta_x\)
- property py
momentum in y, normalized to mass*c, \(p_x = \gamma \beta_x\)
- property pz
momentum in z, normalized to mass*c, \(p_x = \gamma \beta_x\)
- property pt
energy, normalized by rest energy, \(p_t = -\gamma\)
- property gamma
Read-only: Get reference particle relativistic gamma, \(\gamma = 1/\sqrt{1-\beta^2}\)
- property beta
Read-only: Get reference particle relativistic beta, \(\beta = v/c\)
- property beta_gamma
Read-only: Get reference particle \(\beta \cdot \gamma\)
- property qm_qeeV
Read-only: Get reference particle charge to mass ratio (elementary charge/eV)
- set_charge_qe(charge_qe)
Write-only: Set reference particle charge in (positive) elementary charges.
- set_mass_MeV(massE)
Write-only: Set reference particle rest mass (MeV/c^2).
- set_kin_energy_MeV(kin_energy_MeV)
Write-only: Set reference particle kinetic energy (MeV)
- load_file(madx_file)
Load reference particle information from a MAD-X file.
- Parameters
madx_file – file name to MAD-X file with a
BEAMentry
Initial Beam Distributions
This module provides particle beam distributions that can be used to initialize particle beams in an impactx.ParticleContainer.
- class impactx.distribution.Gaussian(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
A 6D Gaussian distribution.
- Parameters
sigx – for zero correlation, these are the related RMS sizes (in meters)
sigy – see sigx
sigt – see sigx
sigpx – RMS momentum
sigpy – see sigpx
sigpt – see sigpx
muxpx – correlation length-momentum
muypy – see muxpx
mutpt – see muxpx
- class impactx.distribution.Kurth4D(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
A 4D Kurth distribution transversely + a uniform distribution it t + a Gaussian distribution in pt.
- class impactx.distribution.Kurth6D(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
A 6D Kurth distribution.
R. Kurth, Quarterly of Applied Mathematics vol. 32, pp. 325-329 (1978) C. Mitchell, K. Hwang and R. D. Ryne, IPAC2021, WEPAB248 (2021)
- class impactx.distribution.KVdist(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
A K-V distribution transversely + a uniform distribution it t + a Gaussian distribution in pt.
- class impactx.distribution.None
This distribution sets all values to zero.
- class impactx.distribution.Semigaussian(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
A 6D Semi-Gaussian distribution (uniform in position, Gaussian in momentum).
- class impactx.distribution.Triangle(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
A triangle distribution for laser-plasma acceleration related applications.
A ramped, triangular current profile with a Gaussian energy spread (possibly correlated). The transverse distribution is a 4D waterbag.
- class impactx.distribution.Waterbag(sigx, sigy, sigt, sigpx, sigpy, sigpt, muxpx=0.0, muypy=0.0, mutpt=0.0)
A 6D Waterbag distribution.
Lattice Elements
This module provides elements for the accelerator lattice.
- class impactx.elements.KnownElementsList
An iterable,
list-like type of elements.- clear()
Clear the list to become empty.
- extend(list)
Add a list of elements to the list.
- append(element)
Add a single element to the list.
- load_file(madx_file, nslice=1)
Load and append an accelerator lattice description from a MAD-X file.
- Parameters
madx_file – file name to MAD-X file with beamline elements
nslice – number of slices used for the application of space charge
- class impactx.elements.CFbend(ds, rc, k, nslice=1)
A combined function bending magnet. This is an ideal Sbend with a normal quadrupole field component.
- Parameters
ds – Segment length in m.
rc – Radius of curvature in m.
k – Quadrupole strength in m^(-2) (MADX convention) = (gradient in T/m) / (rigidity in T-m) k > 0 horizontal focusing k < 0 horizontal defocusing
nslice – number of slices used for the application of space charge
- class impactx.elements.ConstF(ds, kx, ky, kt, nslice=1)
A linear Constant Focusing element.
- Parameters
ds – Segment length in m.
kx – Focusing strength for x in 1/m.
ky – Focusing strength for y in 1/m.
kt – Focusing strength for t in 1/m.
nslice – number of slices used for the application of space charge
- property kx
focusing x strength in 1/m
- property ky
focusing y strength in 1/m
- property kt
focusing t strength in 1/m
- class impactx.elements.DipEdge(psi, rc, g, K2)
Edge focusing associated with bend entry or exit
This model assumes a first-order effect of nonzero gap. Here we use the linear fringe field map, given to first order in g/rc (gap / radius of curvature).
References: * K. L. Brown, SLAC Report No. 75 (1982). * K. Hwang and S. Y. Lee, PRAB 18, 122401 (2015).
- Parameters
psi – Pole face angle in rad
rc – Radius of curvature in m
g – Gap parameter in m
K2 – Fringe field integral (unitless)
- class impactx.elements.Drift(ds, nslice=1)
A drift.
- Parameters
ds – Segment length in m
nslice – number of slices used for the application of space charge
- class impactx.elements.ChrDrift(ds, nslice=1)
A drift with chromatic effects included. The Hamiltonian is expanded through second order in the transverse variables (x,px,y,py), with the exact pt dependence retained.
- Parameters
ds – Segment length in m
nslice – number of slices used for the application of space charge
- class impactx.elements.ExactDrift(ds, nslice=1)
A drift using the exact nonlinear transfer map.
- Parameters
ds – Segment length in m
nslice – number of slices used for the application of space charge
- class impactx.elements.Kicker(xkick, ykick, units)
A thin transverse kicker.
- Parameters
xkick – horizontal kick strength (dimensionless OR T-m)
ykick – vertical kick strength (dimensionless OR T-m)
units – specification of units (
"dimensionless"in units of the magnetic rigidity of the reference particle or"T-m")
- class impactx.elements.Multipole(multipole, K_normal, K_skew)
A general thin multipole element.
- Parameters
multipole – index m (m=1 dipole, m=2 quadrupole, m=3 sextupole etc.)
K_normal – Integrated normal multipole coefficient (1/meter^m)
K_skew – Integrated skew multipole coefficient (1/meter^m)
- class impactx.elements.NonlinearLens(knll, cnll)
Single short segment of the nonlinear magnetic insert element.
A thin lens associated with a single short segment of the nonlinear magnetic insert described by V. Danilov and S. Nagaitsev, PRSTAB 13, 084002 (2010), Sect. V.A. This element appears in MAD-X as type NLLENS.
- Parameters
knll – integrated strength of the nonlinear lens (m)
cnll – distance of singularities from the origin (m)
- class impactx.elements.BeamMonitor(name, backend='default', encoding='g')
A beam monitor, writing all beam particles at fixed
sto openPMD files.If the same element
nameis used multiple times, then an output series is created with multiple outputs.The I/O backend for openPMD data dumps.
bpis the ADIOS2 I/O library,h5is the HDF5 format, andjsonis a simple text format.jsononly works with serial/single-rank jobs. By default, the first available backend in the order given above is taken.openPMD iteration encoding determines if multiple files are created for individual output steps or not. Variable based is an experimental feature with ADIOS2.
- Parameters
name – name of the series
backend – I/O backend, e.g.,
bp,h5,jsonencoding – openPMD iteration encoding: (v)ariable based, (f)ile based, (g)roup based (default)
- class impactx.elements.Programmable
A programmable beam optics element.
This element can be programmed to receive callback hooks into Python functions.
- property beam_particles
This is a function hook for pushing all beam particles. This accepts a function or lambda with the following arguments:
- property ref_particle
This is a function hook for pushing the reference particle. This accepts a function or lambda with the following argument:
- class impactx.elements.Quad(ds, k, nslice=1)
A Quadrupole magnet.
- Parameters
ds – Segment length in m.
k – Quadrupole strength in m^(-2) (MADX convention) = (gradient in T/m) / (rigidity in T-m) k > 0 horizontal focusing k < 0 horizontal defocusing
nslice – number of slices used for the application of space charge
- class impactx.elements.ChrQuad(ds, k, units, nslice=1)
A Quadrupole magnet, with chromatic effects included. The Hamiltonian is expanded through second order in the transverse variables (x,px,y,py), with the exact pt dependence retained.
- Parameters
ds – Segment length in m.
k –
- Quadrupole strength in m^(-2) (MADX convention, if units = 0)
= (gradient in T/m) / (rigidity in T-m)
- OR Quadrupole strength in T/m (MaryLie convention, if units = 1)
k > 0 horizontal focusing k < 0 horizontal defocusing
units – specification of units for quadrupole field strength
nslice – number of slices used for the application of space charge
- class impactx.elements.RFCavity(ds, escale, freq, phase, mapsteps, nslice)
A radiofrequency cavity.
- Parameters
ds – Segment length in m.
escale – scaling factor for on-axis RF electric field in 1/m = (peak on-axis electric field Ez in MV/m) / (particle rest energy in MeV)
freq – RF frequency in Hz
phase – RF driven phase in degrees
cos_coefficients – array of
floatcosine coefficients in Fourier expansion of on-axis electric field Ez (optional); default is a 9-cell TESLA superconducting cavity model from DOI:10.1103/PhysRevSTAB.3.092001cos_coefficients – array of
floatsine coefficients in Fourier expansion of on-axis electric field Ez (optional); default is a 9-cell TESLA superconducting cavity model from DOI:10.1103/PhysRevSTAB.3.092001mapsteps – number of integration steps per slice used for map and reference particle push in applied fields
nslice – number of slices used for the application of space charge
- class impactx.elements.Sbend(ds, rc, nslice=1)
An ideal sector bend.
- Parameters
ds – Segment length in m.
rc – Radius of curvature in m.
nslice – number of slices used for the application of space charge
- class impactx.elements.ExactSbend(ds, phi, B, nslice=1)
An ideal sector bend using the exact nonlinear map. The model consists of a uniform bending field B_y with a hard edge. Pole faces are normal to the entry and exit velocity of the reference particle.
- References:
Bruhwiler et al, in Proc. of EPAC 98, pp. 1171-1173 (1998).
Forest et al, Part. Accel. 45, pp. 65-94 (1994).
- param ds
Segment length in m.
- param phi
Bend angle in degrees.
- param B
Magnetic field in Tesla; when B = 0 (default), the reference bending radius is defined by r0 = length / (angle in rad), corresponding to a magnetic field of B = rigidity / r0; otherwise the reference bending radius is defined by r0 = rigidity / B.
- param nslice
number of slices used for the application of space charge
- class impactx.elements.Buncher(V, k)
A short RF cavity element at zero crossing for bunching (MaryLie model).
- Parameters
V – Normalized RF voltage drop V = Emax*L/(c*Brho)
k – Wavenumber of RF in 1/m
- class impactx.elements.ShortRF(V, freq, phase)
A short RF cavity element (MAD-X model).
- Parameters
V – Normalized RF voltage V = maximum energy gain/(m*c^2)
freq – RF frequency in Hz
phase – RF synchronous phase in degrees (phase = 0 corresponds to maximum energy gain, phase = -90 corresponds go zero energy gain for bunching)
- class impactx.elements.ChrUniformAcc(ds, k, nslice=1)
A region of constant Ez and Bz for uniform acceleration, with chromatic effects included. The Hamiltonian is expanded through second order in the transverse variables (x,px,y,py), with the exact pt dependence retained.
- Parameters
ds – Segment length in m.
ez – Electric field strength in m^(-1) = (particle charge in C * field Ez in V/m) / (particle mass in kg * (speed of light in m/s)^2)
bz – Magnetic field strength in m^(-1) = (particle charge in C * field Bz in T) / (particle mass in kg * speed of light in m/s)
nslice – number of slices used for the application of space charge
- class impactx.elements.SoftSolenoid(ds, bscale, cos_coefficients, sin_coefficients, nslice=1)
A soft-edge solenoid.
- Parameters
ds – Segment length in m.
bscale – Scaling factor for on-axis magnetic field Bz in inverse meters
cos_coefficients – array of
floatcosine coefficients in Fourier expansion of on-axis magnetic field Bz (optional); default is a thin-shell model from DOI:10.1016/J.NIMA.2022.166706sin_coefficients – array of
floatsine coefficients in Fourier expansion of on-axis magnetic field Bz (optional); default is a thin-shell model from DOI:10.1016/J.NIMA.2022.166706mapsteps – number of integration steps per slice used for map and reference particle push in applied fields
nslice – number of slices used for the application of space charge
- class impactx.elements.Sol(ds, ks, nslice=1)
An ideal hard-edge Solenoid magnet.
- Parameters
ds – Segment length in m.
ks – Solenoid strength in m^(-1) (MADX convention) in (magnetic field Bz in T) / (rigidity in T-m)
nslice – number of slices used for the application of space charge
- class impactx.elements.PRot(phi_in, phi_out)
Exact map for a pole-face rotation in the x-z plane.
- Parameters
phi_in – angle of the reference particle with respect to the longitudinal (z) axis in the original frame in degrees
phi_out – angle of the reference particle with respect to the longitudinal (z) axis in the rotated frame in degrees
- class impactx.elements.Aperture(xmax, ymax, shape='rectangular')
A thin collimator element, applying a transverse aperture boundary.
- Parameters
xmax – maximum allowed value of the horizontal coordinate (meter)
ymax – maximum allowed value of the vertical coordinate (meter)
shape – aperture boundary shape:
"rectangular"(default) or"elliptical"
- class impactx.elements.SoftQuadrupole(ds, gscale, cos_coefficients, sin_coefficients, nslice=1)
A soft-edge quadrupole.
- Parameters
ds – Segment length in m.
gscale – Scaling factor for on-axis field gradient in inverse meters
cos_coefficients – array of
floatcosine coefficients in Fourier expansion of on-axis field gradient (optional); default is a tanh fringe field model based on http://www.physics.umd.edu/dsat/docs/MaryLieMan.pdfsin_coefficients – array of
floatsine coefficients in Fourier expansion of on-axis field gradient (optional); default is a tanh fringe field model based on http://www.physics.umd.edu/dsat/docs/MaryLieMan.pdfmapsteps – number of integration steps per slice used for map and reference particle push in applied fields
nslice – number of slices used for the application of space charge
- class impactx.elements.ThinDipole(theta, rc)
A general thin dipole element.
- Parameters
theta – Bend angle (degrees)
rc – Effective curvature radius (meters)
- Reference:
Ripken and F. Schmidt, Thin-Lens Formalism for Tracking, CERN/SL/95-12 (AP), 1995.
Coordinate Transformation
- class impactx.TransformationDirection
Enumerated type indicating whether to transform to fixed \(s\) or fixed \(t\) coordinate system when applying
impactx.coordinate_transformation.- Parameters
to_fixed_t –
to_fixed_s –
Function .. py:method:: impactx.coordinate_transformation(pc, direction)
Function to transform the coordinates of the particles in a particle container either to fixed \(t\) or to fixed \(s\).
- param pc
impactx.particle_containerwhose particle coordinates are to be transformed.- param direction
enumerated type
impactx.TransformationDirection, indicates whether to transform to fixed \(s\) or fixed \(t\).
Parameters: Inputs File
This documents on how to use ImpactX with an inputs file (impactx input_file.in).
Note
The AMReX parser (see Math parser and user-defined constants) is used for the right-hand-side of all input parameters that consist of one or more integers or floats, so expressions like <species_name>.density_max = "2.+1." and/or using user-defined constants are accepted.
Overall simulation parameters
max_step(integer)The number of PIC cycles to perform.
stop_time(float; in seconds)The maximum physical time of the simulation. Can be provided instead of
max_step. If bothmax_stepandstop_timeare provided, both criteria are used and the simulation stops when the first criterion is hit.
amrex.abort_on_out_of_gpu_memory(0or1; default is1for true)When running on GPUs, memory that does not fit on the device will be automatically swapped to host memory when this option is set to
0. This will cause severe performance drops. Note that even with this set to1ImpactX will not catch all out-of-memory events yet when operating close to maximum device memory. Please also see the documentation in AMReX.
amrex.the_arena_is_managed(0or1; default is0for false)When running on GPUs, device memory that is accessed from the host will automatically be transferred with managed memory. This is useful for convenience during development, but has sometimes severe performance and memory footprint implications if relied on (and sometimes vendor bugs). For all regular ImpactX operations, we therefore do explicit memory transfers without the need for managed memory and thus changed the AMReX default to false. Please also see the documentation in AMReX.
amrex.omp_threads(system,nosmtor positive integer; default isnosmt)An integer number can be set in lieu of the
OMP_NUM_THREADSenvironment variable to control the number of OpenMP threads to use for theOMPcompute backend on CPUs. By default, we use thenosmtoption, which overwrites the OpenMP default of spawning one thread per logical CPU core, and instead only spawns a number of threads equal to the number of physical CPU cores on the machine. If set, the environment variableOMP_NUM_THREADStakes precedence oversystemandnosmt, but not over integer numbers set in this option.
amrex.abort_on_unused_inputs(0or1; default is0for false)When set to
1, this option causes the simulation to fail after its completion if there were unused parameters. It is mainly intended for continuous integration and automated testing to check that all tests and inputs are adapted to API changes.
impactx.always_warn_immediately(0or1; default is0for false)If set to
1, ImpactX immediately prints every warning message as soon as it is generated. It is mainly intended for debug purposes, in case a simulation crashes before a global warning report can be printed.
impactx.abort_on_warning_threshold(string:low,mediumorhigh) optionalOptional threshold to abort as soon as a warning is raised. If the threshold is set, warning messages with priority greater than or equal to the threshold trigger an immediate abort. It is mainly intended for debug purposes, and is best used with
impactx.always_warn_immediately=1. For more information on the warning logger, see this section of the WarpX documentation.
Setting up the field mesh
ImpactX uses an AMReX grid of boxes to organize and parallelize the simulation domain. These boxes also contain a field mesh, if space charge calculations are enabled.
amr.n_cell(3 integers) optional (default: 1 blocking_factor per MPI process)The number of grid points along each direction (on the coarsest level)
amr.max_level(integer, default:0)When using mesh refinement, the number of refinement levels that will be used.
Use
0in order to disable mesh refinement.
amr.ref_ratio(integerper refined level, default:2)When using mesh refinement, this is the refinement ratio per level. With this option, all directions are fined by the same ratio.
amr.ref_ratio_vect(3 integers for x,y,z per refined level)When using mesh refinement, this can be used to set the refinement ratio per direction and level, relative to the previous level.
Example: for three levels, a value of
2 2 4 8 8 16refines the first level by 2-fold in x and y and 4-fold in z compared to the coarsest level (level 0/mother grid); compared to the first level, the second level is refined 8-fold in x and y and 16-fold in z.
Note
Field boundaries for space charge calculation are located at the outer ends of the field mesh. We currently assume Dirichlet boundary conditions with zero potential (a mirror charge). Thus, to emulate open boundaries, consider adding enough vacuum padding to the beam. This will be improved in future versions.
Note
Particles that move outside the simulation domain are removed.
geometry.dynamic_size(boolean) optional (default:truefor dynamic)Use dynamic (
true) resizing of the field mesh, viageometry.prob_relative, or static sizing (false), viageometry.prob_lo/geometry.prob_hi.
geometry.prob_relative(positivefloat, unitless) optional (default:3.0)By default, we dynamically extract the minimum and maximum of the particle positions in the beam. The field mesh spans, per direction, multiple times the maximum physical extent of beam particles, as given by this factor. The beam minimum and maximum extent are symmetrically padded by the mesh. For instance,
1.2means the mesh will span 10% above and 10% below the beam;1.0means the beam is exactly covered with the mesh.
geometry.prob_loandgeometry.prob_hi(3 floats, in meters) optional (required ifgeometry.dynamic_sizeisfalse)The extent of the full simulation domain relative to the reference particle position. This can be used to explicitly size the simulation box and ignore
geometry.prob_relative.This box is rectangular, and thus its extent is given here by the coordinates of the lower corner (
geometry.prob_lo) and upper corner (geometry.prob_hi). The first axis of the coordinates is x and the last is z.
Domain Boundary Conditions
Note
TODO :-)
Initial Beam Distributions
beam.npart(integer) number of weighted simulation particlesbeam.units(string) currently, onlystaticis supported.beam.kin_energy(float, in MeV) beam kinetic energybeam.charge(float, in C) bunch chargebeam.particle(string) particle type: currently eitherelectron,positronorprotonbeam.distribution(string)Indicates the initial distribution type. This should be one of:
waterbagfor initial Waterbag distribution. With additional parameters:beam.sigmaX(float, in meters) rms Xbeam.sigmaY(float, in meters) rms Ybeam.sigmaT(float, in radian) rms normalized time difference Tbeam.sigmaPx(float, in momentum) rms Pxbeam.sigmaPy(float, in momentum) rms Pybeam.sigmaPt(float, in energy deviation) rms Ptbeam.muxpx(float, dimensionless, default:0) correlation X-Pxbeam.muypy(float, dimensionless, default:0) correlation Y-Pybeam.mutpt(float, dimensionless, default:0) correlation T-Pt
kurth6dfor initial 6D Kurth distribution. With additional parameters:beam.sigmaX(float, in meters) rms Xbeam.sigmaY(float, in meters) rms Ybeam.sigmaT(float, in radian) rms normalized time difference Tbeam.sigmaPx(float, in momentum) rms Pxbeam.sigmaPy(float, in momentum) rms Pybeam.sigmaPt(float, in energy deviation) rms Ptbeam.muxpx(float, dimensionless, default:0) correlation X-Pxbeam.muypy(float, dimensionless, default:0) correlation Y-Pybeam.mutpt(float, dimensionless, default:0) correlation T-Pt
gaussianfor initial 6D Gaussian (normal) distribution. With additional parameters:beam.sigmaX(float, in meters) rms Xbeam.sigmaY(float, in meters) rms Ybeam.sigmaT(float, in radian) rms normalized time difference Tbeam.sigmaPx(float, in momentum) rms Pxbeam.sigmaPy(float, in momentum) rms Pybeam.sigmaPt(float, in energy deviation) rms Ptbeam.muxpx(float, dimensionless, default:0) correlation X-Pxbeam.muypy(float, dimensionless, default:0) correlation Y-Pybeam.mutpt(float, dimensionless, default:0) correlation T-Pt
kvdistfor initial K-V distribution in the transverse plane. The distribution is uniform in t and Gaussian in pt. With additional parameters:beam.sigmaX(float, in meters) rms Xbeam.sigmaY(float, in meters) rms Ybeam.sigmaT(float, in radian) rms normalized time difference Tbeam.sigmaPx(float, in momentum) rms Pxbeam.sigmaPy(float, in momentum) rms Pybeam.sigmaPt(float, in energy deviation) rms Ptbeam.muxpx(float, dimensionless, default:0) correlation X-Pxbeam.muypy(float, dimensionless, default:0) correlation Y-Pybeam.mutpt(float, dimensionless, default:0) correlation T-Pt
kurth4dfor initial 4D Kurth distribution in the transverse plane. The distribution is uniform in t and Gaussian in pt. With additional parameters:beam.sigmaX(float, in meters) rms Xbeam.sigmaY(float, in meters) rms Ybeam.sigmaT(float, in radian) rms normalized time difference Tbeam.sigmaPx(float, in momentum) rms Pxbeam.sigmaPy(float, in momentum) rms Pybeam.sigmaPt(float, in energy deviation) rms Ptbeam.muxpx(float, dimensionless, default:0) correlation X-Pxbeam.muypy(float, dimensionless, default:0) correlation Y-Pybeam.mutpt(float, dimensionless, default:0) correlation T-Pt
semigaussianfor initial Semi-Gaussian distribution. The distribution is uniform within a cylinder in (x,y,z) and Gaussian in momenta (px,py,pt). With additional parameters:beam.sigmaX(float, in meters) rms Xbeam.sigmaY(float, in meters) rms Ybeam.sigmaT(float, in radian) rms normalized time difference Tbeam.sigmaPx(float, in momentum) rms Pxbeam.sigmaPy(float, in momentum) rms Pybeam.sigmaPt(float, in energy deviation) rms Ptbeam.muxpx(float, dimensionless, default:0) correlation X-Pxbeam.muypy(float, dimensionless, default:0) correlation Y-Pybeam.mutpt(float, dimensionless, default:0) correlation T-Pt
trianglea triangle distribution for laser-plasma acceleration related applications. A ramped, triangular current profile with a Gaussian energy spread (possibly correlated). The transverse distribution is a 4D waterbag. With additional parameters:beam.sigmaX(float, in meters) rms Xbeam.sigmaY(float, in meters) rms Ybeam.sigmaT(float, in radian) rms normalized time difference Tbeam.sigmaPx(float, in momentum) rms Pxbeam.sigmaPy(float, in momentum) rms Pybeam.sigmaPt(float, in energy deviation) rms Ptbeam.muxpx(float, dimensionless, default:0) correlation X-Pxbeam.muypy(float, dimensionless, default:0) correlation Y-Pybeam.mutpt(float, dimensionless, default:0) correlation T-Pt
Lattice Elements
lattice.elements(list of strings) optional (default: no elements)A list of names (one name per lattice element), in the order that they appear in the lattice.
