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, or 3

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_size to False.

Note: particles that move outside the simulation domain are removed.

property prob_relative

This is a list with amr.max_level + 1 entries.

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, 1.2 means the mesh will span 10% above and 10% below the beam; 1.0 means the beam is exactly covered with the mesh.

Default: [3.0 1.0 1.0 ...]. When set, turns dynamic_size to True.

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: False).

Whether to calculate space charge effects.

property mlmg_relative_tolerance

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.

property mlmg_absolute_tolerance

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.

property mlmg_max_iters

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.

property mlmg_verbosity

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.

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.

property particle_lost_diagnostics_backend

Diagnostics for particles lost in apertures. See the BeamMonitor element 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.elements for 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 1 to cause the simulation to fail after its completion if there were unused parameters. (default: 0 for 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: 0 for false) It is mainly intended for debug purposes, in case a simulation crashes before a global warning report can be printed.

property verbose

Controls how much information is printed to the terminal, when running ImpactX. 0 for silent, higher is more verbose. Default is 1.

evolve()

Run the main simulation loop for a number of steps.

resize_mesh()

Resize the mesh domain based on the dynamic_size and 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/False

Note

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_THREADS to 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(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

  • 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

impactx.RefPart

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 BEAM entry

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(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)

A 6D Gaussian distribution.

Parameters

  • lambdax – phase space position axis intercept; for zero correlation, these are the related RMS sizes (in meters)

  • lambday – see lambdax

  • lambdat – see lambdax

  • lambdapx – phase space momentum axis intercept; for zero correlation, these are the related normalized RMS momenta (in radians)

  • lambdapy – see lambdapx

  • lambdapt – see lambdapx

  • muxpx – correlation length-momentum

  • muypy – see muxpx

  • mutpt – see muxpx

class impactx.distribution.Kurth4D(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)

A 4D Kurth distribution transversely + a uniform distribution in t + a Gaussian distribution in pt.

class impactx.distribution.Kurth6D(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, 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(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)

A K-V distribution transversely + a uniform distribution in t + a Gaussian distribution in pt.

class impactx.distribution.None

This distribution sets all values to zero.

class impactx.distribution.Semigaussian(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)

A 6D Semi-Gaussian distribution (uniform in position, Gaussian in momentum).

class impactx.distribution.Triangle(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, 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(lambdax, lambday, lambdat, lambdapx, lambdapy, lambdapt, muxpx=0.0, muypy=0.0, mutpt=0.0)

A 6D Waterbag distribution.

class impactx.distribution.Thermal(k, kT, kT_halo, normalize, normalize_halo, halo)

A 6D stationary thermal or bithermal 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, dx=0, dy=0, rotation=0, 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

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

class impactx.elements.ConstF(ds, kx, ky, kt, dx=0, dy=0, rotation=0, 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.

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • 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, dx=0, dy=0, rotation=0)

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:

      1. Brown, SLAC Report No. 75 (1982).

    1. 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)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

class impactx.elements.Drift(ds, dx=0, dy=0, rotation=0, 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, dx=0, dy=0, rotation=0, 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

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

class impactx.elements.ExactDrift(ds, dx=0, dy=0, rotation=0, nslice=1)

A drift using the exact nonlinear transfer map.

Parameters

  • ds – Segment length in m

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

class impactx.elements.Kicker(xkick, ykick, units, dx=0, dy=0, rotation=0)

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, dx=0, dy=0, rotation=0)

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)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

class impactx.elements.NonlinearLens(knll, cnll, dx=0, dy=0, rotation=0)

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)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

class impactx.elements.BeamMonitor(name, backend='default', encoding='g')

A beam monitor, writing all beam particles at fixed s to openPMD files.

If the same element name is used multiple times, then an output series is created with multiple outputs.

The I/O backend for openPMD data dumps. bp is the ADIOS2 I/O library, h5 is the HDF5 format, and json is a simple text format. json only 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, json

  • encoding – openPMD iteration encoding: (v)ariable based, (f)ile based, (g)roup based (default)

property name

name of the series

property nonlinear_lens_invariants

Compute and output the invariants H and I within the nonlinear magnetic insert element

property alpha

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.

property beta

Twiss beta (in meters) 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.

property tn

Dimensionless strength of the IOTA nonlinear magnetic insert element used for computing H and I.

property cn

Scale factor (in meters^(1/2)) of the IOTA nonlinear magnetic insert element used for computing H and I.

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:

user_defined_function(pti: ImpactXParIter, refpart: RefPart)

This function is called repeatedly for all particle tiles or boxes in the beam particle container. Particles can be pushed and are relative to the reference particle

property ref_particle

This is a function hook for pushing the reference particle. This accepts a function or lambda with the following argument:

another_user_defined_function(refpart: RefPart)

This function is called for the reference particle as it passes through the element. The reference particle is updated before the beam particles are pushed.

class impactx.elements.Quad(ds, k, dx=0, dy=0, rotation=0, 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

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

class impactx.elements.ChrQuad(ds, k, units, dx=0, dy=0, rotation=0, 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

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

property k

quadrupole strength in 1/m^2 (or T/m)

property units

unit specification for quad strength

class impactx.elements.ChrPlasmaLens(ds, g, dx=0, dy=0, rotation=0, nslice=1)

An active cylindrically symmetric plasma lens, 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 –

    focusing strength in m^(-2) (if units = 0)

    = (azimuthal magnetic field gradient in T/m) / (rigidity in T-m)

    OR azimuthal magnetic field gradient in T/m (if units = 1)

  • units – specification of units for plasma lens focusing strength

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

property k

plasma lens focusing strength in 1/m^2 (or T/m)

property units

unit specification for plasma lens focusing strength

class impactx.elements.ChrAcc(ds, ez