lattice.periods(integer) optional (default:1)The number of periods to repeat the lattice.
lattice.reverse(boolean) optional (default:false)Reverse the list of elements in the lattice. If
reverseandperiodsboth appear, thenreverseis applied beforeperiods.
lattice.nslice(integer) optional (default:1)A positive integer specifying the number of slices used for the application of space charge in all elements; overwritten by element parameter “nslice”
<element_name>.type(string)Indicates the element type for this lattice element. This should be one of:
cfbendfor a combined function bending magnet. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.rc(float, in meters) the bend radius<element_name>.k(float, in inverse meters squared) the quadrupole strength= (magnetic field gradient in T/m) / (magnetic rigidity in T-m)
k > 0 horizontal focusing
k < 0 horizontal defocusing
<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
driftfor a free drift. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
drift_chromaticfor a free drift, with chromatic effects included.The Hamiltonian is expanded through second order in the transverse variables (x,px,y,py), with the exact pt dependence retained. This requires these additional parameters:
<element_name>.ds(float, in meters) the segment length<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
drift_exactfor a free drift, using the exact nonlinear map. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
quadfor a quadrupole. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.k(float, in inverse meters squared) the quadrupole strength= (magnetic field gradient in T/m) / (magnetic rigidity in T-m)
k > 0 horizontal focusing
k < 0 horizontal defocusing
<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
quad_chromaticfor A Quadrupole magnet, with chromatic effects included.The Hamiltonian is expanded through second order in the transverse variables (x,px,y,py), with the exact pt dependence retained. This requires these additional parameters:
<element_name>.ds(float, in meters) the segment length<element_name>.k(float, in inverse meters squared OR in T/m) the quadrupole strength= (magnetic field gradient in T/m) / (magnetic rigidity in T-m) - if units = 0
OR = magnetic field gradient in T/m - if units = 1
k > 0 horizontal focusing
k < 0 horizontal defocusing
<element_name>.units(integer) specification of units (default:0)<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
quadrupole_softedgefor a soft-edge quadrupole. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.gscale(float, in inverse meters) Scaling factor for on-axis magnetic field gradient<element_name>.cos_coefficients(array offloat) cos coefficients in Fourier expansion of the on-axis field gradient (optional); default is a tanh fringe field model from MaryLie 3.0<element_name>.sin_coefficients(array offloat) sin coefficients in Fourier expansion of the on-axis field gradient (optional); default is a tanh fringe field model from MaryLie 3.0<element_name>.mapsteps(integer) number of integration steps per slice used for map and reference particle push in applied fields(default:
1)
<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
sbendfor a bending magnet. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.rc(float, in meters) the bend radius<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
sbend_exactfor a bending magnet using the exact nonlinear map for the bend body. The map corresponds to the map described in:D. L. Bruhwiler et al, in Proc. of EPAC 98, pp. 1171-1173 (1998), E. Forest et al, Part. Accel. 45, pp. 65-94 (1994). The model consists of a uniform bending field B_y with a hard edge. Pole faces are normal to the entry and exit velocity of the reference particle. This requires these additional parameters:
<element_name>.ds(float, in meters) the segment length<element_name>.phi(float, in degrees) the bend angle<element_name>.B(float, in Tesla) the bend magnetic field; when B = 0 (default), the reference bending radius is defined by r0 = length / (angle in rad), corresponding to a magnetic field of B = rigidity / r0; otherwise the reference bending radius is defined by r0 = rigidity / B<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
solenoidfor an ideal hard-edge solenoid magnet. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.ks(float, in meters) Solenoid strength in m^(-1) (MADX convention)= (magnetic field Bz in T) / (rigidity in T-m)
<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
solenoid_softedgefor a soft-edge solenoid. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.bscale(float, in inverse meters) Scaling factor for on-axis magnetic field Bz<element_name>.cos_coefficients(array offloat) cos coefficients in Fourier expansion of the on-axis magnetic field Bz (optional); default is a thin-shell model from DOI:10.1016/J.NIMA.2022.166706<element_name>.sin_coefficients(array offloat) sin coefficients in Fourier expansion of the on-axis magnetic field Bz (optional); default is a thin-shell model from DOI:10.1016/J.NIMA.2022.166706<element_name>.mapsteps(integer) number of integration steps per slice used for map and reference particle push in applied fields (default:1)<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
dipedgefor dipole edge focusing. This requires these additional parameters:<element_name>.psi(float, in radians) the pole face rotation angle<element_name>.rc(float, in meters) the bend radius<element_name>.g(float, in meters) the gap size<element_name>.K2(float, dimensionless) normalized field integral for fringe field
constffor a constant focusing element. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.kx(float, in 1/meters) the horizontal focusing strength<element_name>.ky(float, in 1/meters) the vertical focusing strength<element_name>.kt(float, in 1/meters) the longitudinal focusing strength<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
rfcavitya radiofrequency cavity. This requires these additional parameters:<element_name>.ds(float, in meters) the segment length<element_name>.escale(float, in 1/m) scaling factor for on-axis RF electric field= (peak on-axis electric field Ez in MV/m) / (particle rest energy in MeV)
<element_name>.freq(float, in Hz) RF frequency<element_name>.phase(float, in degrees) RF driven phase<element_name>.cos_coefficients(array offloat) cosine coefficients in Fourier expansion of on-axis electric field Ez (optional); default is a 9-cell TESLA superconducting cavity model from DOI:10.1103/PhysRevSTAB.3.092001<element_name>.cos_coefficients(array offloat) sine coefficients in Fourier expansion of on-axis electric field Ez (optional); default is a 9-cell TESLA superconducting cavity model from DOI:10.1103/PhysRevSTAB.3.092001<element_name>.mapsteps(integer) number of integration steps per slice used for map and reference particle push in applied fields (default:1)<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
buncherfor a short RF cavity (linear) bunching element. This requires these additional parameters:<element_name>.V(float, dimensionless) normalized voltage drop across the cavity= (maximum voltage drop in Volts) / (speed of light in m/s * magnetic rigidity in T-m)
<element_name>.k(float, in 1/meters) the RF wavenumber= 2*pi/(RF wavelength in m)
shortrffor a short RF cavity element. This requires these additional parameters:<element_name>.V(float, dimensionless) normalized voltage drop across the cavity= (maximum energy gain in MeV) / (particle rest energy in MeV)
<element_name>.freq(float, in Hz) the RF frequency<element_name>.phase(float, in degrees) the synchronous RF phasephase = 0: maximum energy gain (on-crest)
phase = -90 deg: zero energy gain for bunching
phase = 90 deg: zero energy gain for debunching
uniform_acc_chromaticfor a region of uniform acceleration, with chromatic effects included.The Hamiltonian is expanded through second order in the transverse variables (x,px,y,py), with the exact pt dependence retained. This requires these additional parameters:
<element_name>.ds(float, in meters) the segment length<element_name>.ez(float, in inverse meters) the electric field strength= (particle charge in C * electric field Ez in V/m) / (particle mass in kg * (speed of light in m/s)^2)
<element_name>.bz(float, in inverse meters) the magnetic field strength= (particle charge in C * magnetic field Bz in T) / (particle mass in kg * speed of light in m/s)
<element_name>.nslice(integer) number of slices used for the application of space charge (default:1)
multipolefor a thin multipole element. This requires these additional parameters:<element_name>.multipole(integer, dimensionless) order of multipole(m = 1) dipole, (m = 2) quadrupole, (m = 3) sextupole, etc.
<element_name>.k_normal(float, in 1/meters^m) integrated normal multipole coefficient (MAD-X convention)= 1/(magnetic rigidity in T-m) * (derivative of order m-1 of By with respect to x)
<element_name>.k_skew(float, in 1/meters^m) integrated skew multipole strength (MAD-X convention)
nonlinear_lensfor a thin IOTA nonlinear lens element. This requires these additional parameters:<element_name>.knll(float, in meters) integrated strength of the lens segment (MAD-X convention)= dimensionless lens strength * c parameter**2 * length / Twiss beta
<element_name>.cnll(float, in meters) distance of the singularities from the origin (MAD-X convention)= c parameter * sqrt(Twiss beta)
protfor an exact pole-face rotation in the x-z plane. This requires these additional parameters:<element_name>.phi_in(float, in degrees) angle of the reference particle with respect to the longitudinal (z) axis in the original frame<element_name>.phi_out(float, in degrees) angle of the reference particle with respect to the longitudinal (z) axis in the rotated frame
kickerfor a thin transverse kicker. This requires these additional parameters:<element_name>.xkick(float, dimensionless OR in T-m) the horizontal kick strength<element_name>.ykick(float, dimensionless OR in T-m) the vertical kick strength<element_name>.units(string) specification of units:dimensionless(default, in units of the magnetic rigidity of the reference particle) orT-m
thin_dipolefor a thin dipole element. This requires these additional parameters:<element_name>.theta(float, in degrees) dipole bend angle<element_name>.rc(float, in meters) effective radius of curvature
aperturefor a thin collimator element applying a transverse aperture boundary. This requires these additional parameters:<element_name>.xmax(float, in meters) maximum value of the horizontal coordinate<element_name>.ymax(float, in meters) maximum value of the vertical coordinate<element_name>.shape(string) shape of the aperture boundary:rectangular(default) orelliptical
beam_monitora beam monitor, writing all beam particles at fixedsto openPMD files. If the same element name is used multiple times, then an output series is created with multiple outputs.<element_name>.name(string, default value:<element_name>)The output series name to use. By default, output is created under
diags/openPMD/<element_name>.<backend>.<element_name>.backend(string, default value:default)I/O backend for openPMD data dumps.
bpis the ADIOS2 I/O library,h5is the HDF5 format, andjsonis a simple text format.jsononly works with serial/single-rank jobs. By default, the first available backend in the order given above is taken.<element_name>.encoding(string, default value:g)openPMD iteration encoding: (v)ariable based, (f)ile based, (g)roup based (default) variable based is an experimental feature with ADIOS2.
linea sub-lattice (line) of elements to append to the lattice.<element_name>.elements(list of strings) optional (default: no elements) A list of names (one name per lattice element), in the order that they appear in the lattice.<element_name>.reverse(boolean) optional (default:false) Reverse the list of elements in the line before appending to the lattice.<element_name>.repeat(integer) optional (default:1) Repeat the line multiple times before appending to the lattice. Note: Ifreverseandrepeatboth appear, thenreverseis applied beforerepeat.
Distribution across MPI ranks and parallelization
amr.max_grid_size(integer) optional (default:128)Maximum allowable size of each subdomain (expressed in number of grid points, in each direction). Each subdomain has its own ghost cells, and can be handled by a different MPI rank ; several OpenMP threads can work simultaneously on the same subdomain.
If
max_grid_sizeis such that the total number of subdomains is larger that the number of MPI ranks used, than some MPI ranks will handle several subdomains, thereby providing additional flexibility for load balancing.When using mesh refinement, this number applies to the subdomains of the coarsest level, but also to any of the finer level.
Math parser and user-defined constants
ImpactX uses AMReX’s math parser that reads expressions in the input file. It can be used in all input parameters that consist of one or more integers or floats. Integer input expecting boolean, 0 or 1, are not parsed. Note that when multiple values are expected, the expressions are space delimited. For integer input values, the expressions are evaluated as real numbers and the final result rounded to the nearest integer. See this section of the AMReX documentation for a complete list of functions supported by the math parser.
ImpactX constants
ImpactX will provide a few pre-defined constants, that can be used for any parameter that consists of one or more floats.
Note
Develop, such as:
q_e |
elementary charge |
m_e |
electron mass |
m_p |
proton mass |
m_u |
unified atomic mass unit (Dalton) |
epsilon0 |
vacuum permittivity |
mu0 |
vacuum permeability |
clight |
speed of light |
pi |
math constant pi |
See in WarpX the file Source/Utils/WarpXConst.H for the values.
User-defined constants
Users can define their own constants in the input file.
These constants can be used for any parameter that consists of one or more integers or floats.
User-defined constant names can contain only letters, numbers and the character _.
The name of each constant has to begin with a letter. The following names are used
by ImpactX, and cannot be used as user-defined constants: x, y, z, X, Y, t.
The values of the constants can include the predefined ImpactX constants listed above as well as other user-defined constants.
For example:
my_constants.a0 = 3.0my_constants.z_plateau = 150.e-6my_constants.n0 = 1.e22my_constants.wp = sqrt(n0*q_e**2/(epsilon0*m_e))
Coordinates
Besides, for profiles that depend on spatial coordinates (the plasma momentum distribution or the laser field, see below Particle initialization and Laser initialization), the parser will interpret some variables as spatial coordinates.
These are specified in the input parameter, i.e., density_function(x,y,z) and field_function(X,Y,t).
The parser reads python-style expressions between double quotes, for instance
"a0*x**2 * (1-y*1.e2) * (x>0)" is a valid expression where a0 is a
user-defined constant (see above) and x and y are spatial coordinates. The names are case sensitive. The factor
(x>0) is 1 where x>0 and 0 where x<=0. It allows the user to
define functions by intervals.
Alternatively the expression above can be written as if(x>0, a0*x**2 * (1-y*1.e2), 0).
Numerics and algorithms
algo.particle_shape(integer;1,2, or3)The order of the shape factors (splines) for the macro-particles along all spatial directions: 1 for linear, 2 for quadratic, 3 for cubic. Low-order shape factors result in faster simulations, but may lead to more noisy results. High-order shape factors are computationally more expensive, but may increase the overall accuracy of the results. For production runs it is generally safer to use high-order shape factors, such as cubic order.
algo.space_charge(boolean, optional, default:true)Whether to calculate space charge effects. This is in-development. At the moment, this flag only activates coordinate transformations and charge deposition.
algo.mlmg_relative_tolerance(float, optional, default:1.e-7)The relative precision with which the electrostatic space-charge fields should be calculated. More specifically, the space-charge fields are computed with an iterative Multi-Level Multi-Grid (MLMG) solver. This solver can fail to reach the default precision within a reasonable time.
algo.mlmg_absolute_tolerance(float, optional, default:0, which means: ignored)The absolute tolerance with which the space-charge fields should be calculated in units of V/m^2. More specifically, the acceptable residual with which the solution can be considered converged. In general this should be left as the default, but in cases where the simulation state changes very little between steps it can occur that the initial guess for the MLMG solver is so close to the converged value that it fails to improve that solution sufficiently to reach the mlmg_relative_tolerance value.”
algo.mlmg_max_iters(integer, optional, default:100)Maximum number of iterations used for MLMG solver for space-charge fields calculation. In case if MLMG converges but fails to reach the desired self_fields_required_precision, this parameter may be increased.
algo.mlmg_verbosity(integer, optional, default:1)The verbosity used for MLMG solver for space-charge fields calculation. Currently MLMG solver looks for verbosity levels from 0-5. A higher number results in more verbose output.
Diagnostics and output
diag.enable(boolean, optional, default:true) Enable or disable diagnostics generally. Disabling this is mostly used for benchmarking.This option is ignored for the openPMD output elements (remove them from the lattice to disable).
diag.slice_step_diagnostics(boolean, optional, default:false) By default, diagnostics is performed at the beginning and end of the simulation. Enabling this flag will write diagnostics every step and slice stepdiag.file_min_digits(integer, optional, default:6)The minimum number of digits used for the step number appended to the diagnostic file names.
diag.backend(string, default value:default)Diagnostics for particles lost in apertures, stored as
diags/openPMD/particles_lost.*at the end of the simulation. See thebeam_monitorelement for backend values.
Reduced Diagnostics
Reduced diagnostics allow the user to compute some reduced quantity (invariants of motion, particle temperature, max of a field, …) and write a small amount of data to text files. Reduced diagnostics are run in situ with the simulation.
Diagnostics related to integrable optics in the IOTA nonlinear magnetic insert element:
diag.alpha(float, unitless) Twiss alpha of the bare linear lattice at the location of output for the nonlinear IOTA invariants H and I. Horizontal and vertical values must be equal.diag.beta(float, meters) Twiss beta of the bare linear lattice at the location of output for the nonlinear IOTA invariants H and I. Horizontal and vertical values must be equal.diag.tn(float, unitless) dimensionless strength of the IOTA nonlinear magnetic insert element used for computing H and I.diag.cn(float, meters^(1/2)) scale factor of the IOTA nonlinear magnetic insert element used for computing H and I.
Checkpoints and restart
Note
ImpactX will support checkpoints/restart via AMReX.
The checkpoint capability can be turned with regular diagnostics: <diag_name>.format = checkpoint.
amr.restart(string)Name of the checkpoint file to restart from. Returns an error if the folder does not exist or if it is not properly formatted.
Intervals parser
Note
TODO :-)
ImpactX can parse time step interval expressions of the form start:stop:period, e.g.
1:2:3, 4::, 5:6, :, ::10.
A comma is used as a separator between groups of intervals, which we call slices.
The resulting time steps are the union set of all given slices.
White spaces are ignored.
A single slice can have 0, 1 or 2 colons :, just as numpy slices, but with inclusive upper bound for stop.
For 0 colon the given value is the period
For 1 colon the given string is of the type
start:stopFor 2 colons the given string is of the type
start:stop:period
Any value that is not given is set to default.
Default is 0 for the start, std::numeric_limits<int>::max() for the stop and 1 for the
period.
For the 1 and 2 colon syntax, actually having values in the string is optional
(this means that ::5, 100 ::10 and 100 : are all valid syntaxes).
All values can be expressions that will be parsed in the same way as other integer input parameters.
Examples
something_intervals = 50-> do something at timesteps 0, 50, 100, 150, etc. (equivalent tosomething_intervals = ::50)something_intervals = 300:600:100-> do something at timesteps 300, 400, 500 and 600.something_intervals = 300::50-> do something at timesteps 300, 350, 400, 450, etc.something_intervals = 105:108,205:208-> do something at timesteps 105, 106, 107, 108, 205, 206, 207 and 208. (equivalent tosomething_intervals = 105 : 108 : , 205 : 208 :)something_intervals = :orsomething_intervals = ::-> do something at every timestep.something_intervals = 167:167,253:253,275:425:50do something at timesteps 167, 253, 275, 325, 375 and 425.
This is essentially the python slicing syntax except that the stop is inclusive
(0:100 contains 100) and that no colon means that the given value is the period.
Note that if a given period is zero or negative, the corresponding slice is disregarded.
For example, something_intervals = -1 deactivates something and
something_intervals = ::-1,100:1000:25 is equivalent to something_intervals = 100:1000:25.
Examples
This section allows you to download input files that correspond to different physical situations or test different code features.
FODO Cell
Stable FODO cell with a zero-current phase advance of 67.8 degrees.
The matched Twiss parameters at entry are:
\(\beta_\mathrm{x} = 2.82161941\) m
\(\alpha_\mathrm{x} = -1.59050035\)
\(\beta_\mathrm{y} = 2.82161941\) m
\(\alpha_\mathrm{y} = 1.59050035\)
We use a 2 GeV electron beam with initial unnormalized rms emittance of 2 nm.
The second moments of the particle distribution after the FODO cell should coincide with the second moments of the particle distribution before the FODO cell, to within the level expected due to noise due to statistical sampling.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_fodo.pyorImpactX executable using an input file:
impactx input_fodo.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/fodo/run_fodo.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV electron beam with an initial
# unnormalized rms emittance of 2 nm
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=3.9984884770e-5,
sigmaY=3.9984884770e-5,
sigmaT=1.0e-3,
sigmaPx=2.6623538760e-5,
sigmaPy=2.6623538760e-5,
sigmaPt=2.0e-3,
muxpx=-0.846574929020762,
muypy=0.846574929020762,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice)
ns = 25 # number of slices per ds in the element
fodo = [
monitor,
elements.Drift(ds=0.25, nslice=ns),
monitor,
elements.Quad(ds=1.0, k=1.0, nslice=ns),
monitor,
elements.Drift(ds=0.5, nslice=ns),
monitor,
elements.Quad(ds=1.0, k=-1.0, nslice=ns),
monitor,
elements.Drift(ds=0.25, nslice=ns),
monitor,
]
# assign a fodo segment
sim.lattice.extend(fodo)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/fodo/input_fodo.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 3.9984884770e-5
beam.sigmaY = 3.9984884770e-5
beam.sigmaT = 1.0e-3
beam.sigmaPx = 2.6623538760e-5
beam.sigmaPy = 2.6623538760e-5
beam.sigmaPt = 2.0e-3
beam.muxpx = -0.846574929020762
beam.muypy = 0.846574929020762
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor drift1 monitor quad1 monitor drift2 monitor quad2 monitor drift3 monitor
lattice.nslice = 25
monitor.type = beam_monitor
monitor.backend = h5
drift1.type = drift
drift1.ds = 0.25
quad1.type = quad
quad1.ds = 1.0
quad1.k = 1.0
drift2.type = drift
drift2.ds = 0.5
quad2.type = quad
quad2.ds = 1.0
quad2.k = -1.0
drift3.type = drift
drift3.ds = 0.25
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
Analyze
We run the following script to analyze correctness:
Script analysis_fodo.py
examples/fodo/analysis_fodo.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
7.5451170454175073e-005,
7.5441588239210947e-005,
9.9775878164077539e-004,
1.9959540393751392e-009,
2.0175015289132990e-009,
2.0013820193294972e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
7.4790118496224206e-005,
7.5357525169680140e-005,
9.9775879288128088e-004,
1.9959539836392703e-009,
2.0175014668882125e-009,
2.0013820380883801e-006,
],
rtol=rtol,
atol=atol,
)
Visualize
You can run the following script to visualize the beam evolution over time:
Script plot_fodo.py
examples/fodo/plot_fodo.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import argparse
import glob
import re
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
import openpmd_api as io
import pandas as pd
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
def read_file(file_pattern):
for filename in glob.glob(file_pattern):
df = pd.read_csv(filename, delimiter=r"\s+")
if "step" not in df.columns:
step = int(re.findall(r"[0-9]+", filename)[0])
df["step"] = step
yield df
def read_time_series(file_pattern):
"""Read in all CSV files from each MPI rank (and potentially OpenMP
thread). Concatenate into one Pandas dataframe.
Returns
-------
pandas.DataFrame
"""
return pd.concat(
read_file(file_pattern),
axis=0,
ignore_index=True,
) # .set_index('id')
# options to run this script
parser = argparse.ArgumentParser(description="Plot the FODO benchmark.")
parser.add_argument(
"--save-png", action="store_true", help="non-interactive run: save to PNGs"
)
args = parser.parse_args()
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
ref_particle = read_time_series("diags/ref_particle.*")
# scaling to units
millimeter = 1.0e3 # m->mm
mrad = 1.0e3 # ImpactX uses "static units": momenta are normalized by the magnitude of the momentum of the reference particle p0: px/p0 (rad)
# mm_mrad = 1.e6
nm_rad = 1.0e9
# select a single particle by id
# particle_42 = beam[beam["id"] == 42]
# print(particle_42)
# steps & corresponding z
steps = list(series.iterations)
z = list(
map(lambda step: ref_particle[ref_particle["step"] == step].z.values[0], steps)
)
# print(f"z={z}")
# beam transversal size & emittance over steps
moments = list(
map(
lambda step: (
step,
get_moments(series.iterations[step].particles["beam"].to_df()),
),
steps,
)
)
# print(moments)
sigx = list(map(lambda step_val: step_val[1][0] * millimeter, moments))
sigy = list(map(lambda step_val: step_val[1][1] * millimeter, moments))
emittance_x = list(map(lambda step_val: step_val[1][3] * nm_rad, moments))
emittance_y = list(map(lambda step_val: step_val[1][4] * nm_rad, moments))
# print(sigx, sigy)
# print beam transversal size over steps
f = plt.figure(figsize=(9, 4.8))
ax1 = f.gca()
im_sigx = ax1.plot(z, sigx, label=r"$\sigma_x$")
im_sigy = ax1.plot(z, sigy, label=r"$\sigma_y$")
ax2 = ax1.twinx()
ax2.set_prop_cycle(None) # reset color cycle
im_emittance_x = ax2.plot(z, emittance_x, ":", label=r"$\epsilon_x$")
im_emittance_y = ax2.plot(z, emittance_y, ":", label=r"$\epsilon_y$")
ax1.legend(
handles=im_sigx + im_sigy + im_emittance_x + im_emittance_y, loc="lower center"
)
ax1.set_xlabel(r"$z$ [m]")
ax1.set_ylabel(r"$\sigma_{x,y}$ [mm]")
# ax2.set_ylabel(r"$\epsilon_{x,y}$ [mm-mrad]")
ax2.set_ylabel(r"$\epsilon_{x,y}$ [nm]")
ax2.set_ylim([1.5, 2.5])
ax1.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.tight_layout()
if args.save_png:
plt.savefig("fodo_sigma.png")
else:
plt.show()
# beam transversal scatter plot over steps
num_plots_per_row = len(steps)
fig, axs = plt.subplots(
3, num_plots_per_row, figsize=(9, 4.8), sharex="row", sharey="row"
)
ncol_ax = -1
for step in steps:
# plot initial distribution & at exit of each element
ncol_ax += 1
# x-y
ax = axs[(0, ncol_ax)]
beam_at_step = series.iterations[step].particles["beam"].to_df()
ax.scatter(
beam_at_step.position_x.multiply(millimeter),
beam_at_step.position_y.multiply(millimeter),
s=0.01,
)
ax.set_title(f"$z={z[ncol_ax]}$ [m]")
ax.set_xlabel(r"$x$ [mm]")
# x-px
ax = axs[(1, ncol_ax)]
beam_at_step = series.iterations[step].particles["beam"].to_df()
ax.scatter(
beam_at_step.position_x.multiply(millimeter),
beam_at_step.momentum_x.multiply(mrad),
s=0.01,
)
ax.set_xlabel(r"$x$ [mm]")
# y-py
ax = axs[(2, ncol_ax)]
beam_at_step = series.iterations[step].particles["beam"].to_df()
ax.scatter(
beam_at_step.position_y.multiply(millimeter),
beam_at_step.momentum_y.multiply(mrad),
s=0.01,
)
ax.set_xlabel(r"$y$ [mm]")
axs[(0, 0)].set_ylabel(r"$y$ [mm]")
axs[(1, 0)].set_ylabel(r"$p_x$ [mrad]")
axs[(2, 0)].set_ylabel(r"$p_y$ [mrad]")
plt.tight_layout()
if args.save_png:
plt.savefig("fodo_scatter.png")
else:
plt.show()
FODO transversal beam width and emittance evolution
FODO transversal beam width and phase space evolution
Chicane
Berlin-Zeuthen magnetic bunch compression chicane: https://www.desy.de/csr/
All parameters can be found online. A 5 GeV electron bunch with normalized transverse rms emittance of 1 um undergoes longitudinal compression by a factor of 10 in a standard 4-bend chicane.
The emittances should be preserved, and the rms pulse length should decrease by the compression factor (10).
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_chicane.pyorImpactX executable using an input file:
impactx input_chicane.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/chicane/run_chicane.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Marco Garten, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 5 GeV electron beam with an initial
# normalized transverse rms emittance of 1 um
kin_energy_MeV = 5.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=2.2951017632e-5,
sigmaY=1.3084093142e-5,
sigmaT=5.5555553e-8,
sigmaPx=1.598353425e-6,
sigmaPy=2.803697378e-6,
sigmaPt=2.000000000e-6,
muxpx=0.933345606203060,
muypy=0.933345606203060,
mutpt=0.999999961419755,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
ns = 25 # number of slices per ds in the element
rc = 10.35 # bend radius (meters)
psi = 0.048345620280243 # pole face rotation angle (radians)
# Drift elements
dr1 = elements.Drift(ds=5.0058489435, nslice=ns)
dr2 = elements.Drift(ds=1.0, nslice=ns)
dr3 = elements.Drift(ds=2.0, nslice=ns)
# Bend elements
sbend1 = elements.Sbend(ds=0.50037, rc=-rc, nslice=ns)
sbend2 = elements.Sbend(ds=0.50037, rc=rc, nslice=ns)
# Dipole Edge Focusing elements
dipedge1 = elements.DipEdge(psi=-psi, rc=-rc, g=0.0, K2=0.0)
dipedge2 = elements.DipEdge(psi=psi, rc=rc, g=0.0, K2=0.0)
lattice_half = [sbend1, dipedge1, dr1, dipedge2, sbend2]
# assign a segment with the first half of the lattice
sim.lattice.append(monitor)
sim.lattice.extend(lattice_half)
sim.lattice.append(dr2)
lattice_half.reverse()
# extend the lattice by a reversed half
sim.lattice.extend(lattice_half)
sim.lattice.append(dr3)
sim.lattice.append(monitor)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/chicane/input_chicane.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 5.0e3
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 2.2951017632e-5
beam.sigmaY = 1.3084093142e-5
beam.sigmaT = 5.5555553e-8
beam.sigmaPx = 1.598353425e-6
beam.sigmaPy = 2.803697378e-6
beam.sigmaPt = 2.000000000e-6
beam.muxpx = 0.933345606203060
beam.muypy = 0.933345606203060
beam.mutpt = 0.999999961419755
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor sbend1 dipedge1 drift1 dipedge2 sbend2 drift2 \
sbend2 dipedge2 drift1 dipedge1 sbend1 drift3 monitor
lattice.nslice = 25
sbend1.type = sbend
sbend1.ds = 0.50037 # projected length 0.5 m, angle 2.77 deg
sbend1.rc = -10.35
drift1.type = drift
drift1.ds = 5.0058489435 # projected length 5 m
sbend2.type = sbend
sbend2.ds = 0.50037 # projected length 0.5 m, angle 2.77 deg
sbend2.rc = 10.35
drift2.type = drift
drift2.ds = 1.0
drift3.type = drift
drift3.ds = 2.0
dipedge1.type = dipedge # dipole edge focusing
dipedge1.psi = -0.048345620280243
dipedge1.rc = -10.35
dipedge1.g = 0.0
dipedge1.K2 = 0.0
dipedge2.type = dipedge
dipedge2.psi = 0.048345620280243
dipedge2.rc = 10.35
dipedge2.g = 0.0
dipedge2.K2 = 0.0
monitor.type = beam_monitor
monitor.backend = h5
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
Analyze
We run the following script to analyze correctness:
Script analysis_chicane.py
examples/chicane/analysis_chicane.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
6.4214719960819659e-005,
3.6603372435649773e-005,
1.9955175623579313e-004,
1.0198263116327677e-010,
1.0308359092878036e-010,
4.0035161705244885e-010,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
2.3928429374387210e-005,
8.4424535301423173e-005,
1.9976426324802290e-005,
1.0198281373761584e-010,
1.0308356090529235e-010,
4.0027996099961315e-010,
],
rtol=rtol,
atol=atol,
)
Visualize
You can run the following script to visualize the beam evolution over time:
Script plot_chicane.py
examples/chicane/plot_chicane.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import argparse
import glob
import re
import matplotlib.pyplot as plt
from matplotlib.ticker import MaxNLocator
import openpmd_api as io
import pandas as pd
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
def read_file(file_pattern):
for filename in glob.glob(file_pattern):
df = pd.read_csv(filename, delimiter=r"\s+")
if "step" not in df.columns:
step = int(re.findall(r"[0-9]+", filename)[0])
df["step"] = step
yield df
def read_time_series(file_pattern):
"""Read in all CSV files from each MPI rank (and potentially OpenMP
thread). Concatenate into one Pandas dataframe.
Returns
-------
pandas.DataFrame
"""
return pd.concat(
read_file(file_pattern),
axis=0,
ignore_index=True,
) # .set_index('id')
# options to run this script
parser = argparse.ArgumentParser(description="Plot the chicane benchmark.")
parser.add_argument(
"--save-png", action="store_true", help="non-interactive run: save to PNGs"
)
args = parser.parse_args()
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
ref_particle = read_time_series("diags/ref_particle.*")
# scaling to units
millimeter = 1.0e3 # m->mm
# for "t": the time coordinate is scaled by c, and therefore has units of length (m) by default, so we can label the axis ct (mm)
mrad = 1.0e3 # ImpactX uses "static units": momenta are normalized by the magnitude of the momentum of the reference particle p0: px/p0 (rad)
# mm_mrad = 1.e6
nm_rad = 1.0e9
# select a single particle by id
# particle_42 = beam[beam["id"] == 42]
# print(particle_42)
# steps & corresponding z
steps = list(series.iterations)
z = list(
map(lambda step: ref_particle[ref_particle["step"] == step].z.values[0], steps)
)
x = list(
map(lambda step: ref_particle[ref_particle["step"] == step].x.values[0], steps)
)
# print(f"z={z}")
# beam transversal size & emittance over steps
moments = list(
map(
lambda step: (
step,
get_moments(series.iterations[step].particles["beam"].to_df()),
),
steps,
)
)
# print(moments)
sigx = list(map(lambda step_val: step_val[1][0] * millimeter, moments))
sigt = list(map(lambda step_val: step_val[1][2] * millimeter, moments))
emittance_x = list(map(lambda step_val: step_val[1][3] * nm_rad, moments))
emittance_t = list(map(lambda step_val: step_val[1][5] * nm_rad, moments))
# print(sigx, sigt)
# print beam transversal size over steps
f, axs = plt.subplots(
2, 1, figsize=(9, 4.8), sharex=True, gridspec_kw={"height_ratios": [1, 2]}
)
ax0 = axs[0]
im_xz = ax0.plot(z, x, "--", lw=3, label=r"$x$")
ax0.legend(loc="upper right")
ax0.set_ylim([0, None])
ax0.set_ylabel(r"$x$ [m]")
ax1 = axs[1]
im_sigx = ax1.plot(z, sigx, label=r"$\sigma_x$")
im_sigt = ax1.plot(z, sigt, label=r"$\sigma_t$")
ax2 = ax1.twinx()
ax2.set_prop_cycle(None) # reset color cycle
im_emittance_x = ax2.plot(z, emittance_x, ":", label=r"$\epsilon_x$")
im_emittance_t = ax2.plot(z, emittance_t, ":", label=r"$\epsilon_t$")
ax1.legend(
handles=im_sigx + im_sigt + im_emittance_x + im_emittance_t, loc="upper right"
)
ax1.set_xlabel(r"$z$ [m]")
ax1.set_ylabel(r"$\sigma_{x,t}$ [mm]")
# ax2.set_ylabel(r"$\epsilon_{x,y}$ [mm-mrad]")
ax2.set_ylabel(r"$\epsilon_{x,t}$ [nm]")
ax1.set_ylim([0, None])
ax2.set_ylim([0, None])
ax1.xaxis.set_major_locator(MaxNLocator(integer=True))
plt.tight_layout()
if args.save_png:
plt.savefig("chicane_sigma.png")
else:
plt.show()
# beam transversal scatter plot over steps
num_plots_per_row = len(steps)
fig, axs = plt.subplots(
4, num_plots_per_row, figsize=(9, 6.4), sharex="row", sharey="row"
)
ncol_ax = -1
for step in steps:
# plot initial distribution & at exit of each element
ncol_ax += 1
# t-pt
ax = axs[(0, ncol_ax)]
beam_at_step = series.iterations[step].particles["beam"].to_df()
ax.scatter(
beam_at_step.position_t.multiply(millimeter),
beam_at_step.momentum_t.multiply(mrad),
s=0.01,
)
ax.set_xlabel(r"$ct$ [mm]")
z_unit = ""
if ncol_ax == num_plots_per_row - 1:
z_unit = " [m]"
ax.set_title(f"$z={z[ncol_ax]:.1f}${z_unit}")
# x-px
ax = axs[(1, ncol_ax)]
beam_at_step = series.iterations[step].particles["beam"].to_df()
ax.scatter(
beam_at_step.position_x.multiply(millimeter),
beam_at_step.momentum_x.multiply(mrad),
s=0.01,
)
ax.set_xlabel(r"$x$ [mm]")
# t-x
ax = axs[(2, ncol_ax)]
beam_at_step = series.iterations[step].particles["beam"].to_df()
ax.scatter(
beam_at_step.position_t.multiply(millimeter),
beam_at_step.position_x.multiply(millimeter),
s=0.01,
)
ax.set_xlabel(r"$ct$ [mm]")
# t-px
ax = axs[(3, ncol_ax)]
beam_at_step = series.iterations[step].particles["beam"].to_df()
ax.scatter(
beam_at_step.position_t.multiply(millimeter),
beam_at_step.momentum_x.multiply(mrad),
s=0.01,
)
ax.set_xlabel(r"$ct$ [mm]")
axs[(0, 0)].set_ylabel(r"$p_t$ [mrad]")
axs[(1, 0)].set_ylabel(r"$p_x$ [mrad]")
axs[(2, 0)].set_ylabel(r"$x$ [mm]")
axs[(3, 0)].set_ylabel(r"$p_x$ [mrad]")
plt.tight_layout()
if args.save_png:
plt.savefig("chicane_scatter.png")
else:
plt.show()
(top) Chicane floorplan. (bottom) Chicane beam width and emittance evolution.
Chicane beam width and emittance evolution
Constant Focusing Channel
Stationary beam in a constant focusing channel (without space charge).
The matched Twiss parameters at entry are:
\(\beta_\mathrm{x} = 1.0\) m
\(\alpha_\mathrm{x} = 0.0\)
\(\beta_\mathrm{y} = 1.0\) m
\(\alpha_\mathrm{y} = 0.0\)
We use a 2 GeV proton beam with initial unnormalized rms emittance of 1 um. The longitudinal beam parameters are chosen so that the bunch has radial symmetry when viewed in the beam rest frame.
The particle distribution should remain unchanged, to within the level expected due to numerical particle noise. This fact is independent of the length of the channel. This is tested using the second moments of the distribution.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_cfchannel.pyorImpactX executable using an input file:
impactx input_cfchannel.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/cfchannel/run_cfchannel.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Marco Garten, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV proton beam with an initial
# normalized transverse rms emittance of 1 um
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.0e-3,
sigmaY=1.0e-3,
sigmaT=3.369701494258956e-4,
sigmaPx=1.0e-3,
sigmaPy=1.0e-3,
sigmaPt=2.9676219145931020e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
sim.lattice.extend(
[
monitor,
elements.ConstF(ds=2.0, kx=1.0, ky=1.0, kt=1.0),
monitor,
]
)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/cfchannel/input_cfchannel.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.0e-3
beam.sigmaY = 1.0e-3
beam.sigmaT = 3.369701494258956e-4
beam.sigmaPx = 1.0e-3
beam.sigmaPy = 1.0e-3
beam.sigmaPt = 2.9676219145931020e-3
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor constf1 monitor
monitor.type = beam_monitor
monitor.backend = h5
constf1.type = constf
constf1.ds = 2.0
constf1.kx = 1.0
constf1.ky = 1.0
constf1.kt = 1.0
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
Analyze
We run the following script to analyze correctness:
Script analysis_cfchannel.py
examples/cfchannel/analysis_cfchannel.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # a big number
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.0e-003,
1.0e-003,
3.369701494258956e-4,
1.0e-006,
1.0e-006,
1.0e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # a big number
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.0e-003,
1.0e-003,
3.369701494258956e-4,
1.0e-006,
1.0e-006,
1.0e-006,
],
rtol=rtol,
atol=atol,
)
Constant Focusing Channel with Space Charge
RMS-matched beam in a constant focusing channel with space charge.
The matched Twiss parameters at entry are:
\(\beta_\mathrm{x} = 1.477305\) m
\(\alpha_\mathrm{x} = 0.0\)
\(\beta_\mathrm{y} = 1.477305\) m
\(\alpha_\mathrm{y} = 0.0\)
We use a 2 GeV proton beam with initial unnormalized rms emittance of 1 um. The longitudinal beam parameters are chosen so that the bunch has radial symmetry when viewed in the beam rest frame. The bunch charge is set to 10 nC, resulting in a transverse tune depression ratio of 0.67. The initial distribution used is a 6D waterbag.
The beam second moments should remain nearly unchanged, except for some small emittance growth due to nonlinear space charge. This is tested using the second moments of the distribution.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and :math:`
Run
This example can be run as a Python script (python3 run_cfchannel_10nC.py) or as an app with an input file (impactx input_cfchannel_10nC.in).
Each can also be prefixed with an MPI executor, such as mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/cfchannel/run_cfchannel_10nC.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Marco Garten, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.n_cell = [48, 48, 40] # [72, 72, 64] for increased precision
sim.particle_shape = 2 # B-spline order
sim.space_charge = True
sim.prob_relative = 3.0
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV proton beam with an initial
# normalized transverse rms emittance of 1 um
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-8 # used with space charge
npart = 10000 # number of macro particles; use 1e5 for increased precision
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.2154443728379865788e-3,
sigmaY=1.2154443728379865788e-3,
sigmaT=4.0956844276541331005e-4,
sigmaPx=8.2274435782286157175e-4,
sigmaPy=8.2274435782286157175e-4,
sigmaPt=2.4415943602685364584e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
nslice = 50 # use 1e5 for increased precision
# design the accelerator lattice
sim.lattice.extend(
[
monitor,
elements.ConstF(ds=2.0, kx=1.0, ky=1.0, kt=1.0, nslice=nslice),
monitor,
]
)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/cfchannel/input_cfchannel_10nC.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
#beam.npart = 100000 # optional for increased precision
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-8
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.2154443728379865788e-3
beam.sigmaY = 1.2154443728379865788e-3
beam.sigmaT = 4.0956844276541331005e-4
beam.sigmaPx = 8.2274435782286157175e-4
beam.sigmaPy = 8.2274435782286157175e-4
beam.sigmaPt = 2.4415943602685364584e-3
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor constf1 monitor
lattice.nslice = 50
#lattice.nslice = 60 # optional for increased precision
monitor.type = beam_monitor
monitor.backend = h5
constf1.type = constf
constf1.ds = 2.0
constf1.kx = 1.0
constf1.ky = 1.0
constf1.kt = 1.0
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = true
amr.n_cell = 48 48 40
#amr.n_cell = 72 72 64 # optional for increased precision
geometry.prob_relative = 3.0
Analyze
We run the following script to analyze correctness:
Script analysis_cfchannel_10nC.py
examples/cfchannel/analysis_cfchannel_10nC.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.2154443728379865788e-003,
1.2154443728379865788e-003,
4.0956844276541331005317e-004,
1.000000000e-006,
1.000000000e-006,
1.000000000e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.2154443728379865788e-003,
1.2154443728379865788e-003,
4.0956844276541331005317e-004,
1.000000000e-006,
1.000000000e-006,
1.000000000e-006,
],
rtol=rtol,
atol=atol,
)
Expanding Beam in Free Space
A coasting bunch expanding freely in free space under its own space charge.
We use a cold (zero emittance) 250 MeV electron bunch whose initial distribution is a uniformly-populated 3D ball of radius R0 = 1 mm when viewed in the bunch rest frame.
In the laboratory frame, the bunch is a uniformly-populated ellipsoid, which expands to twice its original size. This is tested using the second moments of the distribution.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_expanding.pyorImpactX executable using an input file:
impactx input_expanding.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/expanding/run_expanding.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.n_cell = [56, 56, 48]
sim.particle_shape = 2 # B-spline order
sim.space_charge = True
sim.dynamic_size = True
sim.prob_relative = 3.0
# beam diagnostics
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = False
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV electron beam with an initial
# unnormalized rms emittance of 2 nm
kin_energy_MeV = 250 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles (outside tests, use 1e5 or more)
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Kurth6D(
sigmaX=4.472135955e-4,
sigmaY=4.472135955e-4,
sigmaT=9.12241869e-7,
sigmaPx=0.0,
sigmaPy=0.0,
sigmaPt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
sim.lattice.extend([monitor, elements.Drift(ds=6.0, nslice=40), monitor])
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/expanding/input_expanding.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000 # outside tests, use 1e5 or more
beam.units = static
beam.kin_energy = 250.0
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = kurth6d
beam.sigmaX = 4.472135955e-4
beam.sigmaY = 4.472135955e-4
beam.sigmaT = 9.12241869e-7
beam.sigmaPx = 0.0
beam.sigmaPy = 0.0
beam.sigmaPt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor drift1 monitor
lattice.nslice = 40
drift1.type = drift
drift1.ds = 6.0
monitor.type = beam_monitor
monitor.backend = h5
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = true
amr.n_cell = 56 56 48
geometry.prob_relative = 3.0
Analyze
We run the following script to analyze correctness:
Script analysis_expanding.py
examples/expanding/analysis_expanding.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.4721359550e-004,
4.4721359550e-004,
9.1224186858e-007,
0.0e-006,
0.0e-006,
0.0e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt],
[
8.9442719100e-004,
8.9442719100e-004,
1.8244837370e-006,
],
rtol=rtol,
atol=atol,
)
atol = 1.0e-8
rtol = 0.0 # ignored
assert np.allclose(
[emittance_x, emittance_y, emittance_t],
[
0.0,
0.0,
0.0,
],
rtol=rtol,
atol=atol,
)
Kurth Distribution in a Periodic Focusing Channel
Matched Kurth distribution in a periodic focusing channel (without space charge).
The distribution is radially symmetric in (x,y,t) space, and matched to a radially symmetric periodic linear focusing lattice with a phase advance of 121 degrees.
We use a 2 GeV proton beam with initial unnormalized rms emittance of 1 um in all three phase planes.
The particle distribution should remain unchanged, to within the level expected due to numerical particle noise. This is tested using the second moments of the distribution.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_kurth_periodic.pyorImpactX executable using an input file:
impactx input_kurth_periodic.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/kurth/run_kurth_periodic.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV proton beam with an initial
# unnormalized rms emittance of 1 um in each
# coordinate plane
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-8 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Kurth6D(
sigmaX=1.11e-3,
sigmaY=1.11e-3,
sigmaT=3.74036839224568e-4,
sigmaPx=9.00900900901e-4,
sigmaPy=9.00900900901e-4,
sigmaPt=2.6735334467940146e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
constf1 = elements.ConstF(ds=2.0, kx=0.7, ky=0.7, kt=0.7)
drift1 = elements.Drift(ds=1.0)
sim.lattice.extend([monitor, drift1, constf1, drift1, monitor])
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/kurth/input_kurth_periodic.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-8
beam.particle = proton
beam.distribution = kurth6d
beam.sigmaX = 1.11e-3
beam.sigmaY = 1.11e-3
beam.sigmaT = 3.74036839224568e-4
beam.sigmaPx = 9.00900900901e-4
beam.sigmaPy = 9.00900900901e-4
beam.sigmaPt = 2.6735334467940146e-3
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor drift1 constf1 drift1 monitor
monitor.type = beam_monitor
monitor.backend = h5
drift1.type = drift
drift1.ds = 1.0
constf1.type = constf
constf1.ds = 2.0
constf1.kx = 0.7
constf1.ky = 0.7
constf1.kt = 0.7
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
amr.n_cell = 40 40 32
geometry.prob_relative = 3.0
Analyze
We run the following script to analyze correctness:
Script analysis_kurth_periodic.py
examples/kurth/analysis_kurth_periodic.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.11e-03,
1.11e-03,
3.74036839224568e-04,
1.000000000e-006,
1.000000000e-006,
1.000000000e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.11e-03,
1.11e-03,
3.74036839224568e-04,
1.000000000e-006,
1.000000000e-006,
1.000000000e-006,
],
rtol=rtol,
atol=atol,
)
Kurth Distribution in a Periodic Focusing Channel with Space Charge
Matched Kurth distribution in a periodic focusing channel with space charge.
The distribution is radially symmetric in (x,y,t) space, and matched to a radially symmetric constant linear focusing.
We use a 2 GeV proton beam with initial unnormalized rms emittance of 1 um in all three phase planes. The bunch charge is set to 10 nC, depressing the phase advance from 121 degrees to 74 degrees.
The particle distribution should remain unchanged, to within the level expected due to numerical particle noise. This is tested using the second moments of the distribution.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and :math:`
Run
This example can be run as a Python script (python3 run_kurth_10nC_periodic.py) or as an app with an input file (impactx input_kurth_10nC_periodic.in).
Each can also be prefixed with an MPI executor, such as mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/kurth/run_kurth_10nC_periodic.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.n_cell = [48, 48, 40] # use [72, 72, 72] for increased precision
sim.particle_shape = 2 # B-spline order
sim.space_charge = True
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV proton beam with an initial
# unnormalized rms emittance of 1 um in each
# coordinate plane
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-8 # used with space charge
npart = 10000 # number of macro particles; use 1e5 for increased precision
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Kurth6D(
sigmaX=1.46e-3,
sigmaY=1.46e-3,
sigmaT=4.9197638312420749e-4,
sigmaPx=6.84931506849e-4,
sigmaPy=6.84931506849e-4,
sigmaPt=2.0326178944803812e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
nslice = 20 # use 30 for increased precision
constf1 = elements.ConstF(ds=2.0, kx=0.7, ky=0.7, kt=0.7, nslice=nslice)
drift1 = elements.Drift(ds=1.0, nslice=nslice)
sim.lattice.extend([monitor, drift1, constf1, drift1, monitor])
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/kurth/input_kurth_10nC_periodic.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
#beam.npart = 100000 #optional for increased precision
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-8
beam.particle = proton
beam.distribution = kurth6d
beam.sigmaX = 1.46e-3
beam.sigmaY = 1.46e-3
beam.sigmaT = 4.9197638312420749e-4
beam.sigmaPx = 6.84931506849e-4
beam.sigmaPy = 6.84931506849e-4
beam.sigmaPt = 2.0326178944803812e-3
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor drift1 constf1 drift1 monitor
lattice.nslice = 20
#lattice.nslice = 30 #optional for increased precision
monitor.type = beam_monitor
monitor.backend = h5
drift1.type = drift
drift1.ds = 1.0
constf1.type = constf
constf1.ds = 2.0
constf1.kx = 0.7
constf1.ky = 0.7
constf1.kt = 0.7
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = true
amr.n_cell = 48 48 40
#amr.n_cell = 72 72 72 # optional for increased precision
geometry.prob_relative = 3.0
Analyze
We run the following script to analyze correctness:
Script analysis_kurth_10nC_periodic.py
examples/kurth/analysis_kurth_10nC_periodic.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 2.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.46e-3,
1.46e-3,
4.9197638312420749e-4,
1.000000000e-006,
1.000000000e-006,
1.000000000e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 2.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.46e-3,
1.46e-3,
4.9197638312420749e-4,
1.000000000e-006,
1.000000000e-006,
1.000000000e-006,
],
rtol=rtol,
atol=atol,
)
Acceleration by RF Cavities
Beam accelerated through a sequence of 4 RF cavities (without space charge).
We use a 230 MeV electron beam with initial normalized rms emittance of 1 um.
The lattice and beam parameters are based on Example 2 of the IMPACT-Z examples folder:
https://github.com/impact-lbl/IMPACT-Z/tree/master/examples/Example2
The final target beam energy and beam moments are based on simulation in IMPACT-Z, without space charge.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_rfcavity.pyorImpactX executable using an input file:
impactx input_rfcavity.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/rfcavity/run_rfcavity.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Marco Garten, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = False
# domain decomposition & space charge mesh
sim.init_grids()
# load a 230 MeV electron beam with an initial
# unnormalized rms emittance of 1 mm-mrad in all
# three phase planes
kin_energy_MeV = 230.0 # reference energy
bunch_charge_C = 1.0e-10 # used with space charge
npart = 10000 # number of macro particles (outside tests, use 1e5 or more)
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=0.352498964601e-3,
sigmaY=0.207443478142e-3,
sigmaT=0.70399950746e-4,
sigmaPx=5.161852770e-6,
sigmaPy=9.163582894e-6,
sigmaPt=0.260528852031e-3,
muxpx=0.5712386101751441,
muypy=-0.514495755427526,
mutpt=-5.05773e-10,
)
sim.add_particles(bunch_charge_C, distr, npart)
# design the accelerator lattice
# Drift elements
dr1 = elements.Drift(ds=0.4, nslice=1)
dr2 = elements.Drift(ds=0.032997, nslice=1)
# RF cavity element
rf = elements.RFCavity(
ds=1.31879807,
escale=62.0,
freq=1.3e9,
phase=85.5,
cos_coefficients=[
0.1644024074311037,
-0.1324009958969339,
4.3443060026047219e-002,
8.5602654094946495e-002,
-0.2433578169042885,
0.5297150596779437,
0.7164884680963959,
-5.2579522442877296e-003,
-5.5025369142193678e-002,
4.6845673335028933e-002,
-2.3279346335638568e-002,
4.0800777539657775e-003,
4.1378326533752169e-003,
-2.5040533340490805e-003,
-4.0654981400000964e-003,
9.6630592067498289e-003,
-8.5275895985990214e-003,
-5.8078747006425020e-002,
-2.4044337836660403e-002,
1.0968240064697212e-002,
-3.4461179858301418e-003,
-8.1201564869443749e-004,
2.1438992904959380e-003,
-1.4997753525697276e-003,
1.8685171825676386e-004,
],
sin_coefficients=[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
],
mapsteps=100,
nslice=4,
)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
sim.lattice.extend(
[
monitor,
dr1,
dr2,
rf,
dr2,
dr2,
rf,
dr2,
dr2,
rf,
dr2,
dr2,
rf,
dr2,
monitor,
]
)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/rfcavity/input_rfcavity.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000 # outside tests, use 1e5 or more
beam.units = static
beam.kin_energy = 230
beam.charge = 1.0e-10
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 0.352498964601e-3
beam.sigmaY = 0.207443478142e-3
beam.sigmaT = 0.70399950746e-4
beam.sigmaPx = 5.161852770e-6
beam.sigmaPy = 9.163582894e-6
beam.sigmaPt = 0.260528852031e-3
beam.muxpx = 0.5712386101751441
beam.muypy = -0.514495755427526
beam.mutpt = -5.05773e-10
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor dr1 dr2 rf dr2 dr2 rf dr2 dr2 rf dr2 dr2 rf dr2 monitor
monitor.type = beam_monitor
monitor.backend = h5
dr1.type = drift
dr1.ds = 0.4
dr1.nslice = 1
dr2.type = drift
dr2.ds = 0.032997
dr1.nslice = 1
rf.type = rfcavity
rf.ds = 1.31879807
rf.escale = 62.0
rf.freq = 1.3e9
rf.phase = 85.5
rf.mapsteps = 100
rf.nslice = 4
rf.cos_coefficients = \
0.1644024074311037 \
-0.1324009958969339 \
4.3443060026047219e-002 \
8.5602654094946495e-002 \
-0.2433578169042885 \
0.5297150596779437 \
0.7164884680963959 \
-5.2579522442877296e-003 \
-5.5025369142193678e-002 \
4.6845673335028933e-002 \
-2.3279346335638568e-002 \
4.0800777539657775e-003 \
4.1378326533752169e-003 \
-2.5040533340490805e-003 \
-4.0654981400000964e-003 \
9.6630592067498289e-003 \
-8.5275895985990214e-003 \
-5.8078747006425020e-002 \
-2.4044337836660403e-002 \
1.0968240064697212e-002 \
-3.4461179858301418e-003 \
-8.1201564869443749e-004 \
2.1438992904959380e-003 \
-1.4997753525697276e-003 \
1.8685171825676386e-004
rf.sin_coefficients = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 \
0 0 0 0 0 0 0
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = false
Analyze
We run the following script to analyze correctness:
Script analysis_rfcavity.py
examples/rfcavity/analysis_rfcavity.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.29466150443e-4,
2.41918588389e-4,
7.0399951912e-5,
2.21684103818e-9,
2.21684103818e-9,
1.83412186547e-8,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
3.52596000000e-4,
2.41775000000e-4,
7.0417917357e-5,
1.70893497973e-9,
1.70893497973e-9,
1.413901564889e-8,
],
rtol=rtol,
atol=atol,
)
FODO Cell with RF
Stable FODO cell with short RF (buncher) cavities added for longitudinal focusing. The phase advance in all three phase planes is between 86-89 degrees.
The matched Twiss parameters at entry are:
\(\beta_\mathrm{x} = 9.80910407\) m
\(\alpha_\mathrm{x} = 0.0\)
\(\beta_\mathrm{y} = 1.31893788\) m
\(\alpha_\mathrm{y} = 0.0\)
\(\beta_\mathrm{t} = 4.6652668782\) m
\(\alpha_\mathrm{t} = 0.0\)
We use a 250 MeV proton beam with initial unnormalized rms emittance of 1 mm-mrad in all three phase planes.
The second moments of the particle distribution after the FODO cell should coincide with the second moments of the particle distribution before the FODO cell, to within the level expected due to noise due to statistical sampling.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_fodo_rf.pyorImpactX executable using an input file:
impactx input_fodo_rf.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/fodo_rf/run_fodo_rf.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Marco Garten, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 250 MeV proton beam with an initial
# unnormalized rms emittance of 1 mm-mrad in all
# three phase planes
kin_energy_MeV = 250.0 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=3.131948925200e-3,
sigmaY=1.148450209423e-3,
sigmaT=2.159922887089e-3,
sigmaPx=3.192900088357e-4,
sigmaPy=8.707386631090e-4,
sigmaPt=4.62979491526e-4,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
sim.lattice.append(monitor)
# Quad elements
quad1 = elements.Quad(ds=0.15, k=2.5)
quad2 = elements.Quad(ds=0.3, k=-2.5)
# Drift element
drift1 = elements.Drift(ds=1.0)
# Short RF cavity element
shortrf1 = elements.Buncher(V=0.01, k=15.0)
lattice_no_drifts = [quad1, shortrf1, quad2, shortrf1, quad1]
# set first lattice element
sim.lattice.append(lattice_no_drifts[0])
# intersperse all remaining elements of the lattice with a drift element
for element in lattice_no_drifts[1:]:
sim.lattice.extend([drift1, element])
sim.lattice.append(monitor)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/fodo_rf/input_fodo_rf.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 250.0
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 3.131948925200e-3
beam.sigmaY = 1.148450209423e-3
beam.sigmaT = 2.159922887089e-3
beam.sigmaPx = 3.192900088357e-4
beam.sigmaPy = 8.707386631090e-4
beam.sigmaPt = 4.62979491526e-4
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor quad1 drift1 shortrf1 drift1 quad2 drift1 \
shortrf1 drift1 quad1 monitor
monitor.type = beam_monitor
monitor.backend = h5
quad1.type = quad
quad1.ds = 0.15
quad1.k = 2.5
drift1.type = drift
drift1.ds = 1.0
shortrf1.type = buncher
shortrf1.V = 0.01
shortrf1.k = 15.0
quad2.type = quad
quad2.ds = 0.3
quad2.k = -2.5
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
Analyze
We run the following script to analyze correctness:
Script analysis_fodo_rf.py
examples/fodo_rf/analysis_fodo_rf.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
3.145694e-03,
1.153344e-03,
2.155082e-03,
9.979770e-07,
1.008751e-06,
1.000691e-06,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
3.112318e-03,
1.153322e-03,
2.166501e-03,
9.979770e-07,
1.008751e-06,
1.000691e-06,
],
rtol=rtol,
atol=atol,
)
FODO Cell, Chromatic
Stable FODO cell with a zero-current phase advance of 67.8 degrees, with chromatic focusing effects included.
The matched Twiss parameters at entry are:
\(\beta_\mathrm{x} = 2.82161941\) m
\(\alpha_\mathrm{x} = -1.59050035\)
\(\beta_\mathrm{y} = 2.82161941\) m
\(\alpha_\mathrm{y} = 1.59050035\)
We use a 2 GeV electron beam with initial unnormalized rms emittance of 2 nm.
The second moments of the particle distribution after the FODO cell should coincide with the second moments of the particle distribution before the FODO cell, to within the level expected due to noise due to statistical sampling.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_fodo_chr.pyorImpactX executable using an input file:
impactx input_fodo_chr.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/fodo/run_fodo_chr.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV electron beam with an initial
# unnormalized rms emittance of 2 nm
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=3.9984884770e-5,
sigmaY=3.9984884770e-5,
sigmaT=1.0e-3,
sigmaPx=2.6623538760e-5,
sigmaPy=2.6623538760e-5,
sigmaPt=2.0e-3,
muxpx=-0.846574929020762,
muypy=0.846574929020762,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice)
ns = 25 # number of slices per ds in the element
fodo = [
monitor,
elements.ChrDrift(ds=0.25, nslice=ns),
monitor,
elements.ChrQuad(ds=1.0, k=1.0, nslice=ns),
monitor,
elements.ChrDrift(ds=0.5, nslice=ns),
monitor,
elements.ChrQuad(ds=1.0, k=-1.0, nslice=ns),
monitor,
elements.ChrDrift(ds=0.25, nslice=ns),
monitor,
]
# assign a fodo segment
sim.lattice.extend(fodo)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/fodo/input_fodo_chr.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 3.9984884770e-5
beam.sigmaY = 3.9984884770e-5
beam.sigmaT = 1.0e-3
beam.sigmaPx = 2.6623538760e-5
beam.sigmaPy = 2.6623538760e-5
beam.sigmaPt = 2.0e-3
beam.muxpx = -0.846574929020762
beam.muypy = 0.846574929020762
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor drift1 monitor quad1 monitor drift2 monitor quad2 monitor drift3 monitor
lattice.nslice = 25
monitor.type = beam_monitor
monitor.backend = h5
drift1.type = drift_chromatic
drift1.ds = 0.25
quad1.type = quad_chromatic
quad1.ds = 1.0
quad1.k = 1.0
drift2.type = drift_chromatic
drift2.ds = 0.5
quad2.type = quad_chromatic
quad2.ds = 1.0
quad2.k = -1.0
drift3.type = drift_chromatic
drift3.ds = 0.25
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
Analyze
We run the following script to analyze correctness:
Script analysis_fodo_chr.py
examples/fodo/analysis_fodo_chr.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
7.5451170454175073e-005,
7.5441588239210947e-005,
9.9775878164077539e-004,
1.9959540393751392e-009,
2.0175015289132990e-009,
2.0013820193294972e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
7.4790118496224206e-005,
7.5357525169680140e-005,
9.9775879288128088e-004,
1.9959539836392703e-009,
2.0175014668882125e-009,
2.0013820380883801e-006,
],
rtol=rtol,
atol=atol,
)
Chain of thin multipoles
A series of thin multipoles (quad, sext, oct) with both normal and skew coefficients.
We use a 2 GeV electron beam.
The second moments of x, y, and t should be unchanged, but there is large emittance growth in the x and y phase planes.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_multipole.pyorImpactX executable using an input file:
impactx input_multipole.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/multipole/run_multipole.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV electron beam with an initial
# unnormalized rms emittance of nm
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used without space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=4.0e-3,
sigmaY=4.0e-3,
sigmaT=1.0e-3,
sigmaPx=3.0e-4,
sigmaPy=3.0e-4,
sigmaPt=2.0e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
multipole = [
monitor,
elements.Multipole(multiple=2, K_normal=3.0, K_skew=0.0),
elements.Multipole(multiple=3, K_normal=100.0, K_skew=-50.0),
elements.Multipole(multiple=4, K_normal=65.0, K_skew=6.0),
monitor,
]
# assign a fodo segment
sim.lattice.extend(multipole)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/multipole/input_multipole.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 4.0e-3
beam.sigmaY = 4.0e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 3.0e-4
beam.sigmaPy = 3.0e-4
beam.sigmaPt = 2.0e-3
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor thin_quadrupole thin_sextupole thin_octupole monitor
monitor.type = beam_monitor
monitor.backend = h5
thin_quadrupole.type = multipole
thin_quadrupole.multipole = 2 //Thin quadrupole
thin_quadrupole.k_normal = 3.0
thin_quadrupole.k_skew = 0.0
thin_sextupole.type = multipole
thin_sextupole.multipole = 3 //Thin sextupole
thin_sextupole.k_normal = 100.0
thin_sextupole.k_skew = -50.0
thin_octupole.type = multipole
thin_octupole.multipole = 4 //Thin octupole
thin_octupole.k_normal = 65.0
thin_octupole.k_skew = 6.0
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
Analyze
We run the following script to analyze correctness:
Script analysis_multipole.py
examples/multipole/analysis_multipole.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.017554e-03,
4.017044e-03,
9.977588e-04,
1.197572e-06,
1.210501e-06,
2.001382e-06,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.017554e-03,
4.017044e-03,
9.977588e-04,
6.532644e-06,
6.630912e-06,
2.001382e-06,
],
rtol=rtol,
atol=atol,
)
A nonlinear focusing channel based on the IOTA nonlinear lens
A constant focusing channel with nonlinear focusing, using a string of thin IOTA nonlinear lens elements alternating with constant focusing elements.
We use a 2.5 MeV proton beam, corresponding to the nominal IOTA proton energy.
The two functions H (Hamiltonian) and I (the second invariant) should remain unchanged for all particles.
In this test, the initial and final values of \(\mu_H\), \(\sigma_H\), \(\mu_I\), \(\sigma_I\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_iotalens.pyorImpactX executable using an input file:
impactx input_iotalens.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/iota_lens/run_iotalens.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# diagnostics: IOTA nonlinear lens invariants calculation
sim.set_diag_iota_invariants(alpha=0.0, beta=1.0, tn=0.4, cn=0.01)
# load a 2.5 MeV proton beam
kin_energy_MeV = 2.5 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=2.0e-3,
sigmaY=2.0e-3,
sigmaT=1.0e-3,
sigmaPx=3.0e-4,
sigmaPy=3.0e-4,
sigmaPt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# design the accelerator lattice
constEnd = elements.ConstF(ds=0.05, kx=1.0, ky=1.0, kt=1.0e-12)
nllens = elements.NonlinearLens(knll=4.0e-6, cnll=0.01)
const = elements.ConstF(ds=0.1, kx=1.0, ky=1.0, kt=1.0e-12)
num_lenses = 18
nllens_lattice = [constEnd] + [nllens, const] * (num_lenses - 1) + [nllens, constEnd]
# add elements to the lattice segment
sim.lattice.extend(nllens_lattice)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/iota_lens/input_iotalens.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.5
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 2.0e-3
beam.sigmaY = 2.0e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 3.0e-4
beam.sigmaPy = 3.0e-4
beam.sigmaPt = 0.0
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = const_end nllens foclens const_end
foclens.type = line
foclens.elements = const nllens
foclens.repeat = 17
nllens.type = nonlinear_lens
nllens.knll = 4.0e-6
nllens.cnll = 0.01
const_end.type = constf
const_end.ds = 0.05
const_end.kx = 1.0
const_end.ky = 1.0
const_end.kt = 1.0e-12
const.type = constf
const.ds = 0.1
const.kx = 1.0
const.ky = 1.0
const.kt = 1.0e-12
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.alpha = 0.0
diag.beta = 1.0
diag.tn = 0.4
diag.cn = 0.01
Analyze
We run the following script to analyze correctness:
Script analysis_iotalens.py
examples/iota_lens/analysis_iotalens.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import glob
import numpy as np
import pandas as pd
from scipy.stats import moment
def get_moments(beam):
"""Calculate mean and std dev of functions defining the IOTA invariants
Returns
-------
meanH, sigH, meanI, sigI
"""
meanH = np.mean(beam["H"])
sigH = moment(beam["H"], moment=2) ** 0.5
meanI = np.mean(beam["I"])
sigI = moment(beam["I"], moment=2) ** 0.5
return (meanH, sigH, meanI, sigI)
def read_all_files(file_pattern):
"""Read in all CSV files from each MPI rank (and potentially OpenMP
thread). Concatenate into one Pandas dataframe.
Returns
-------
pandas.DataFrame
"""
return pd.concat(
(
pd.read_csv(filename, delimiter=r"\s+")
for filename in glob.glob(file_pattern)
),
axis=0,
ignore_index=True,
).set_index("id")
# initial/final beam
initial = read_all_files("diags/nonlinear_lens_invariants_000000.*")
final = read_all_files("diags/nonlinear_lens_invariants_final.*")
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
meanH, sigH, meanI, sigI = get_moments(initial)
print(f" meanH={meanH:e} sigH={sigH:e} meanI={meanI:e} sigI={sigI:e}")
atol = 0.0 # a big number
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[meanH, sigH, meanI, sigI],
[4.122650e-02, 4.235181e-02, 7.356057e-02, 8.793753e-02],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
meanH, sigH, meanI, sigI = get_moments(final)
print(f" meanH={meanH:e} sigH={sigH:e} meanI={meanI:e} sigI={sigI:e}")
atol = 0.0 # a big number
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[meanH, sigH, meanI, sigI],
[4.122704e-02, 4.230576e-02, 7.348275e-02, 8.783157e-02],
rtol=rtol,
atol=atol,
)
# join tables on particle ID, so we can compare the same particle initial->final
beam_joined = final.join(initial, lsuffix="_final", rsuffix="_initial")
# add new columns: dH and dI
beam_joined["dH"] = (beam_joined["H_initial"] - beam_joined["H_final"]).abs()
beam_joined["dI"] = (beam_joined["I_initial"] - beam_joined["I_final"]).abs()
# print(beam_joined)
# particle-wise comparison of H & I initial to final
atol = 2.0e-3
rtol = 0.0 # large number
print()
print(f" atol={atol} (ignored: rtol~={rtol})")
print(f" dH_max={beam_joined['dH'].max()}")
assert np.allclose(beam_joined["dH"], 0.0, rtol=rtol, atol=atol)
atol = 3.0e-3
print(f" atol={atol} (ignored: rtol~={rtol})")
print(f" dI_max={beam_joined['dI'].max()}")
assert np.allclose(beam_joined["dI"], 0.0, rtol=rtol, atol=atol)
A nonlinear focusing channel based on the physical IOTA nonlinear magnet
A representation of the physical IOTA nonlinear magnetic element with realistic s-dependence, obtained using a sequence of nonlinear lenses and drifts equivalent to the use of a second-order symplectic integrator.
A thin linear lens is added at the exit of the nonlinear element, representing the ideal map associated with the remainder of the lattice.
We use a 2.5 MeV proton beam, corresponding to the nominal IOTA proton energy.
The two functions H (Hamiltonian) and I (the second invariant) are evaluated at the entrance to the nonlinear element, and then again after the thin lens (representing a single period). These values should be unchanged for all particles (to within acceptable tolerance).
In this test, the initial and final values of \(\mu_H\), \(\sigma_H\), \(\mu_I\), \(\sigma_I\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_iotalens_sdep.pyorImpactX executable using an input file:
impactx input_iotalens_sdep.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/iota_lens/run_iotalens_sdep.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import math
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# diagnostics: IOTA nonlinear lens invariants calculation
sim.set_diag_iota_invariants(
alpha=1.376381920471173, beta=1.892632003628881, tn=0.4, cn=0.01
)
# load a 2.5 MeV proton beam
kin_energy_MeV = 2.5 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.397456296195e-003,
sigmaY=1.397456296195e-003,
sigmaT=1.0e-4,
sigmaPx=1.256184325020e-003,
sigmaPy=1.256184325020e-003,
sigmaPt=0.0,
muxpx=0.8090169943749474,
muypy=0.8090169943749474,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
sim.lattice.append(monitor)
# defining parameters of the nonlinear lens
lens_length = 1.8
num_lenses = 18
tune_advance = 0.3
c_parameter = 0.01
t_strength = 0.4
ds = lens_length / num_lenses
# drift elements
ds_half = ds / 2.0
dr = elements.Drift(ds=ds_half)
# define the nonlinear lens segments
for j in range(0, num_lenses):
s = -lens_length / 2.0 + ds_half + j * ds
beta_star = lens_length / 2.0 * 1.0 / math.tan(math.pi * tune_advance)
beta = beta_star * (
1.0 + (2.0 * s * math.tan(math.pi * tune_advance) / lens_length) ** 2
)
knll_s = t_strength * c_parameter**2 * ds / beta
cnll_s = c_parameter * math.sqrt(beta)
nllens = elements.NonlinearLens(knll=knll_s, cnll=cnll_s)
segments = [dr, nllens, dr]
sim.lattice.extend(segments)
# focusing lens
const = elements.ConstF(
ds=1.0e-8, kx=12060.113295833, ky=12060.113295833, kt=1.0e-12, nslice=1
)
sim.lattice.append(const)
sim.lattice.append(monitor)
# number of periods
sim.periods = 1
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/iota_lens/input_iotalens_sdep.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.5
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
#beam.sigmaX = 2.0e-3
#beam.sigmaY = 2.0e-3
#beam.sigmaT = 1.0e-3
#beam.sigmaPx = 3.0e-4
#beam.sigmaPy = 3.0e-4
#beam.sigmaPt = 0.0
#beam.muxpx = 0.0
#beam.muypy = 0.0
#beam.mutpt = 0.0
beam.sigmaX = 1.397456296195e-003
beam.sigmaY = 1.397456296195e-003
beam.sigmaT = 1.0e-4
beam.sigmaPx = 1.256184325020e-003
beam.sigmaPy = 1.256184325020e-003
beam.sigmaPt = 0.0
beam.muxpx = 0.8090169943749474
beam.muypy = 0.8090169943749474
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor lens const monitor
lens.type = line
lens.elements = = dr_end nll1 dr nll2 dr nll3 dr nll4 dr nll5 dr nll6 \
dr nll7 dr nll8 dr nll9 dr nll9 dr nll8 dr nll7 \
dr nll6 dr nll5 dr nll4 dr nll3 dr nll2 dr nll1 \
dr_end
# Nonlinear lens segments
nll1.type = nonlinear_lens
nll1.knll = 2.2742558121e-6
nll1.cnll = 0.013262040169952
nll2.type = nonlinear_lens
nll2.knll = 2.641786366e-6
nll2.cnll = 0.012304986694423
nll3.type = nonlinear_lens
nll3.knll = 3.076868353e-6
nll3.cnll = 0.011401855643727
nll4.type = nonlinear_lens
nll4.knll = 3.582606522e-6
nll4.cnll = 0.010566482535866
nll5.type = nonlinear_lens
nll5.knll = 4.151211157e-6
nll5.cnll = 0.009816181575902
nll6.type = nonlinear_lens
nll6.knll = 4.754946985e-6
nll6.cnll = 0.0091718544892154
nll7.type = nonlinear_lens
nll7.knll = 5.337102374e-6
nll7.cnll = 0.008657195579489
nll8.type = nonlinear_lens
nll8.knll = 5.811437818e-6
nll8.cnll = 0.008296371635942
nll9.type = nonlinear_lens
nll9.knll = 6.081693334e-6
nll9.cnll = 0.008109941789663
dr.type = drift
dr.ds = 0.1
dr_end.type = drift
dr_end.ds = 0.05
# Focusing of the external lattice
const.type = constf
const.ds = 1.0e-8
const.kx = 12060.113295833
const.ky = 12060.113295833
const.kt = 1.0e-12
const.nslice = 1
# Beam Monitor: Diagnostics
monitor.type = beam_monitor
monitor.backend = h5
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.alpha = 1.376381920471173
diag.beta = 1.892632003628881
diag.tn = 0.4
diag.cn = 0.01
Analyze
We run the following script to analyze correctness:
Script analysis_iotalens_sdep.py
examples/iota_lens/analysis_iotalens_sdep.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import glob
import numpy as np
import pandas as pd
from scipy.stats import moment
def get_moments(beam):
"""Calculate mean and std dev of functions defining the IOTA invariants
Returns
-------
meanH, sigH, meanI, sigI
"""
meanH = np.mean(beam["H"])
sigH = moment(beam["H"], moment=2) ** 0.5
meanI = np.mean(beam["I"])
sigI = moment(beam["I"], moment=2) ** 0.5
return (meanH, sigH, meanI, sigI)
def read_all_files(file_pattern):
"""Read in all CSV files from each MPI rank (and potentially OpenMP
thread). Concatenate into one Pandas dataframe.
Returns
-------
pandas.DataFrame
"""
return pd.concat(
(
pd.read_csv(filename, delimiter=r"\s+")
for filename in glob.glob(file_pattern)
),
axis=0,
ignore_index=True,
).set_index("id")
# initial/final beam
initial = read_all_files("diags/nonlinear_lens_invariants_000000.*")
final = read_all_files("diags/nonlinear_lens_invariants_final.*")
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
meanH, sigH, meanI, sigI = get_moments(initial)
print(f" meanH={meanH:e} sigH={sigH:e} meanI={meanI:e} sigI={sigI:e}")
atol = 0.0 # a big number
rtol = 3.0 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[meanH, sigH, meanI, sigI],
# [5.993291e-02, 3.426664e-02, 8.513875e-02, 7.022481e-02],
[6.016450e-02, 3.502064e-02, 8.560226e-02, 7.148169e-02],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
meanH, sigH, meanI, sigI = get_moments(final)
print(f" meanH={meanH:e} sigH={sigH:e} meanI={meanI:e} sigI={sigI:e}")
atol = 0.0 # a big number
rtol = 3.0 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[meanH, sigH, meanI, sigI],
# [5.993291e-02, 3.426664e-02, 8.513875e-02, 7.022481e-02],
[6.016450e-02, 3.502064e-02, 8.560226e-02, 7.148169e-02],
rtol=rtol,
atol=atol,
)
# join tables on particle ID, so we can compare the same particle initial->final
beam_joined = final.join(initial, lsuffix="_final", rsuffix="_initial")
# add new columns: dH and dI
beam_joined["dH"] = (beam_joined["H_initial"] - beam_joined["H_final"]).abs()
beam_joined["dI"] = (beam_joined["I_initial"] - beam_joined["I_final"]).abs()
# print(beam_joined)
# particle-wise comparison of H & I initial to final
Hrms = np.sqrt(sigH**2 + meanH**2)
Irms = np.sqrt(sigI**2 + meanI**2)
atol = 2.5e-3 * Hrms
rtol = 0.0 # large number
print()
print(f" atol={atol} (ignored: rtol~={rtol})")
print(f" dH_max={beam_joined['dH'].max()}")
assert np.allclose(beam_joined["dH"], 0.0, rtol=rtol, atol=atol)
atol = 3.5e-3 * Irms
rtol = 0.0
print()
print(f" atol={atol} (ignored: rtol~={rtol})")
print(f" dI_max={beam_joined['dI'].max()}")
assert np.allclose(beam_joined["dI"], 0.0, rtol=rtol, atol=atol)
The “bare” linear lattice of the Fermilab IOTA storage ring
The linear lattice of the IOTA storage ring, configured for operation with a 2.5 MeV proton beam.
The drift regions available for insertion of the special nonlinear magnetic element for integrable optics experiments are denoted dnll.
The second moments of the particle distribution after a single turn should coincide with the initial section moments of the particle distribution, to within the level expected due to numerical particle noise. The example runs 5 turns.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_iotalattice.pyorImpactX executable using an input file:
impactx input_iotalattice.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/iota_lattice/run_iotalattice.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Chad Mitchell, Axel Huebl
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# init particle beam
kin_energy_MeV = 2.5
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.588960728035e-3,
sigmaY=2.496625268437e-3,
sigmaT=1.0e-3,
sigmaPx=2.8320397837724e-3,
sigmaPy=1.802433091137e-3,
sigmaPt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# init accelerator lattice
ns = 10 # number of slices per ds in the element
# Drift elements
dra1 = elements.Drift(ds=0.9125, nslice=ns)
dra2 = elements.Drift(ds=0.135, nslice=ns)
dra3 = elements.Drift(ds=0.725, nslice=ns)
dra4 = elements.Drift(ds=0.145, nslice=ns)
dra5 = elements.Drift(ds=0.3405, nslice=ns)
drb1 = elements.Drift(ds=0.3205, nslice=ns)
drb2 = elements.Drift(ds=0.14, nslice=ns)
drb3 = elements.Drift(ds=0.1525, nslice=ns)
drb4 = elements.Drift(ds=0.31437095, nslice=ns)
drc1 = elements.Drift(ds=0.42437095, nslice=ns)
drc2 = elements.Drift(ds=0.355, nslice=ns)
dnll = elements.Drift(ds=1.8, nslice=ns)
drd1 = elements.Drift(ds=0.62437095, nslice=ns)
drd2 = elements.Drift(ds=0.42, nslice=ns)
drd3 = elements.Drift(ds=1.625, nslice=ns)
drd4 = elements.Drift(ds=0.6305, nslice=ns)
dre1 = elements.Drift(ds=0.5305, nslice=ns)
dre2 = elements.Drift(ds=1.235, nslice=ns)
dre3 = elements.Drift(ds=0.8075, nslice=ns)
# Bend elements
rc30 = 0.822230996255981
sbend30 = elements.Sbend(ds=0.4305191429, rc=rc30)
edge30 = elements.DipEdge(psi=0.0, rc=rc30, g=0.058, K2=0.5)
rc60 = 0.772821121503940
sbend60 = elements.Sbend(ds=0.8092963858, rc=rc60)
edge60 = elements.DipEdge(psi=0.0, rc=rc60, g=0.058, K2=0.5)
# Quad elements
ds_quad = 0.21
qa1 = elements.Quad(ds=ds_quad, k=-8.78017699, nslice=ns)
qa2 = elements.Quad(ds=ds_quad, k=13.24451745, nslice=ns)
qa3 = elements.Quad(ds=ds_quad, k=-13.65151327, nslice=ns)
qa4 = elements.Quad(ds=ds_quad, k=19.75138652, nslice=ns)
qb1 = elements.Quad(ds=ds_quad, k=-10.84199727, nslice=ns)
qb2 = elements.Quad(ds=ds_quad, k=16.24844348, nslice=ns)
qb3 = elements.Quad(ds=ds_quad, k=-8.27411104, nslice=ns)
qb4 = elements.Quad(ds=ds_quad, k=-7.45719247, nslice=ns)
qb5 = elements.Quad(ds=ds_quad, k=14.03362243, nslice=ns)
qb6 = elements.Quad(ds=ds_quad, k=-12.23595641, nslice=ns)
qc1 = elements.Quad(ds=ds_quad, k=-13.18863768, nslice=ns)
qc2 = elements.Quad(ds=ds_quad, k=11.50601829, nslice=ns)
qc3 = elements.Quad(ds=ds_quad, k=-11.10445869, nslice=ns)
qd1 = elements.Quad(ds=ds_quad, k=-6.78179218, nslice=ns)
qd2 = elements.Quad(ds=ds_quad, k=5.19026998, nslice=ns)
qd3 = elements.Quad(ds=ds_quad, k=-5.8586173, nslice=ns)
qd4 = elements.Quad(ds=ds_quad, k=4.62460039, nslice=ns)
qe1 = elements.Quad(ds=ds_quad, k=-4.49607687, nslice=ns)
qe2 = elements.Quad(ds=ds_quad, k=6.66737146, nslice=ns)
qe3 = elements.Quad(ds=ds_quad, k=-6.69148177, nslice=ns)
# build lattice: first half, qe3, then mirror
# fmt: off
lattice_half = [
dra1, qa1, dra2, qa2, dra3, qa3, dra4, qa4, dra5,
edge30, sbend30, edge30, drb1, qb1, drb2, qb2, drb2, qb3,
drb3, dnll, drb3, qb4, drb2, qb5, drb2, qb6, drb4,
edge60, sbend60, edge60, drc1, qc1, drc2, qc2, drc2, qc3, drc1,
edge60, sbend60, edge60, drd1, qd1, drd2, qd2, drd3, qd3, drd2, qd4, drd4,
edge30, sbend30, edge30, dre1, qe1, dre2, qe2, dre3
]
# fmt:on
sim.lattice.append(monitor)
sim.lattice.extend(lattice_half)
sim.lattice.append(qe3)
lattice_half.reverse()
sim.lattice.extend(lattice_half)
sim.lattice.append(monitor)
# number of turns in the ring
sim.periods = 5
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/iota_lattice/input_iotalattice.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.5
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.588960728035e-3
beam.sigmaY = 2.496625268437e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 2.8320397837724e-3
beam.sigmaPy = 1.802433091137e-3
beam.sigmaPt = 0.0
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.periods = 5
lattice.elements = monitor first_half qe3 second_half monitor
# lines
first_half.type = line
first_half.elements = dra1 qa1 dra2 qa2 dra3 qa3 dra4 qa4 dra5 \
edge30 sbend30 edge30 drb1 qb1 drb2 qb2 drb2 qb3 \
drb3 dnll drb3 qb4 drb2 qb5 drb2 qb6 drb4 \
edge60 sbend60 edge60 drc1 qc1 drc2 qc2 drc2 qc3 drc1 \
edge60 sbend60 edge60 drd1 qd1 drd2 qd2 drd3 qd3 drd2 qd4 drd4 \
edge30 sbend30 edge30 dre1 qe1 dre2 qe2 dre3
second_half.type = line
second_half.reverse = true
second_half.elements = dra1 qa1 dra2 qa2 dra3 qa3 dra4 qa4 dra5 \
edge30 sbend30 edge30 drb1 qb1 drb2 qb2 drb2 qb3 \
drb3 dnll drb3 qb4 drb2 qb5 drb2 qb6 drb4 \
edge60 sbend60 edge60 drc1 qc1 drc2 qc2 drc2 qc3 drc1 \
edge60 sbend60 edge60 drd1 qd1 drd2 qd2 drd3 qd3 drd2 qd4 drd4 \
edge30 sbend30 edge30 dre1 qe1 dre2 qe2 dre3
# thick element splitting for space charge
lattice.nslice = 10
# Drift elements:
dra1.type = drift
dra1.ds = 0.9125
dra2.type = drift
dra2.ds = 0.135
dra3.type = drift
dra3.ds = 0.725
dra4.type = drift
dra4.ds = 0.145
dra5.type = drift
dra5.ds = 0.3405
drb1.type = drift
drb1.ds = 0.3205
drb2.type = drift
drb2.ds = 0.14
drb3.type = drift
drb3.ds = 0.1525
drb4.type = drift
drb4.ds = 0.31437095
drc1.type = drift
drc1.ds = 0.42437095
drc2.type = drift
drc2.ds = 0.355
dnll.type = drift
dnll.ds = 1.8
drd1.type = drift
drd1.ds = 0.62437095
drd2.type = drift
drd2.ds = 0.42
drd3.type = drift
drd3.ds = 1.625
drd4.type = drift
drd4.ds = 0.6305
dre1.type = drift
dre1.ds = 0.5305
dre2.type = drift
dre2.ds = 1.235
dre3.type = drift
dre3.ds = 0.8075
# Bend elements:
sbend30.type = sbend
sbend30.ds = 0.4305191429
sbend30.rc = 0.822230996255981
edge30.type = dipedge
edge30.psi = 0.0
edge30.rc = 0.822230996255981
edge30.g = 0.058
edge30.K2 = 0.5
sbend60.type = sbend
sbend60.ds = 0.8092963858
sbend60.rc = 0.772821121503940
edge60.type = dipedge
edge60.psi = 0.0
edge60.rc = 0.772821121503940
edge60.g = 0.058
edge60.K2 = 0.5
# Quad elements:
qa1.type = quad
qa1.ds = 0.21
qa1.k = -8.78017699
qa2.type = quad
qa2.ds = 0.21
qa2.k = 13.24451745
qa3.type = quad
qa3.ds = 0.21
qa3.k = -13.65151327
qa4.type = quad
qa4.ds = 0.21
qa4.k = 19.75138652
qb1.type = quad
qb1.ds = 0.21
qb1.k = -10.84199727
qb2.type = quad
qb2.ds = 0.21
qb2.k = 16.24844348
qb3.type = quad
qb3.ds = 0.21
qb3.k = -8.27411104
qb4.type = quad
qb4.ds = 0.21
qb4.k = -7.45719247
qb5.type = quad
qb5.ds = 0.21
qb5.k = 14.03362243
qb6.type = quad
qb6.ds = 0.21
qb6.k = -12.23595641
qc1.type = quad
qc1.ds = 0.21
qc1.k = -13.18863768
qc2.type = quad
qc2.ds = 0.21
qc2.k = 11.50601829
qc3.type = quad
qc3.ds = 0.21
qc3.k = -11.10445869
qd1.type = quad
qd1.ds = 0.21
qd1.k = -6.78179218
qd2.type = quad
qd2.ds = 0.21
qd2.k = 5.19026998
qd3.type = quad
qd3.ds = 0.21
qd3.k = -5.8586173
qd4.type = quad
qd4.ds = 0.21
qd4.k = 4.62460039
qe1.type = quad
qe1.ds = 0.21
qe1.k = -4.49607687
qe2.type = quad
qe2.ds = 0.21
qe2.k = 6.66737146
qe3.type = quad
qe3.ds = 0.21
qe3.k = -6.69148177
# Beam Monitor: Diagnostics
monitor.type = beam_monitor
monitor.backend = h5
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
Analyze
We run the following script to analyze correctness:
Script analysis_iotalattice.py
examples/iota_lattice/analysis_iotalattice.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # a big number
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[1.595934e-03, 2.507263e-03, 9.977588e-04, 4.490896e-06, 4.539378e-06, 0.000000e00],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # a big number
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, emittance_x, emittance_y, emittance_t],
[
1.579848e-03,
2.510900e-03,
4.490897e-06,
4.539378e-06,
0.0,
],
rtol=rtol,
atol=atol,
)
The full nonlinear lattice of the Fermilab IOTA storage ring
The full nonlinear lattice of the IOTA storage ring, configured for operation with a 2.5 MeV proton beam.
The special nonlinear magnetic element for integrable optics experiments is denoted nll. To simplify analysis,
the lattice has been arranged so that nll appears as the first element in the sequence.
The two functions H (Hamiltonian) and I (the second invariant) are evaluated at the entrance to the nonlinear element. These values should be unchanged for all particles (to within acceptable tolerance), over the specified number of periods (default 5).
In this test, the initial and final values of \(\mu_H\), \(\sigma_H\), \(\mu_I\), \(\sigma_I\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_iotalattice_sdep.pyorImpactX executable using an input file:
impactx input_iotalattice_sdep.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/iota_lattice/run_iotalattice_sdep.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Chad Mitchell, Axel Huebl
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import math
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# diagnostics: IOTA nonlinear lens invariants calculation
sim.set_diag_iota_invariants(
alpha=1.376381920471173, beta=1.892632003628881, tn=0.4, cn=0.01
)
# init particle beam
energy_MeV = 2.5
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.865379469388e-003,
sigmaY=2.0192133150418e-003,
sigmaT=1.0e-3,
sigmaPx=1.402566720991e-003,
sigmaPy=9.57593913381e-004,
sigmaPt=0.0,
muxpx=0.482260919078473,
muypy=0.762127656873158,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# init accelerator lattice
ns = 10 # number of slices per ds in the element
# Drift elements
dra1 = elements.Drift(ds=0.9125, nslice=ns)
dra2 = elements.Drift(ds=0.135, nslice=ns)
dra3 = elements.Drift(ds=0.725, nslice=ns)
dra4 = elements.Drift(ds=0.145, nslice=ns)
dra5 = elements.Drift(ds=0.3405, nslice=ns)
drb1 = elements.Drift(ds=0.3205, nslice=ns)
drb2 = elements.Drift(ds=0.14, nslice=ns)
drb3 = elements.Drift(ds=0.1525, nslice=ns)
drb4 = elements.Drift(ds=0.31437095, nslice=ns)
drc1 = elements.Drift(ds=0.42437095, nslice=ns)
drc2 = elements.Drift(ds=0.355, nslice=ns)
dnll = elements.Drift(ds=1.8, nslice=ns)
drd1 = elements.Drift(ds=0.62437095, nslice=ns)
drd2 = elements.Drift(ds=0.42, nslice=ns)
drd3 = elements.Drift(ds=1.625, nslice=ns)
drd4 = elements.Drift(ds=0.6305, nslice=ns)
dre1 = elements.Drift(ds=0.5305, nslice=ns)
dre2 = elements.Drift(ds=1.235, nslice=ns)
dre3 = elements.Drift(ds=0.8075, nslice=ns)
# Bend elements
rc30 = 0.822230996255981
sbend30 = elements.Sbend(ds=0.4305191429, rc=rc30)
edge30 = elements.DipEdge(psi=0.0, rc=rc30, g=0.058, K2=0.5)
rc60 = 0.772821121503940
sbend60 = elements.Sbend(ds=0.8092963858, rc=rc60)
edge60 = elements.DipEdge(psi=0.0, rc=rc60, g=0.058, K2=0.5)
# Quad elements
ds_quad = 0.21
qa1 = elements.Quad(ds=ds_quad, k=-8.78017699, nslice=ns)
qa2 = elements.Quad(ds=ds_quad, k=13.24451745, nslice=ns)
qa3 = elements.Quad(ds=ds_quad, k=-13.65151327, nslice=ns)
qa4 = elements.Quad(ds=ds_quad, k=19.75138652, nslice=ns)
qb1 = elements.Quad(ds=ds_quad, k=-10.84199727, nslice=ns)
qb2 = elements.Quad(ds=ds_quad, k=16.24844348, nslice=ns)
qb3 = elements.Quad(ds=ds_quad, k=-8.27411104, nslice=ns)
qb4 = elements.Quad(ds=ds_quad, k=-7.45719247, nslice=ns)
qb5 = elements.Quad(ds=ds_quad, k=14.03362243, nslice=ns)
qb6 = elements.Quad(ds=ds_quad, k=-12.23595641, nslice=ns)
qc1 = elements.Quad(ds=ds_quad, k=-13.18863768, nslice=ns)
qc2 = elements.Quad(ds=ds_quad, k=11.50601829, nslice=ns)
qc3 = elements.Quad(ds=ds_quad, k=-11.10445869, nslice=ns)
qd1 = elements.Quad(ds=ds_quad, k=-6.78179218, nslice=ns)
qd2 = elements.Quad(ds=ds_quad, k=5.19026998, nslice=ns)
qd3 = elements.Quad(ds=ds_quad, k=-5.8586173, nslice=ns)
qd4 = elements.Quad(ds=ds_quad, k=4.62460039, nslice=ns)
qe1 = elements.Quad(ds=ds_quad, k=-4.49607687, nslice=ns)
qe2 = elements.Quad(ds=ds_quad, k=6.66737146, nslice=ns)
qe3 = elements.Quad(ds=ds_quad, k=-6.69148177, nslice=ns)
# Special (elliptic) nonlinear element:
# set basic parameters of the nonlinear element
lens_length = 1.8
num_lenses = 18
tune_advance = 0.3
c_parameter = 0.01
t_strength = 0.4
ds = lens_length / num_lenses
# build up the nonlinear lens in segments
ds_half = ds / 2.0
dr = elements.Drift(ds=ds_half, nslice=1)
nll = []
for j in range(0, num_lenses):
s = -lens_length / 2.0 + ds_half + j * ds
beta_star = lens_length / 2.0 * 1.0 / math.tan(math.pi * tune_advance)
beta = beta_star * (
1.0 + (2.0 * s * math.tan(math.pi * tune_advance) / lens_length) ** 2
)
knll_s = t_strength * c_parameter**2 * ds / beta
cnll_s = c_parameter * math.sqrt(beta)
nllens = elements.NonlinearLens(knll=knll_s, cnll=cnll_s)
segment = [dr, nllens, dr]
nll.extend(segment)
lattice_before_nll = [
dra1,
qa1,
dra2,
qa2,
dra3,
qa3,
dra4,
qa4,
dra5,
edge30,
sbend30,
edge30,
drb1,
qb1,
drb2,
qb2,
drb2,
qb3,
drb3,
]
lattice_after_nll = [
drb3,
qb4,
drb2,
qb5,
drb2,
qb6,
drb4,
edge60,
sbend60,
edge60,
drc1,
qc1,
drc2,
qc2,
drc2,
qc3,
drc1,
edge60,
sbend60,
edge60,
drd1,
qd1,
drd2,
qd2,
drd3,
qd3,
drd2,
qd4,
drd4,
edge30,
sbend30,
edge30,
dre1,
qe1,
dre2,
qe2,
dre3,
]
# build lattice: first half, qe3, then mirror
# modified to place nll as the first element
# fmt:on
sim.lattice.append(monitor)
sim.lattice.extend(nll)
sim.lattice.extend(lattice_after_nll)
sim.lattice.append(qe3)
lattice_after_nll.reverse()
sim.lattice.extend(lattice_after_nll)
sim.lattice.append(dnll)
lattice_before_nll.reverse()
sim.lattice.extend(lattice_before_nll)
lattice_before_nll.reverse()
sim.lattice.extend(lattice_before_nll)
sim.lattice.append(monitor)
# number of turns in the ring
sim.periods = 5
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/iota_lattice/input_iotalattice_sdep.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.5
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.865379469388e-003
beam.sigmaY = 2.0192133150418e-003
beam.sigmaT = 1.0e-3
beam.sigmaPx = 1.402566720991e-003
beam.sigmaPy = 9.57593913381e-004
beam.sigmaPt = 0.0
beam.muxpx = 0.482260919078473
beam.muypy = 0.762127656873158
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.periods = 5
lattice.elements = monitor nll after_nll qe3 after_nll_rev dnll before_nll_rev \
before_nll monitor
# lines
before_nll.type = line
before_nll.elements = dra1 qa1 dra2 qa2 dra3 qa3 dra4 qa4 dra5 \
edge30 sbend30 edge30 drb1 qb1 drb2 qb2 drb2 qb3 \
drb3
after_nll.type = line
after_nll.elements = drb3 qb4 drb2 qb5 drb2 qb6 drb4 \
edge60 sbend60 edge60 drc1 qc1 drc2 qc2 drc2 qc3 drc1 \
edge60 sbend60 edge60 drd1 qd1 drd2 qd2 drd3 qd3 drd2 qd4 drd4 \
edge30 sbend30 edge30 dre1 qe1 dre2 qe2 dre3
before_nll_rev.type = line
before_nll_rev.reverse = true
before_nll_rev.elements = dra1 qa1 dra2 qa2 dra3 qa3 dra4 qa4 dra5 \
edge30 sbend30 edge30 drb1 qb1 drb2 qb2 drb2 qb3 \
drb3
after_nll_rev.type = line
after_nll_rev.reverse = true
after_nll_rev.elements = drb3 qb4 drb2 qb5 drb2 qb6 drb4 \
edge60 sbend60 edge60 drc1 qc1 drc2 qc2 drc2 qc3 drc1 \
edge60 sbend60 edge60 drd1 qd1 drd2 qd2 drd3 qd3 drd2 qd4 drd4 \
edge30 sbend30 edge30 dre1 qe1 dre2 qe2 dre3
nll.type = line
nll.elements = = dr_end nll1 dr nll2 dr nll3 dr nll4 dr nll5 dr nll6 \
dr nll7 dr nll8 dr nll9 dr nll9 dr nll8 dr nll7 \
dr nll6 dr nll5 dr nll4 dr nll3 dr nll2 dr nll1 \
dr_end
# thick element splitting for space charge
lattice.nslice = 10
# Nonlinear lens segments
nll1.type = nonlinear_lens
nll1.knll = 2.2742558121e-6
nll1.cnll = 0.013262040169952
nll2.type = nonlinear_lens
nll2.knll = 2.641786366e-6
nll2.cnll = 0.012304986694423
nll3.type = nonlinear_lens
nll3.knll = 3.076868353e-6
nll3.cnll = 0.011401855643727
nll4.type = nonlinear_lens
nll4.knll = 3.582606522e-6
nll4.cnll = 0.010566482535866
nll5.type = nonlinear_lens
nll5.knll = 4.151211157e-6
nll5.cnll = 0.009816181575902
nll6.type = nonlinear_lens
nll6.knll = 4.754946985e-6
nll6.cnll = 0.0091718544892154
nll7.type = nonlinear_lens
nll7.knll = 5.337102374e-6
nll7.cnll = 0.008657195579489
nll8.type = nonlinear_lens
nll8.knll = 5.811437818e-6
nll8.cnll = 0.008296371635942
nll9.type = nonlinear_lens
nll9.knll = 6.081693334e-6
nll9.cnll = 0.008109941789663
# Drift elements:
dr.type = drift
dr.ds = 0.1
dr_end.type = drift
dr_end.ds = 0.05
dra1.type = drift
dra1.ds = 0.9125
dra2.type = drift
dra2.ds = 0.135
dra3.type = drift
dra3.ds = 0.725
dra4.type = drift
dra4.ds = 0.145
dra5.type = drift
dra5.ds = 0.3405
drb1.type = drift
drb1.ds = 0.3205
drb2.type = drift
drb2.ds = 0.14
drb3.type = drift
drb3.ds = 0.1525
drb4.type = drift
drb4.ds = 0.31437095
drc1.type = drift
drc1.ds = 0.42437095
drc2.type = drift
drc2.ds = 0.355
dnll.type = drift
dnll.ds = 1.8
drd1.type = drift
drd1.ds = 0.62437095
drd2.type = drift
drd2.ds = 0.42
drd3.type = drift
drd3.ds = 1.625
drd4.type = drift
drd4.ds = 0.6305
dre1.type = drift
dre1.ds = 0.5305
dre2.type = drift
dre2.ds = 1.235
dre3.type = drift
dre3.ds = 0.8075
# Bend elements:
sbend30.type = sbend
sbend30.ds = 0.4305191429
sbend30.rc = 0.822230996255981
edge30.type = dipedge
edge30.psi = 0.0
edge30.rc = 0.822230996255981
edge30.g = 0.058
edge30.K2 = 0.5
sbend60.type = sbend
sbend60.ds = 0.8092963858
sbend60.rc = 0.772821121503940
edge60.type = dipedge
edge60.psi = 0.0
edge60.rc = 0.772821121503940
edge60.g = 0.058
edge60.K2 = 0.5
# Quad elements:
qa1.type = quad
qa1.ds = 0.21
qa1.k = -8.78017699
qa2.type = quad
qa2.ds = 0.21
qa2.k = 13.24451745
qa3.type = quad
qa3.ds = 0.21
qa3.k = -13.65151327
qa4.type = quad
qa4.ds = 0.21
qa4.k = 19.75138652
qb1.type = quad
qb1.ds = 0.21
qb1.k = -10.84199727
qb2.type = quad
qb2.ds = 0.21
qb2.k = 16.24844348
qb3.type = quad
qb3.ds = 0.21
qb3.k = -8.27411104
qb4.type = quad
qb4.ds = 0.21
qb4.k = -7.45719247
qb5.type = quad
qb5.ds = 0.21
qb5.k = 14.03362243
qb6.type = quad
qb6.ds = 0.21
qb6.k = -12.23595641
qc1.type = quad
qc1.ds = 0.21
qc1.k = -13.18863768
qc2.type = quad
qc2.ds = 0.21
qc2.k = 11.50601829
qc3.type = quad
qc3.ds = 0.21
qc3.k = -11.10445869
qd1.type = quad
qd1.ds = 0.21
qd1.k = -6.78179218
qd2.type = quad
qd2.ds = 0.21
qd2.k = 5.19026998
qd3.type = quad
qd3.ds = 0.21
qd3.k = -5.8586173
qd4.type = quad
qd4.ds = 0.21
qd4.k = 4.62460039
qe1.type = quad
qe1.ds = 0.21
qe1.k = -4.49607687
qe2.type = quad
qe2.ds = 0.21
qe2.k = 6.66737146
qe3.type = quad
qe3.ds = 0.21
qe3.k = -6.69148177
# Beam Monitor: Diagnostics
monitor.type = beam_monitor
monitor.backend = h5
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
diag.alpha = 1.376381920471173
diag.beta = 1.892632003628881
diag.tn = 0.4
diag.cn = 0.01
Analyze
We run the following script to analyze correctness:
Script analysis_iotalattice_sdep.py
examples/iota_lattice/analysis_iotalattice_sdep.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import glob
import numpy as np
import pandas as pd
from scipy.stats import moment
def get_moments(beam):
"""Calculate mean and std dev of functions defining the IOTA invariants
Returns
-------
meanH, sigH, meanI, sigI
"""
meanH = np.mean(beam["H"])
sigH = moment(beam["H"], moment=2) ** 0.5
meanI = np.mean(beam["I"])
sigI = moment(beam["I"], moment=2) ** 0.5
return (meanH, sigH, meanI, sigI)
def read_all_files(file_pattern):
"""Read in all CSV files from each MPI rank (and potentially OpenMP
thread). Concatenate into one Pandas dataframe.
Returns
-------
pandas.DataFrame
"""
return pd.concat(
(
pd.read_csv(filename, delimiter=r"\s+")
for filename in glob.glob(file_pattern)
),
axis=0,
ignore_index=True,
).set_index("id")
# initial/final beam
initial = read_all_files("diags/nonlinear_lens_invariants_000000.*")
final = read_all_files("diags/nonlinear_lens_invariants_final.*")
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
meanH, sigH, meanI, sigI = get_moments(initial)
print(f" meanH={meanH:e} sigH={sigH:e} meanI={meanI:e} sigI={sigI:e}")
atol = 0.0 # a big number
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[meanH, sigH, meanI, sigI],
[7.263202e-02, 4.454371e-02, 9.288060e-02, 8.211506e-02],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
meanH, sigH, meanI, sigI = get_moments(final)
print(f" meanH={meanH:e} sigH={sigH:e} meanI={meanI:e} sigI={sigI:e}")
atol = 0.0 # a big number
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[meanH, sigH, meanI, sigI],
[7.263202e-02, 4.454371e-02, 9.288060e-02, 8.211506e-02],
rtol=rtol,
atol=atol,
)
# join tables on particle ID, so we can compare the same particle initial->final
beam_joined = final.join(initial, lsuffix="_final", rsuffix="_initial")
# add new columns: dH and dI
beam_joined["dH"] = (beam_joined["H_initial"] - beam_joined["H_final"]).abs()
beam_joined["dI"] = (beam_joined["I_initial"] - beam_joined["I_final"]).abs()
# print(beam_joined)
# particle-wise comparison of H & I initial to final
Hrms = np.sqrt(sigH**2 + meanH**2)
Irms = np.sqrt(sigI**2 + meanI**2)
atol = 4.0e-3 * Hrms
rtol = 0.0 # large number
print()
print(f" atol={atol} (ignored: rtol~={rtol})")
print(f" dH_max={beam_joined['dH'].max()}")
assert np.allclose(beam_joined["dH"], 0.0, rtol=rtol, atol=atol)
atol = 5.5e-3 * Irms
rtol = 0.0
print()
print(f" atol={atol} (ignored: rtol~={rtol})")
print(f" dI_max={beam_joined['dI'].max()}")
assert np.allclose(beam_joined["dI"], 0.0, rtol=rtol, atol=atol)
Solenoid channel
Proton beam undergoing 90 deg X-Y rotation in an ideal solenoid channel.
The matched Twiss parameters at entry are:
\(\beta_\mathrm{x} = 2.4321374875\) m
\(\alpha_\mathrm{x} = 0.0\)
\(\beta_\mathrm{y} = 2.4321374875\) m
\(\alpha_\mathrm{y} = 0.0\)
We use a 250 MeV proton beam with initial unnormalized rms emittance of 1 micron in the horizontal plane, and 2 micron in the vertical plane.
The solenoid magnetic field corresponds to B = 2 T.
The second moments of the particle distribution after the solenoid channel are rotated by 90 degrees: the final horizontal moments should coincide with the initial vertical moments, and vice-versa, to within the level expected due to noise due to statistical sampling.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_solenoid.pyorImpactX executable using an input file:
impactx input_solenoid.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/solenoid/run_solenoid.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Marco Garten, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 250 MeV proton beam with an initial
# horizontal rms emittance of 1 um and an
# initial vertical rms emittance of 2 um
kin_energy_MeV = 250.0 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.559531175539e-3,
sigmaY=2.205510139392e-3,
sigmaT=1.0e-3,
sigmaPx=6.41218345413e-4,
sigmaPy=9.06819680526e-4,
sigmaPt=1.0e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
sim.lattice.extend(
[
monitor,
elements.Sol(ds=3.820395, ks=0.8223219329893234),
monitor,
]
)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/solenoid/input_solenoid.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 250.0
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.559531175539e-3
beam.sigmaY = 2.205510139392e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 6.41218345413e-4
beam.sigmaPy = 9.06819680526e-4
beam.sigmaPt = 1.0e-3
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor sol1 monitor
lattice.nslice = 1
monitor.type = beam_monitor
monitor.backend = h5
sol1.type = solenoid
sol1.ds = 3.820395
sol1.ks = 0.8223219329893234
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
Analyze
We run the following script to analyze correctness:
Script analysis_solenoid.py
examples/solenoid/analysis_solenoid.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.559531175539e-3,
2.205510139392e-3,
1.0e-3,
1.0e-6,
2.0e-6,
1.0e-6,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
2.205510139392e-3,
1.559531175539e-3,
6.404930308742e-3,
2.0e-6,
1.0e-6,
1.0e-6,
],
rtol=rtol,
atol=atol,
)
Drift using a Pole-Face Rotation
A drift that takes place in a rotated frame, using initial and final
applications of a pole rotation (prot).
We use a 2 GeV electron beam.
The second moments of x, y, and t should be nearly unchanged.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_rotation.pyorImpactX executable using an input file:
impactx input_rotation.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/rotation/run_rotation.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV electron beam with an initial
# unnormalized rms emittance of nm
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used without space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=4.0e-3,
sigmaY=4.0e-3,
sigmaT=1.0e-3,
sigmaPx=3.0e-4,
sigmaPy=3.0e-4,
sigmaPt=2.0e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
rotated_drift = [
monitor,
elements.PRot(phi_in=0.0, phi_out=-5.0),
elements.Drift(ds=2.0, nslice=1),
elements.PRot(phi_in=-5.0, phi_out=0.0),
monitor,
]
# assign a lattice segment
sim.lattice.extend(rotated_drift)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/rotation/input_rotation.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 4.0e-3
beam.sigmaY = 4.0e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 3.0e-4
beam.sigmaPy = 3.0e-4
beam.sigmaPt = 2.0e-3
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor rotation1 drift1 rotation2 monitor
monitor.type = beam_monitor
monitor.backend = h5
drift1.type = drift
drift1.ds = 2.0
rotation1.type = prot
rotation1.phi_in = 0.0
rotation1.phi_out = -5.0
rotation2.type = prot
rotation2.phi_in = -5.0
rotation2.phi_out = 0.0
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
Analyze
We run the following script to analyze correctness:
Script analysis_rotation.py
examples/rotation/analysis_rotation.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.0e-03,
4.0e-03,
1.0e-03,
1.2e-06,
1.2e-06,
2.0e-06,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.5 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.061349e-03,
4.042332e-03,
1.002804e-03,
1.2e-06,
1.2e-06,
2.0e-06,
],
rtol=rtol,
atol=atol,
)
Soft-edge solenoid
Proton beam propagating through a 6 m region containing a soft-edge solenoid.
The solenoid model used is the default thin-shell model described in: P. Granum et al, “Efficient calculations of magnetic fields of solenoids for simulations,” NIMA 1034, 166706 (2022) DOI:10.1016/j.nima.2022.166706
The solenoid is a cylindrical current sheet with a length of 1 m and a radius of 0.1667 m, corresponding to an aspect ratio diameter/length = 1/3. The peak magnetic field on-axis is 3 T.
We use a 250 MeV proton beam with initial unnormalized rms emittance of 1 micron in the horizontal plane, and 2 micron in the vertical plane.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_solenoid_softedge.pyorImpactX executable using an input file:
impactx input_solenoid_softedge.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/solenoid_softedge/run_solenoid_softedge.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Chad Mitchell, Axel Huebl
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = False
# domain decomposition & space charge mesh
sim.init_grids()
# load a 250 MeV proton beam with an initial
# horizontal rms emittance of 1 um and an
# initial vertical rms emittance of 2 um
kin_energy_MeV = 250.0 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.559531175539e-3,
sigmaY=2.205510139392e-3,
sigmaT=1.0e-3,
sigmaPx=6.41218345413e-4,
sigmaPy=9.06819680526e-4,
sigmaPt=1.0e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# design the accelerator lattice
sol = elements.SoftSolenoid(
ds=6.0,
bscale=1.233482899483985,
cos_coefficients=[
0.350807812299706,
0.323554693720069,
0.260320578919415,
0.182848575294969,
0.106921016050403,
4.409581845710694e-002,
-9.416427163897508e-006,
-2.459452716865687e-002,
-3.272762575737291e-002,
-2.936414401076162e-002,
-1.995780078926890e-002,
-9.102893342953847e-003,
-2.456410658713271e-006,
5.788233017324325e-003,
8.040408292420691e-003,
7.480064552867431e-003,
5.230254569468851e-003,
2.447614547094685e-003,
-1.095525090532255e-006,
-1.614586867387170e-003,
-2.281365457438345e-003,
-2.148709081338292e-003,
-1.522541739363011e-003,
-7.185505862719508e-004,
-6.171194824600157e-007,
4.842109305036943e-004,
6.874508102002901e-004,
6.535550288205728e-004,
4.648795813759210e-004,
2.216564722797528e-004,
-4.100982995210341e-007,
-1.499332112463395e-004,
-2.151538438342482e-004,
-2.044590946652016e-004,
-1.468242784844341e-004,
],
sin_coefficients=[
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
],
mapsteps=200,
nslice=4,
)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
sim.lattice.extend(
[
monitor,
sol,
monitor,
]
)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/solenoid_softedge/input_solenoid_softedge.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 250.0
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.559531175539e-3
beam.sigmaY = 2.205510139392e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 6.41218345413e-4
beam.sigmaPy = 9.06819680526e-4
beam.sigmaPt = 1.0e-3
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor sol1 monitor
lattice.nslice = 1
monitor.type = beam_monitor
monitor.backend = h5
sol1.type = solenoid_softedge
sol1.ds = 6.0
sol1.bscale = 1.233482899483985
sol1.mapsteps = 800
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = false
Analyze
We run the following script to analyze correctness:
Script analysis_solenoid_softedge.py
examples/solenoid_softedge/analysis_solenoid_softedge.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Chad Mitchell, Axel Huebl
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 2.0 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.559531175539e-3,
2.205510139392e-3,
1.0e-3,
1.0e-6,
2.0e-6,
1.0e-6,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 2.0 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
2.425578906459e-3,
2.654015302646e-3,
9.985897906860e-3,
1.365357890e-6,
1.634641555e-6,
1.000000000e-6,
],
rtol=rtol,
atol=atol,
)
Soft-Edge Quadrupole
This is a modification of the test for a matched electron beam propagating through a stable FODO cell, in which the quadrupoles have been replaced with soft-edge quadrupole elements. The on-axis field profile in this example has been chosen to correspond to the hard-edge limit, so the two tests should coincide.
We use a 2 GeV electron beam with initial unnormalized rms emittance of 2 nm.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_quadrupole_softedge.pyorImpactX executable using an input file:
impactx input_quadrupole_softedge.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/quadrupole_softedge/run_quadrupole_softedge.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV electron beam with an initial
# unnormalized rms emittance of 2 nm
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=3.9984884770e-5,
sigmaY=3.9984884770e-5,
sigmaT=1.0e-3,
sigmaPx=2.6623538760e-5,
sigmaPy=2.6623538760e-5,
sigmaPt=2.0e-3,
muxpx=-0.846574929020762,
muypy=0.846574929020762,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
ns = 1 # number of slices per ds in the element
quad1 = elements.SoftQuadrupole(
ds=1.0,
gscale=1.0,
cos_coefficients=[2],
sin_coefficients=[0],
mapsteps=400,
nslice=ns,
)
quad2 = elements.SoftQuadrupole(
ds=1.0,
gscale=-1.0,
cos_coefficients=[2],
sin_coefficients=[0],
mapsteps=200,
nslice=ns,
)
drift1 = elements.Drift(ds=0.25, nslice=ns)
drift2 = elements.Drift(ds=0.5, nslice=ns)
# assign a fodo segment
sim.lattice.extend([monitor, drift1, quad1, drift2, quad2, drift1, monitor])
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/quadrupole_softedge/input_quadrupole_softedge.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 3.9984884770e-5
beam.sigmaY = 3.9984884770e-5
beam.sigmaT = 1.0e-3
beam.sigmaPx = 2.6623538760e-5
beam.sigmaPy = 2.6623538760e-5
beam.sigmaPt = 2.0e-3
beam.muxpx = -0.846574929020762
beam.muypy = 0.846574929020762
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor drift1 quad1 drift2 quad2 drift1 monitor
lattice.nslice = 1
monitor.type = beam_monitor
monitor.backend = h5
drift1.type = drift
drift1.ds = 0.25
quad1.type = quadrupole_softedge
quad1.ds = 1.0
quad1.gscale = 1.0
quad1.cos_coefficients = 2.0
quad1.sin_coefficients = 0.0
quad1.mapsteps = 400
drift2.type = drift
drift2.ds = 0.5
quad2.type = quadrupole_softedge
quad2.ds = 1.0
quad2.gscale = -1.0
quad2.cos_coefficients = 2.0
quad2.sin_coefficients = 0.0
quad2.mapsteps = 400
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = false
Analyze
We run the following script to analyze correctness:
Script analysis_quadrupole_softedge.py
examples/quadrupole_softedge/analysis_quadrupole_softedge.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
7.5451170454175073e-005,
7.5441588239210947e-005,
9.9775878164077539e-004,
1.9959540393751392e-009,
2.0175015289132990e-009,
2.0013820193294972e-006,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
7.4790118496224206e-005,
7.5357525169680140e-005,
9.9775879288128088e-004,
1.9959539836392703e-009,
2.0175014668882125e-009,
2.0013820380883801e-006,
],
rtol=rtol,
atol=atol,
)
Positron Channel
Acceleration of a positron beam with large (10%) energy spread, from 10 GeV to 2.5 TeV, for parameters based on possible staging of a laser-wakefield accelerator.
The lattice consists of 250 periods, each consisting of a quadrupole triplet followed by 10 GeV energy gain in a uniform field.
We use a 190 pC positron beam with initial normalized rms emittance of 10 nm, rms beam size of 5 microns, and a triangular current pulse with end-to-end pulse length of 0.12 ps.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_positron.pyorImpactX executable using an input file:
impactx input_positron.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/positron_channel/run_positron.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = False
# domain decomposition & space charge mesh
sim.init_grids()
# load a 10 GeV positron beam with an initial
# normalized rms emittance of 10 nm
kin_energy_MeV = 10.0e3 # reference energy
bunch_charge_C = 190.0e-12 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Triangle(
sigmaX=5.054566450e-6,
sigmaY=5.054566450e-6,
sigmaT=8.43732950e-7,
sigmaPx=1.01091329e-7,
sigmaPy=1.01091329e-7,
sigmaPt=1.0e-2,
muxpx=0.0,
muypy=0.0,
mutpt=0.995037190209989,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice)
ns = 1 # number of slices per ds in the element
period = [
monitor,
elements.ChrQuad(ds=0.1, k=-6.674941, units=1, nslice=ns),
elements.ChrDrift(ds=0.3, nslice=ns),
elements.ChrQuad(ds=0.2, k=6.674941, units=1, nslice=ns),
elements.ChrDrift(ds=0.3, nslice=ns),
elements.ChrQuad(ds=0.1, k=-6.674941, units=1, nslice=ns),
elements.ChrDrift(ds=0.1, nslice=ns),
elements.ChrAcc(ds=1.8, ez=10871.950994502130424, bz=1.0e-12, nslice=ns),
elements.ChrDrift(ds=0.1, nslice=ns),
monitor,
]
sim.lattice.extend(period)
# number of periods through the lattice
sim.periods = 250
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/positron_channel/input_positron.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 10.0e3
beam.charge = 190.0e-12
beam.particle = positron
beam.distribution = triangle
beam.sigmaX = 5.054566450e-6
beam.sigmaY = 5.054566450e-6
beam.sigmaT = 8.43732950e-7
beam.sigmaPx = 1.01091329e-7
beam.sigmaPy = 1.01091329e-7
beam.sigmaPt = 1.0e-2
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.995037190209989
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.periods = 250
lattice.elements = monitor quad1 drift1 quad2 drift1 quad1 drift2 unifacc drift2 monitor
lattice.nslice = 25
monitor.type = beam_monitor
monitor.backend = h5
quad1.type = quad_chromatic
quad1.ds = 0.1
quad1.k = -6.674941
quad1.units = 1
drift1.type = drift_chromatic
drift1.ds = 0.3
quad2.type = quad_chromatic
quad2.ds = 0.2
quad2.k = 6.674941
quad2.units = 1
drift2.type = drift_chromatic
drift2.ds = 0.1
unifacc.type = uniform_acc_chromatic
unifacc.ds = 1.8
unifacc.ez = 10871.950994502130424
unifacc.bz = 1.0e-12
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
#amr.n_cell = 56 56 48
#geometry.prob_relative = 1.0
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = false
Analyze
We run the following script to analyze correctness:
Script analysis_positron.py
examples/positron_channel/analysis_positron.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
5.05456645029333603e-006,
5.05456645029333603e-006,
8.47941120001532497e-006,
5.1097284000861952e-13,
5.1097284000861952e-13,
8.47941120001532497e-008,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 2.0 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
5.26e-006,
5.26e-006,
8.47941120001532497e-006,
2.0439953822082447e-15,
2.0439953822082447e-15,
3.3919371010764148e-10,
],
rtol=rtol,
atol=atol,
)
Cyclotron
This demonstrates a simple cyclotron as published by Ernest O. Lawrence and M. Stanley Livingston, The Production of High Speed Light Ions Without the Use of High Voltages, Phys. Rev. 40, 19 (1932). DOI: 10.1103/PhysRev.40.19
Run
This example can be run either as:
Python script:
python3 run_cyclotron.pyorImpactX executable using an input file:
impactx input_cyclotron.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/cyclotron/run_cyclotron.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load initial beam
kin_energy_MeV = 4.0e-3 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.0e-3,
sigmaY=1.0e-3,
sigmaT=0.3,
sigmaPx=2.0e-4,
sigmaPy=2.0e-4,
sigmaPt=2.0e-5,
muxpx=-0.0,
muypy=0.0,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice)
ns = 25 # number of slices per ds in the element
period = [
monitor,
elements.ChrAcc(ds=0.038, ez=1.12188308693e-4, bz=1.0e-14, nslice=ns),
elements.ExactSbend(ds=0.25, phi=180.0, B=1),
elements.ChrAcc(ds=0.038, ez=1.12188308693e-4, bz=1.0e-14, nslice=ns),
elements.ExactSbend(ds=0.25, phi=180.0, B=1),
monitor,
]
sim.lattice.extend(period)
# number of periods through the lattice
sim.periods = 150
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/cyclotron/input_cyclotron.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 4.0e-3
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.0e-3
beam.sigmaY = 1.0e-3
beam.sigmaT = 0.3
beam.sigmaPx = 2.0e-4
beam.sigmaPy = 2.0e-4
beam.sigmaPt = 2.0e-5
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor half half monitor
lattice.periods = 150
lattice.nslice = 25
monitor.type = beam_monitor
monitor.backend = h5
half.type = line
half.elements = gap bend
gap.type = uniform_acc_chromatic
gap.ds = 0.038
gap.ez = 1.12188308693e-4
gap.bz = 1.0e-14
bend.type = sbend_exact
bend.ds = 0.25
bend.phi = 180.0
bend.B = 1.0
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
Analyze
We run the following script to analyze correctness:
Script analysis_cyclotron.py
examples/cyclotron/analysis_cyclotron.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.0e-3,
1.0e-3,
3.0e-1,
2.0e-7,
2.0e-7,
6.0e-6,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.040898e-03,
2.221367e-03,
3.426366e-01,
1.151532e-08,
1.160797e-08,
3.440357e-07,
],
rtol=rtol,
atol=atol,
)
Visualize
Note
TODO :)
Combined Function Bend
A single combined function bending magnet (an ideal sector bend with an upright quadrupole field component added). The magnet parameters are based a single CSBEND element appearing in the ELEGANT input file for the ALS-U lattice.
The beam parameters are based on: C. Steier et al, “Status of the Conceptual Design of ALS-U”, IPAC2017, WEPAB104, DOI:10.18429/JACoW-IPAC2017-WEPAB104 (2017).
A 2 GeV electron bunch with normalized transverse rms emittance of 50 pm undergoes a 3.76 deg bend.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_cfbend.pyorImpactX executable using an input file:
impactx input_cfbend.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/cfbend/run_cfbend.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Chad Mitchell, Axel Huebl
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 5 GeV electron beam with an initial
# normalized transverse rms emittance of 1 um
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=5.0e-6, # 5 um
sigmaY=8.0e-6, # 8 um
sigmaT=0.0599584916, # 200 ps
sigmaPx=2.5543422003e-9, # exn = 50 pm-rad
sigmaPy=1.5964638752e-9, # eyn = 50 pm-rad
sigmaPt=9.0e-4, # approximately dE/E
muxpx=0.0,
muypy=0.0,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
ns = 25 # number of slices per ds in the element
bend = [
monitor,
elements.CFbend(ds=0.5, rc=7.613657587094493, k=-7.057403, nslice=ns),
monitor,
]
# assign a lattice segment
sim.lattice.extend(bend)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/cfbend/input_cfbend.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3 #2 GeV
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 5.0e-6 #5 um
beam.sigmaY = 8.0e-6 #8 um
beam.sigmaT = 0.0599584916 #200 ps
beam.sigmaPx = 2.5543422003e-9 #exn = 50 pm-rad
beam.sigmaPy = 1.5964638752e-9 #eyn = 50 pm-rad
beam.sigmaPt = 9.0e-4 #approximately dE/E
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor cfbend1 monitor
lattice.nslice = 25
cfbend1.type = cfbend
cfbend1.ds = 0.5 # projected length 0.5 m, angle 3.76 deg
cfbend1.rc = 7.613657587094493 # bending radius [m]
cfbend1.k = -7.057403 # (upright) quadrupole component [m^(-2)]
monitor.type = beam_monitor
monitor.backend = h5
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = false
Analyze
We run the following script to analyze correctness:
Script analysis_cfbend.py
examples/cfbend/analysis_cfbend.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
5.0e-6,
8.0e-6,
0.0599584916,
1.277171100130637e-14,
1.277171100130637e-14,
5.396264243e-005,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.98301912761436476154e-005,
1.92110147814673522465e-006,
5.99584916026070271843e-002,
3.90166131470905952893e-010,
1.27717110013063679910e-014,
5.396264244141050920556e-005,
],
rtol=rtol,
atol=atol,
)
Ballistic Compression Using a Short RF Element
A 20 MeV electron beam propagates through a short RF element near zero-crossing, inducing a head-tail energy correlation. This is followed by ballistic motion in a drift, which is used to compress the rms bunch length from 16 ps to 10 ps (compression of 5/3).
The beam is not exactly on-crest (phase = -89.5 deg), so there is an energy gain of 4.5 MeV.
The transverse emittance is sufficiently small that the horizontal and verticle beam size are essentially unchanged. Due to RF curvature, there is some growth of the longitudinal emittance.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_compression.pyorImpactX executable using an input file:
impactx input_compression.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/compression/run_compression.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Marco Garten, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 250 MeV proton beam with an initial
# unnormalized rms emittance of 1 mm-mrad in all
# three phase planes
kin_energy_MeV = 20.0 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=0.5e-3,
sigmaY=0.5e-3,
sigmaT=5.0e-3,
sigmaPx=1.0e-5,
sigmaPy=1.0e-5,
sigmaPt=4.0e-6,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
sim.lattice.append(monitor)
# Short RF cavity element
shortrf1 = elements.ShortRF(V=1000.0, freq=1.3e9, phase=-89.5)
# Drift element
drift1 = elements.Drift(ds=1.7)
sim.lattice.extend([shortrf1, drift1])
sim.lattice.append(monitor)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/compression/input_compression.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 20.0
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 0.5e-3
beam.sigmaY = 0.5e-3
beam.sigmaT = 5.0e-3
beam.sigmaPx = 1.0e-5
beam.sigmaPy = 1.0e-5
beam.sigmaPt = 4.0e-6
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor shortrf1 drift1 monitor
monitor.type = beam_monitor
monitor.backend = h5
shortrf1.type = shortrf
shortrf1.V = 1000.0
shortrf1.freq = 1.3e9
shortrf1.phase = -89.5
drift1.type = drift
drift1.ds = 1.7
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
Analyze
We run the following script to analyze correctness:
Script analysis_compression.py
examples/compression/analysis_compression.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# openPMD data series at the beam monitors
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
# first and last step
final_step = list(series.iterations)[-1]
first_it = series.iterations[1]
final_it = series.iterations[final_step]
# initial beam & reference particle gamma
initial = first_it.particles["beam"].to_df()
initial_gamma_ref = first_it.particles["beam"].get_attribute("gamma_ref")
# final beam & reference particle gamma
final = final_it.particles["beam"].to_df()
final_gamma_ref = final_it.particles["beam"].get_attribute("gamma_ref")
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
print(f" gamma={initial_gamma_ref:e}")
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t, initial_gamma_ref],
[
5.0e-04,
5.0e-04,
5.0e-03,
4.952764e-09,
5.028325e-09,
1.997821e-08,
40.1389432485322889,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
print(f" gamma={final_gamma_ref:e}")
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t, final_gamma_ref],
[
5.004995e-04,
5.005865e-04,
3.033949e-03,
4.067876e-09,
4.129937e-09,
6.432081e-05,
48.8654787469061860,
],
rtol=rtol,
atol=atol,
)
Test of a Transverse Kicker
This test applies two transverse momentum kicks, first in the horizontal direction (2 mrad) and then in the vertical direction (3 mrad).
We use a 2 GeV electron beam.
The second beam moments should be unchanged, but the first beam moments corresponding to \(p_x\) and \(p_y\) should change according to the size of the kick.
In this test, the initial and final values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values.
Run
This example can be run either as:
Python script:
python3 run_kicker.pyorImpactX executable using an input file:
impactx input_kicker.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/kicker/run_kicker.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 2 GeV electron beam with an initial
# unnormalized rms emittance of nm
kin_energy_MeV = 2.0e3 # reference energy
bunch_charge_C = 1.0e-9 # used without space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=4.0e-3,
sigmaY=4.0e-3,
sigmaT=1.0e-3,
sigmaPx=3.0e-4,
sigmaPy=3.0e-4,
sigmaPt=2.0e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
kicklattice = [
monitor,
elements.Kicker(xkick=2.0e-3, ykick=0.0, units="dimensionless"),
elements.Kicker(xkick=0.0, ykick=3.0e-3, units="dimensionless"),
monitor,
]
# assign a lattice
sim.lattice.extend(kicklattice)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/kicker/input_kicker.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 2.0e3
beam.charge = 1.0e-9
beam.particle = electron
beam.distribution = waterbag
beam.sigmaX = 4.0e-3
beam.sigmaY = 4.0e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 3.0e-4
beam.sigmaPy = 3.0e-4
beam.sigmaPt = 2.0e-3
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor hkick vkick monitor
monitor.type = beam_monitor
monitor.backend = h5
hkick.type = kicker
hkick.xkick = 2.0e-3 # 2 mrad horizontal kick
hkick.ykick = 0.0
vkick.type = kicker
vkick.xkick = 0.0
vkick.ykick = 3.0e-3 # 3 mrad vertical kick
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
Analyze
We run the following script to analyze correctness:
Script analysis_kicker.py
examples/kicker/analysis_kicker.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import describe, moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t, meanpx, meanpy
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
meanpx = describe(beam["momentum_x"]).mean
meanpy = describe(beam["momentum_y"]).mean
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t, meanpx, meanpy)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t, meanpx, meanpy = get_moments(
initial
)
print(
f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e} meanpx={meanpx:e} meanpy={meanpy:e}"
)
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 5.0 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.017554e-03,
4.017044e-03,
9.977588e-04,
1.197572e-06,
1.210501e-06,
2.001382e-06,
],
rtol=rtol,
atol=atol,
)
atol = rtol * emittance_x / sigx # relative to rms beam size
assert np.allclose(
[meanpx, meanpy],
[
0.0,
0.0,
],
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t, meanpx, meanpy = get_moments(
final
)
print(
f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e} meanpx={meanpx:e} meanpy={meanpy:e}"
)
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 5.0 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
4.017554e-03,
4.017044e-03,
9.977588e-04,
1.197572e-06,
1.210501e-06,
2.001382e-06,
],
rtol=rtol,
atol=atol,
)
atol = rtol * emittance_x / sigx # relative to rms beam size
print(f" atol~={atol}")
assert np.allclose(
[meanpx, meanpy],
[
2.0e-3,
3.0e-3,
],
atol=atol,
)
Thin Dipole
This test involves tracking a 5 MeV proton beam through a 90 degree sector bend, using two different methods:
#. Using a sequence of drifts and thin kicks as described by: G. Ripken and F. Schmidt, “A Symplectic Six-Dimensional Thin-Lens Formalism for Tracking,” CERN/SL/95-12 (1995).
#. Using the exact nonlinear transfer map for a sector bend as described by: D. Bruhwiler et al, “Symplectic Propagation of the Map, Tangent Map and Tangent Map Derivative through Quadrupole and Combined-Function Dipole Magnets without Truncation,” THP41C, EPAC98, pp. 1171-1173 (1998).
To compare the two models, the beam is tracked using 1), followed by the inverse of 2). The beam moments and emittances should coincide with those of the initial distribution.
Run
This example can be run either as:
Python script:
python3 run_thin_dipole.pyorImpactX executable using an input file:
impactx input_thin_dipole.in
For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/thin_dipole/run_thin_dipole.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load initial beam
kin_energy_MeV = 5.0 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.0e-3,
sigmaY=1.0e-3,
sigmaT=0.3,
sigmaPx=2.0e-4,
sigmaPy=2.0e-4,
sigmaPt=2.0e-4,
muxpx=-0.0,
muypy=0.0,
mutpt=0.0,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice)
ns = 1 # number of slices per ds in the element
segment = [
elements.Drift(ds=0.003926990816987, nslice=ns),
elements.ThinDipole(theta=0.45, rc=1.0),
elements.Drift(ds=0.003926990816987, nslice=ns),
]
bend = 200 * segment
inverse_bend = elements.ExactSbend(ds=-1.570796326794897, phi=-90.0)
sim.lattice.append(monitor)
sim.lattice.extend(bend)
sim.lattice.append(inverse_bend)
sim.lattice.append(monitor)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/thin_dipole/input_thin_dipole.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 5.0
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.0e-3
beam.sigmaY = 1.0e-3
beam.sigmaT = 0.3
beam.sigmaPx = 2.0e-4
beam.sigmaPy = 2.0e-4
beam.sigmaPt = 2.0e-4
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor bend inverse_bend monitor
lattice.nslice = 1
monitor.type = beam_monitor
monitor.backend = h5
#90 degree sbend using drift-kick-drift:
bend.type = line
bend.elements = dr kick dr
bend.repeat = 200
dr.type = drift
dr.ds = 0.003926990816987
kick.type = thin_dipole
kick.theta = 0.45
kick.rc = 1.0
#inverse of a 90 degree sbend using exact nonlinear map:
inverse_bend.type = sbend_exact
inverse_bend.ds = -1.570796326794897
inverse_bend.phi = -90.0
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
Analyze
We run the following script to analyze correctness:
Script analysis_thin_dipole.py
examples/thin_dipole/analysis_thin_dipole.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
assert num_particles == len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.0e-3,
1.0e-3,
3.0e-1,
2.0e-7,
2.0e-7,
6.0e-5,
],
rtol=rtol,
atol=atol,
)
print("")
print("Final Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(final)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.0e-3,
1.0e-3,
3.0e-1,
2.0e-7,
2.0e-7,
6.0e-5,
],
rtol=rtol,
atol=atol,
)
Visualize
Note
TODO :)
Aperture Collimation
Proton beam undergoing collimation by a rectangular boundary aperture.
We use a 250 MeV proton beam with a horizontal rms beam size of 1.56 mm and a vertical rms beam size of 2.21 mm.
After a short drift of 0.123, the beam is scraped by a 1 mm x 1.5 mm rectangular aperture.
In this test, the initial values of \(\sigma_x\), \(\sigma_y\), \(\sigma_t\), \(\epsilon_x\), \(\epsilon_y\), and \(\epsilon_t\) must agree with nominal values. The test fails if:
any of the final coordinates for the valid (not lost) particles lie outside the aperture boundary or
any of the lost particles are inside the aperture boundary or
if the sum of lost and kept particles is not equal to the initial particles or
if the recorded position \(s\) for the lost particles does not coincide with the drift distance.
Run
This example can be run as a Python script (python3 run_aperture.py) or with an app with an input file (impactx input_aperture.in).
Each can also be prefixed with an MPI executor, such as mpiexec -n 4 ... or srun -n 4 ..., depending on the system.
examples/aperture/run_aperture.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import amrex.space3d as amr
from impactx import ImpactX, RefPart, distribution, elements
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
sim.particle_lost_diagnostics_backend = "h5"
# domain decomposition & space charge mesh
sim.init_grids()
# load a 250 MeV proton beam with an initial
# horizontal rms emittance of 1 um and an
# initial vertical rms emittance of 2 um
kin_energy_MeV = 250.0 # reference energy
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
ref = sim.particle_container().ref_particle()
ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Waterbag(
sigmaX=1.559531175539e-3,
sigmaY=2.205510139392e-3,
sigmaT=1.0e-3,
sigmaPx=6.41218345413e-4,
sigmaPy=9.06819680526e-4,
sigmaPt=1.0e-3,
)
sim.add_particles(bunch_charge_C, distr, npart)
# add beam diagnostics
monitor = elements.BeamMonitor("monitor", backend="h5")
# design the accelerator lattice
sim.lattice.extend(
[
monitor,
elements.Drift(0.123),
elements.Aperture(xmax=1.0e-3, ymax=1.5e-3, shape="rectangular"),
monitor,
]
)
# run simulation
sim.evolve()
# clean shutdown
del sim
amr.finalize()
examples/aperture/input_aperture.in.###############################################################################
# Particle Beam(s)
###############################################################################
beam.npart = 10000
beam.units = static
beam.kin_energy = 250.0
beam.charge = 1.0e-9
beam.particle = proton
beam.distribution = waterbag
beam.sigmaX = 1.559531175539e-3
beam.sigmaY = 2.205510139392e-3
beam.sigmaT = 1.0e-3
beam.sigmaPx = 6.41218345413e-4
beam.sigmaPy = 9.06819680526e-4
beam.sigmaPt = 1.0e-3
beam.muxpx = 0.0
beam.muypy = 0.0
beam.mutpt = 0.0
###############################################################################
# Beamline: lattice elements and segments
###############################################################################
lattice.elements = monitor drift collimator monitor
lattice.nslice = 1
monitor.type = beam_monitor
monitor.backend = h5
drift.type = drift
drift.ds = 0.123
collimator.type = aperture
collimator.shape = rectangular
collimator.xmax = 1.0e-3
collimator.ymax = 1.5e-3
###############################################################################
# Algorithms
###############################################################################
algo.particle_shape = 2
algo.space_charge = false
###############################################################################
# Diagnostics
###############################################################################
diag.slice_step_diagnostics = true
diag.backend = h5
Analyze
We run the following script to analyze correctness:
Script analysis_aperture.py
examples/aperture/analysis_aperture.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
import numpy as np
import openpmd_api as io
from scipy.stats import moment
def get_moments(beam):
"""Calculate standard deviations of beam position & momenta
and emittance values
Returns
-------
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t
"""
sigx = moment(beam["position_x"], moment=2) ** 0.5 # variance -> std dev.
sigpx = moment(beam["momentum_x"], moment=2) ** 0.5
sigy = moment(beam["position_y"], moment=2) ** 0.5
sigpy = moment(beam["momentum_y"], moment=2) ** 0.5
sigt = moment(beam["position_t"], moment=2) ** 0.5
sigpt = moment(beam["momentum_t"], moment=2) ** 0.5
epstrms = beam.cov(ddof=0)
emittance_x = (
sigx**2 * sigpx**2 - epstrms["position_x"]["momentum_x"] ** 2
) ** 0.5
emittance_y = (
sigy**2 * sigpy**2 - epstrms["position_y"]["momentum_y"] ** 2
) ** 0.5
emittance_t = (
sigt**2 * sigpt**2 - epstrms["position_t"]["momentum_t"] ** 2
) ** 0.5
return (sigx, sigy, sigt, emittance_x, emittance_y, emittance_t)
# initial/final beam
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
last_step = list(series.iterations)[-1]
initial = series.iterations[1].particles["beam"].to_df()
final = series.iterations[last_step].particles["beam"].to_df()
series_lost = io.Series("diags/openPMD/particles_lost.h5", io.Access.read_only)
particles_lost = series_lost.iterations[0].particles["beam"].to_df()
# compare number of particles
num_particles = 10000
assert num_particles == len(initial)
# we lost particles in apertures
assert num_particles > len(final)
assert num_particles == len(particles_lost) + len(final)
print("Initial Beam:")
sigx, sigy, sigt, emittance_x, emittance_y, emittance_t = get_moments(initial)
print(f" sigx={sigx:e} sigy={sigy:e} sigt={sigt:e}")
print(
f" emittance_x={emittance_x:e} emittance_y={emittance_y:e} emittance_t={emittance_t:e}"
)
atol = 0.0 # ignored
rtol = 1.8 * num_particles**-0.5 # from random sampling of a smooth distribution
print(f" rtol={rtol} (ignored: atol~={atol})")
assert np.allclose(
[sigx, sigy, sigt, emittance_x, emittance_y, emittance_t],
[
1.559531175539e-3,
2.205510139392e-3,
1.0e-3,
1.0e-6,
2.0e-6,
1.0e-6,
],
rtol=rtol,
atol=atol,
)
# particle-wise comparison against the rectangular aperture boundary
xmax = 1.0e-3
ymax = 1.5e-3
# kept particles
dx = abs(final["position_x"]) - xmax
dy = abs(final["position_y"]) - ymax
print()
print(f" x_max={final['position_x'].max()}")
print(f" x_min={final['position_x'].min()}")
assert np.less_equal(dx.max(), 0.0)
print(f" y_max={final['position_y'].max()}")
print(f" y_min={final['position_y'].min()}")
assert np.less_equal(dy.max(), 0.0)
# lost particles
dx = abs(particles_lost["position_x"]) - xmax
dy = abs(particles_lost["position_y"]) - ymax
print()
print(f" x_max={particles_lost['position_x'].max()}")
print(f" x_min={particles_lost['position_x'].min()}")
assert np.greater_equal(dx.max(), 0.0)
print(f" y_max={particles_lost['position_y'].max()}")
print(f" y_min={particles_lost['position_y'].min()}")
assert np.greater_equal(dy.max(), 0.0)
# check that s is set correctly
lost_at_s = particles_lost["s_lost"]
drift_s = np.ones_like(lost_at_s) * 0.123
assert np.allclose(lost_at_s, drift_s)
Unit tests
Transformation
Test the t/s transformations on an electron beam.
We use a long electron beam, \(L_z=1\) cm, with significant correlations in \(x-px\), \(y-py\), and \(t-pt\). The beam has average energy 1 GeV.
This tests that the t/s transforms are inverses of each other
Specifically, in this test the \(t\)- and \(s\)-coordinates of the beam must differ substantially
and the forward-inverse transformed coordinates must agree with the initial coordinates.
That is, we require that to_fixed_s (to_fixed_t (initial beam)) = initial beam.
Run
This file is run from pytest.
tests/python/test_transformation.py.#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Ryan Sandberg, Axel Huebl, Chad Mitchell
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
import numpy as np
from impactx import (
Config,
ImpactX,
ImpactXParIter,
RefPart,
TransformationDirection,
coordinate_transformation,
distribution,
elements,
)
def test_transformation():
"""
This test ensures s->t and t->s transformations
do round-trip.
"""
sim = ImpactX()
# set numerical parameters and IO control
sim.particle_shape = 2 # B-spline order
sim.space_charge = False
# sim.diagnostics = False # benchmarking
sim.slice_step_diagnostics = True
# domain decomposition & space charge mesh
sim.init_grids()
# load a 1 GeV electron beam with an initial
# unnormalized rms emittance of 2 nm
kin_energy_MeV = 1e3 # reference energy
energy_gamma = kin_energy_MeV / 0.510998950 + 1.0
bunch_charge_C = 1.0e-9 # used with space charge
npart = 10000 # number of macro particles
# reference particle
pc = sim.particle_container()
ref = pc.ref_particle()
ref.set_charge_qe(-1.0).set_mass_MeV(0.510998950).set_kin_energy_MeV(kin_energy_MeV)
# particle bunch
distr = distribution.Gaussian(
sigmaX=3e-6,
sigmaY=3e-6,
sigmaT=1e-2,
sigmaPx=1.33 / energy_gamma,
sigmaPy=1.33 / energy_gamma,
sigmaPt=100 / energy_gamma,
muxpx=-0.5,
muypy=0.4,
mutpt=0.8,
)
sim.add_particles(bunch_charge_C, distr, npart)
rbc_s0 = pc.reduced_beam_characteristics()
coordinate_transformation(pc, TransformationDirection.to_fixed_t)
rbc_t = pc.reduced_beam_characteristics()
coordinate_transformation(pc, TransformationDirection.to_fixed_s)
rbc_s = pc.reduced_beam_characteristics()
# clean shutdown
del sim
# assert that forward-inverse transformation of the beam leaves beam unchanged
atol = 1e-14
rtol = 1e-10
for key, val in rbc_s0.items():
if not np.isclose(val, rbc_s[key], rtol=rtol, atol=atol):
print(f"initial[{key}]={val}, final[{key}]={rbc_s[key]} not equal")
assert np.isclose(val, rbc_s[key], rtol=rtol, atol=atol)
# assert that the t-based beam is different, at least in the following keys:
large_st_diff_keys = [
"beta_x",
"beta_y",
"emittance_y",
"emittance_x",
"sig_y",
"sig_x",
"t_mean",
]
for key in large_st_diff_keys:
rel_error = (rbc_s0[key] - rbc_t[key]) / rbc_s0[key]
assert abs(rel_error) > 1
For every change of the ImpactX code base, each of these examples and tests are continuously tested and benchmarked.
Workflows
This section collects typical user workflows and best practices for ImpactX.
Note
TODO: Add more workflows as in https://warpx.readthedocs.io/en/latest/usage/workflows.html
Data Analysis
Data Analysis
Beam Monitor
ImpactX provides a zero-sized beam monitor element that can be placed in lattices to output the particle beam at multiple positions in a lattice. Output is written in the standardized, open particle-mesh data schema (openPMD) and is compatible with many codes and data analysis frameworks.
For data analysis of openPMD data, see examples of many supported tools, Python libraries and frameworks. Exporting data to ASCII is possible, too.
See also WarpX’ documentation on openPMD.
Additional Beam Attributes
We add the following additional attributes on the openPMD beam species at the monitor position.
Reference particle:
beta_refreference particle normalized velocity \(\beta = v/c\)gamma_refreference particle Lorentz factor \(\gamma = 1/\sqrt{1-\beta^2}\)s_refintegrated orbit path length, in metersx_refhorizontal position x, in metersy_refvertical position y, in metersz_reflongitudinal position z, in meterst_refclock time * c in meterspx_refmomentum in x, normalized to mass*c, \(p_x = \gamma \beta_x\)py_refmomentum in y, normalized to mass*c, \(p_y = \gamma \beta_y\)pz_refmomentum in z, normalized to mass*c, \(p_z = \gamma \beta_z\)pt_refenergy, normalized by rest energy, \(p_t = -\gamma\)massreference rest mass, in kgchargereference charge, in C
Example to print the integrated orbit path length s at each beam monitor position:
import openpmd_api as io
series = io.Series("diags/openPMD/monitor.h5", io.Access.read_only)
for k_i, i in series.iterations.items():
beam = i.particles["beam"]
s_ref = beam.get_attribute("s_ref")
print(f"step {k_i:>3}: s_ref={s_ref}")
Reduced Beam Characteristics
ImpactX calculates reduced beam characteristics like averaged positions, momenta, beam emittances and Courant-Snyder (Twiss) parameters during runtime.
These quantities are calculated before, after, and during each step of the simulation.
If diag.slice_step_diagnostics is enabled, they will also be calculated during each slice of each beamline element.
The code writes out the values in an ASCII file prefixed reduced_beam_characteristics containing the follow columns:
stepIteration within the simulation
s,ref_beta_gammaReference particle coordinate
s(unit: meter) and relativistic momentum normalized by the particle mass and the speed of light (unit: dimensionless)
x_mean/min/max,y_mean/min/max,t_mean/min/maxAverage / minimum / maximum beam particle position in the dimensions of
x,y(transverse coordinates, unit: meter), andt(normalized time difference \(ct\), unit: meter)
sig_x,sig_y,sig_tRMS of the average beam particle positions (unit: meter)
px_mean/min/max,py_mean/min/max,pt_mean/min/maxAverage / minimum / maximum beam momenta normalized by reference particle momentum (unit: dimensionless, radians for transverse momenta)
sig_px,sig_py,sig_ptRMS of the average beam momenta (energy difference for
pt) (unit: dimensionless)
emittance_x,emittance_y,emittance_tNormalized beam emittance (unit: meter)
alpha_x,alpha_y,alpha_tCourant-Snyder (Twiss) alpha (unit: dimensionless)
beta_x,beta_y,beta_tCourant-Snyder (Twiss) beta (unit: meter)
chargeCumulated beam charge (unit: Coulomb)
Theory
Introduction
Concepts
Reference Trajectory
ImpactX is an s-based beam dynamics code with space charge. Particles are tracked using the longitudinal accelerator lattice position \(s\) as the independent dynamical variable. Particle phase space coordinates are specified relative to a nominal reference trajectory.
The reference trajectory plays an important role in ImpactX. In addition to specifying the nominal machine orbit, it specifies the relationship between the local beam coordinate system and the global lab coordinate system. A reference trajectory is favorable instead of, e.g., differences to the beam centroid, because:
the reference trajectory is the ideal single-particle orbit used as part of the optics design, so it is better that it can be computed independently of the beam distribution,
differences between the beam centroid and the reference particle are important when investigating the effects of misalignments and errors for beamline designs,
the fields are usually specified relative to the reference trajectory, and the dynamics becomes more nonlinear as one moves away from the reference trajectory, so knowing how far the beam particles are form the reference trajectory is important for accuracy,
we want to keep track of the reference trajectory in global coordinates, and that global information is not available in the particle data alone, so it would need to be specified in some other way.
The reference values of \(z=ct\) and \(s\) should be identical until reaching a bending element. (If the lattice contains no bending elements, then they should coincide.) Also, the reference value of \(ct\) coincides with the value of \(s\) in the ultrarelativistic limit. More generally, the derivative \(ds/d(ct) = \beta\), where the relativistic \(\beta = \sqrt{1-\frac{1}{p_t^2}}\).
Collective Effects
Collective effects from space charge of the particle beam are solved between steps in \(s\). One can set the number of slice steps through each lattice element for the application of the space charge push.
Note
Currently, space charge kicks are calculated in 3D. A 2D space-charge solver for purely transversal effects will be added in the future.
Coordinates and Units
Each particle in the beam is described at fixed \(s\) by a set of 6 canonical phase space variables (x [m], px, y [m], py, t [m], pt). Coordinates x and y denote the horizontal and vertical displacement from the reference particle, respectively, and describe motion in the plane transverse to the velocity of the reference particle. The longitudinal coordinate t denotes the difference between the arrival time of the particle and the arrival time of the reference particle, multiplied by the speed of light \(c\).
The momenta conjugate to x, y, and t are denoted px, py, and pt, respectively. These variables are normalized by the magnitude of the momentum of the reference particle, and are therefore dimensionless. In a region of zero vector potential, for example, \(p_x = \Delta(\beta_x\gamma)/(\beta_0\gamma_0)\), where \(\beta_0\) and \(\gamma_0\) denote the relativistic factors associated with the reference velocity. In a region of zero scalar potential, pt denotes the deviation from the reference energy normalized by the design momentum times the speed of light, so that \(p_t = \Delta(\gamma)/(\beta_0\gamma_0)\).
Unlike particles within the beam, the reference particle is described by a set of 8 phase space variables (x [m], px, y [m], py, z [m], pz, t [m], pt) that are specified in a global laboratory coordinate system (x,y,z). The momenta of the reference particle are normalized by \(mc\), so that \(p_x=\beta_x\gamma\), etc. A parameteric plot of the reference trajectory variables (x,z) allows the user to view the global geometry of the accelerator structure (footprint).
Assumptions
This is an overview of physical assumptions implemented in the numerics of ImpactX.
Tracking and Lattice Optics
Tracking through lattice optics in ImpactX is performed by updating the canonical phase space variables (x,px,y,py,t,pt) using symplectic transport. The elements supported currently fall into one of the following categories:
zero-length (thin) elements, such as multipole kicks and coordinate transformations
ideal (thick) elements using a hard-edge fringe field approximation, such as drifts, quadrupoles, and dipoles
soft-edge elements described by \(s\)-dependent, user-provided field data, such as RF cavities
ML surrogate models using a trained neural network (not necessarily symplectic)
Transport may be performed using one of three possible levels of approximation to the underlying Hamiltonian:
linear transfer map (default): obtained by expanding the Hamiltonian through terms of degree 2 in the deviation of phase space variables from those of the reference particle
chromatic or paraxial approximation: obtained by expanding the Hamiltonian through terms of degree 2 in the transverse phase space variables, while retaining the nonlinear dependence on the energy variable pt
exact Hamiltonian: obtained using the exact nonlinear Hamiltonian
Space Charge (Poisson Solver)
velocity spread: when solving for space-charge effects, we assume that the relative spread of velocities of particles in the beam is negligible compared to the velocity of the reference particle, so that in the bunch frame (rest frame of the reference particle) particle velocities are nonrelativistic
electrostatic in the bunch frame: we assume there are no retardation effects and we solve the Poisson equation in the bunch frame
Development
Contribute to ImpactX
We welcome new contributors! Here is how to participate to the ImpactX development.
Git workflow
The ImpactX project uses git for version control. If you are new to git, you can follow one of these tutorials:
Configure your GitHub Account & Development Machine
First, let’s setup your Git environment and GitHub account.
Go to https://github.com/settings/profile and add your real name and affiliation
Go to https://github.com/settings/emails and add & verify the professional e-mails you want to be associated with.
Configure
giton the machine you develop on to use the same spelling of your name and email:git config --global user.name "FIRSTNAME LASTNAME"git config --global user.email EMAIL@EXAMPLE.com
Go to https://github.com/settings/keys and add the SSH public key of the machine you develop on. (Check out the GitHub guide to generating SSH keys or troubleshoot common SSH problems. )
Make your own fork
First, fork the ImpactX “mainline” repo on GitHub by pressing the Fork button on the top right of the page. A fork is a copy of ImpactX on GitHub, which is under your full control.
Then, we create local copies, for development:
# Clone the mainline ImpactX source code to your local computer.
# You cannot write to this repository, but you can read from it.
git clone git@github.com:ECP-WarpX/impactx.git
cd impactx
# rename what we just cloned: call it "mainline"
git remote rename origin mainline
# Add your own fork. You can get this address on your fork's Github page.
# Here is where you will publish new developments, so that they can be
# reviewed and integrated into "mainline" later on.
# "myGithubUsername" needs to be replaced with your user name on GitHub.
git remote add myGithubUsername git@github.com:myGithubUsername/impactx.git
Now you are free to play with your fork (for additional information, you can visit the Github fork help page).
Note
We only need to do the above steps for the first time.
Let’s Develop
You are all set! Now, the basic ImpactX development workflow is:
Implement your changes and push them on a new branch
branch_nameon your fork.Create a Pull Request from branch
branch_nameon your fork to branchdevelopmenton the main ImpactX repo.
Create a branch branch_name (the branch name should reflect the piece of code you want to add, like fix-spectral-solver) with
# start from an up-to-date development branch
git checkout development
git pull mainline development
# create a fresh branch
git checkout -b branch_name
and do the coding you want.
It is probably a good time to look at the AMReX documentation and at the Doxygen reference pages:
ImpactX Doxygen: https://impactx.readthedocs.io/en/latest/_static/doxyhtml
AMReX Doxygen: https://amrex-codes.github.io/amrex/doxygen
WarpX Doxygen: https://warpx.readthedocs.io/en/latest/_static/doxyhtml
Once you are done developing, add the files you created and/or modified to the git staging area with
git add <file_I_created> <and_file_I_modified>
Build your changes
If you changed C++ files, then now is a good time to test those changes by compiling ImpactX locally. Follow the developer instructions in our manual to set up a local development environment, then compile and run ImpactX.
Commit & push your changes
Periodically commit your changes with
git commit
The commit message (between quotation marks) is super important in order to follow the developments during code-review and identify bugs. A typical format is:
This is a short, 40-character title
After a newline, you can write arbitray paragraphs. You
usually limit the lines to 70 characters, but if you don't, then
nothing bad will happen.
The most important part is really that you find a descriptive title
and add an empty newline after it.
For the moment, commits are on your local repo only. You can push them to your fork with
git push -u myGithubUsername branch_name
If you want to synchronize your branch with the development branch (this is useful when the development branch is being modified while you are working on branch_name), you can use
git pull mainline development
and fix any conflict that may occur.
Submit a Pull Request
A Pull Request (PR) is the way to efficiently visualize the changes you made and to propose your new feature/improvement/fix to the ImpactX project.
Right after you push changes, a banner should appear on the Github page of your fork, with your branch_name.
Click on the
compare & pull requestbutton to prepare your PR.It is time to communicate your changes: write a title and a description for your PR. People who review your PR are happy to know
what feature/fix you propose, and why
how you made it (added new/edited files, created a new class than inherits from…)
how you tested it and what was the output you got
and anything else relevant to your PR (attach images and scripts, link papers, etc.)
Press
Create pull request. Now you can navigate through your PR, which highlights the changes you made.
Please DO NOT write large pull requests, as they are very difficult and time-consuming to review. As much as possible, split them into small, targeted PRs. For example, if find typos in the documentation open a pull request that only fixes typos. If you want to fix a bug, make a small pull request that only fixes a bug.
If you want to implement a feature and are not too sure how to split it, just open an issue about your plans and ping other ImpactX developers on it to chime in. Generally, write helper functionality first, test it and then write implementation code. Submit tests, documentation changes and implementation of a feature together for pull request review.
Even before your work is ready to merge, it can be convenient to create a PR (so you can use Github tools to visualize your changes).
In this case, please put the [WIP] tag (for Work-In-Progress) at the beginning of the PR title.
You can also use the GitHub project tab in your fork to organize the work into separate tasks/PRs and share it with the ImpactX community to get feedback.
Include a test to your PR
A new feature is great, a working new feature is even better! Please test your code and add your test to the automated test suite. It’s the way to protect your work from adventurous developers.
Note
TOOD: Write a workflow how to add a test.
Include documentation about your PR
Now, let users know about your new feature by describing its usage in the ImpactX documentation.
Our documentation uses Sphinx, and it is located in docs/source/.
Note
TODO: For instance, if you introduce a new runtime parameter in the input file, you can add it to Docs/source/running_cpp/parameters.rst.
If Sphinx is installed on your computer, you should be able to generate the html documentation with
make html
in docs/. Then open docs/build/html/index.html with your favorite web browser and look
for your changes.
Once your code is ready with documentation and automated test, congratulations!
You can create the PR (or remove the [WIP] tag if you already created it).
Reviewers will interact with you if they have comments/questions.
Style and conventions
For indentation, ImpactX uses four spaces (no tabs)
Some text editors automatically modify the files you open. We recommend to turn on to remove trailing spaces and replace Tabs with 4 spaces.
The number of characters per line should be <100
Exception: in documentation files (
.rst/.md) use one sentence per line independent of its number of characters, which will allow easier edits.Space before and after assignment operator (
=)To define a function , for e.g.,
myfunction()use a space between the name of the function and the paranthesis -myfunction (). To call the function, the space is not required, i.e., just usemyfunction().The reason this is beneficial is that when we do a
git grepto search formyfunction (), we can clearly see the locations wheremyfunction ()is defined and wheremyfunction()is called.Also, using
git grep "myfunction ()"searches for files only in the git repo, which is more efficient compared to thegrep "myfunction ()"command that searches through all the files in a directory, including plotfiles for example.It is recommended that style changes are not included in the PR where new code is added. This is to avoid any errors that may be introduced in a PR just to do style change.
ImpactX uses
CamelCaseconvention for file names and class names, rather thansnake_case.The names of all member variables should be prefixed with
m_. This is particularly useful to avoid capturing member variables by value in a lambda function, which causes the whole object to be copied to GPU when running on a GPU-accelerated architecture. This convention should be used for all new piece of code, and it should be applied progressively to old code.#includedirectives in C++ have a distinct order to avoid bugs, see the ImpactX repo structure for detailsFor all new code, we should avoid relying on
using namespace amrex;and all amrex types should be prefixed withamrex::. Inside limited scopes, AMReX type literals can be included withusing namespace amrex::literals;. Ideally, old code should be modified accordingly.
Testing
Preparation
Prepare for running tests of ImpactX by building ImpactX from source.
In order to run our tests, you need to have a few Python packages installed:
python3 -m pip install -U pip
python3 -m pip install -U build packaging setuptools wheel pytest
python3 -m pip install -r examples/requirements.txt
Further Options
help:
ctest --test-dir build --helplist all tests:
ctest --test-dir build -Nonly run tests that have “FODO” in their name:
ctest --test-dir build -R FODO
Documentation
Doxygen documentation
WarpX uses a Doxygen documentation. Whenever you create a new class, please document it where it is declared (typically in the header file):
/** A brief title
*
* few-line description explaining the purpose of my_class.
*
* If you are kind enough, also quickly explain how things in my_class work.
* (typically a few more lines)
*/
class my_class
{ ... }
Doxygen reads this docstring, so please be accurate with the syntax! See Doxygen manual for more information. Similarly, please document functions when you declare them (typically in a header file) like:
/** A brief title
*
* few-line description explaining the purpose of my_function.
*
* \param[in,out] my_int a pointer to an integer variable on which
* my_function will operate.
* \return what is the meaning and value range of the returned value
*/
int my_class::my_function(int* my_int);
An online version of this documentation is linked here.
Breathe documentation
Your Doxygen documentation is not only useful for people looking into the code, it is also part of the ImpactX online documentation based on Sphinx!
This is done using the Python module Breathe, that allows you to read Doxygen documentation dorectly in the source and include it in your Sphinx documentation, by calling Breathe functions.
For instance, the following line will get the Doxygen documentation for ImpactXParticleContainer in src/particles/ImpactXParticleContainer.H and include it to the html page generated by Sphinx:
-
class ImpactXParticleContainer : public amrex::ParticleContainer_impl<0, 0, RealSoA::nattribs, IntSoA::nattribs>
Beam Particles in ImpactX
This class stores particles, distributed over MPI ranks.
Building the documentation
To build the documentation on your local computer, you will need to install Doxygen as well as the Python module breathe.
First, change into docs/ and install the Python requirements:
cd docs/
pip install -U -r requirements.txt
You will also need Doxygen (macOS: brew install doxygen; Ubuntu: sudo apt install doxygen).
Then, to compile the documentation, use
make html
# This will first compile the Doxygen documentation (execute doxygen)
# and then build html pages from rst files using sphinx and breathe.
Open the created build/html/index.html file with your favorite browser.
Rebuild and refresh as needed.
ImpactX Structure
Repo Organization
All the ImpactX source code is located in src/.
All sub-directories have a pretty straightforward name.
Here is a visual representation of the repository structure.
Code organization
The main ImpactX class is ImpactX, implemented in src/ImpactX.cpp.
Build System
ImpactX uses the CMake build system generator.
Each sub-folder contains a file CMakeLists.txt with the names of the source files (.cpp) that are added to the build.
Do not list header files (.H) here.
C++ Includes
All ImpactX header files need to be specified relative to the src/ directory.
e.g.
#include "Utils/ImpactXConst.H"files in the same directory as the including header-file can be included with
#include "FileName.H"
By default, in a MyName.cpp source file we do not include headers already included in MyName.H. Besides this exception, if a function or a class
is used in a source file, the header file containing its declaration must be included, unless the inclusion of a facade header is more appropriate. This is
sometimes the case for AMReX headers. For instance AMReX_GpuLaunch.H is a façade header for AMReX_GpuLaunchFunctsC.H and AMReX_GpuLaunchFunctsG.H, which
contain respectively the CPU and the GPU implemetation of some methods, and which should not be included directly.
Whenever possible, forward declarations headers are included instead of the actual headers, in order to save compilation time (see dedicated section below). In ImpactX forward
declaration headers have the suffix *_fwd.H, while in AMReX they have the suffix *Fwd.H.
The include order (see PR #874 and PR #1947) and proper quotation marks are:
In a MyName.cpp file:
#include "MyName.H"(its header) then(further) ImpactX header files
#include "..."thenImpactX forward declaration header files
#include "..._fwd.H"AMReX header files
#include <...>thenAMReX forward declaration header files
#include <...Fwd.H>thenPICSAR header files
#include <...>thenother third party includes
#include <...>thenstandard library includes, e.g.
#include <vector>
In a MyName.H file:
#include "MyName_fwd.H"(the corresponding forward declaration header, if it exists) thenImpactX header files
#include "..."thenImpactX forward declaration header files
#include "..._fwd.H"AMReX header files
#include <...>thenAMReX forward declaration header files
#include <...Fwd.H>thenPICSAR header files
#include <...>thenother third party includes
#include <...>thenstandard library includes, e.g.
#include <vector>
Each of these groups of header files should ideally be sorted alphabetically, and a blank line should be placed between the groups.
For details why this is needed, please see PR #874, PR #1947, the LLVM guidelines, and include-what-you-use.
Forward Declaration Headers
Forward declarations can be used when a header file needs only to know that a given class exists, without any further detail (e.g., when only a pointer to an instance of
that class is used). Forward declaration headers are a convenient way to organize forward declarations. If a forward declaration is needed for a given class MyClass, declared in MyClass.H,
the forward declaration should appear in a header file named MyClass_fwd.H, placed in the same folder containing MyClass.H. As for regular header files, forward declaration headers must have
include guards. Below we provide a simple example:
MyClass_fwd.H:
#ifndef MY_CLASS_FWD_H
#define MY_CLASS_FWD_H
class MyClass;
#endif //MY_CLASS_FWD_H
MyClass.H:
#ifndef MY_CLASS_H
#define MY_CLASS_H
#include "MyClass_fwd.H"
#include "someHeader.H"
class MyClass{/* stuff */};
#endif //MY_CLASS_H
MyClass.cpp:
#include "MyClass.H"
class MyClass{/* stuff */};
Usage: in SimpleUsage.H
#include "MyClass_fwd.H"
#include <memory>
/* stuff */
std::unique_ptr<MyClass> p_my_class;
/* stuff */
Implementation Details
Note
TODO :-)
C++ Objects & Functions
We generate the documentation of C++ objects and functions from our C++ source code by adding Doxygen strings.
Our Doxygen C++ API documentation in classic formatting is located here.
Python interface
Note
TODO :-)
Debugging the code
Sometimes, the code does not give you the result that you are expecting. This can be due to a variety of reasons, from misunderstandings or changes in the input parameters, system specific quirks, or bugs. You might also want to debug your code as you implement new features in ImpactX during development.
This section gives a step-by-step guidance on how to systematically check what might be going wrong.
Debugging Workflow
Try the following steps to debug a simulation:
Check the output text file, usually called
output.txt: are there warnings or errors present?On an HPC system, look for the job output and error files, usually called
ImpactX.e...andImpactX.o.... Read long messages from the top and follow potential guidance.If your simulation already created output data files: Check if they look reasonable before the problem occurred; are the initial conditions of the simulation as you expected? Do you spot numerical artifacts or instabilities that could point to missing resolution or unexpected/incompatible numerical parameters?
Did the job output files indicate a crash? Check the
Backtrace.<mpirank>files for the location of the code that triggered the crash. Backtraces are read from bottom (high-level) to top (most specific line that crashed).In case of a crash, Backtraces can be more detailed if you re-compile with debug flags: for example, try compiling with
-DCMAKE_BUILD_TYPE=RelWithDebInfo(some slowdown) or even-DCMAKE_BUILD_TYPE=Debug(this will make the simulation way slower) and rerun.If debug builds are too costly, try instead compiling with
-DAMReX_ASSERTIONS=ONto activate more checks and rerun.If the problem looks like a memory violation, this could be from an invalid field or particle index access. Try compiling with
-DAMReX_BOUND_CHECK=ON(this will make the simulation very slow), and rerun.If the problem looks like a random memory might be used, try initializing memory with signaling Not-a-Number (NaN) values through the runtime option
fab.init_snan = 1. Further useful runtime options areamrex.fpe_trap_invalid,amrex.fpe_trap_zeroandamrex.fpe_trap_overflow(see details in the AMReX link below).On Nvidia GPUs, if you suspect the problem might be a race condition due to a missing host / device synchronization, set the environment variable
export CUDA_LAUNCH_BLOCKING=1and rerun.Consider simplifying your input options and re-adding more options after having found a working baseline.
Fore more information, see also the AMReX Debugging Manual.
Last but not least: the community of ImpactX developers and users can help if you get stuck. Collect your above findings, describe where and what you are running and how you installed the code, describe the issue you are seeing with details and input files used and what you already tried. Can you reproduce the problem with a smaller setup (less parallelism and/or less resolution)? Report these details in a ImpactX GitHub issue.
Debuggers
See the AMReX debugger section on additional runtime parameters to
disable backtraces
rethrow exceptions
avoid AMReX-level signal handling
You will need to set those runtime options to work directly with debuggers.
Maintenance
Dependencies & Releases
Update ImpactX’ Core Dependencies
ImpactX has direct dependencies on AMReX and WarpX, which we periodically update.
The following scripts automate this workflow, in case one needs a newer commit of AMReX or WarpX between releases:
Note
./Tools/Release/updateAMReX.py
./Tools/Release/updateWarpX.py
Create a new ImpactX release
ImpactX has one release per month.
The version number is set at the beginning of the month and follows the format YY.MM.
In order to create a GitHub release, you need to:
Create a new branch from
developmentand update the version number in all source files. We usually wait for the AMReX release to be tagged first, then we also point to its tag.There is a script for updating core dependencies of ImpactX and the ImpactX version:
./Tools/Release/updateAMReX.py ./Tools/Release/updateWarpX.py ./Tools/Release/newVersion.shFor a ImpactX release, ideally a git tag of AMReX & WarpX shall be used instead of an unnamed commit.
Then open a PR, wait for tests to pass and then merge.
Local Commit (Optional): at the moment,
@ax3lis managing releases and signs tags (naming:YY.MM) locally with his GPG key before uploading them to GitHub.Publish: On the GitHub Release page, create a new release via
Draft a new release. Either select the locally created tag or create one online (naming:YY.MM) on the merged commit of the PR from step 1.In the release description, please specify the compatible versions of dependencies (see previous releases), and provide info on the content of the release. In order to get a list of PRs merged since last release, you may run
git log <last-release-tag>.. --format='- %s'Optional/future: create a
release-<version>branch, write a changelog, and backport bug-fixes for a few days.
Epilogue
Glossary
In daily communication, we tend to abbreviate a lot of terms. It is important to us to make it easy to interact with the ImpactX community and thus, this list shall help to clarify often used terms.
Please see: https://warpx.readthedocs.io/en/latest/glossary.html
Funding and Acknowledgements
This work was supported by the Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under U.S. Department of Energy Contract No. DE-AC02-05CH11231.
ImpactX is supported by the CAMPA collaboration, a project of the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research and Office of High Energy Physics, Scientific Discovery through Advanced Computing (SciDAC) program.
We acknowledge all the contributors and users of the ImpactX community who participate to the code quality with valuable code improvement and important feedback.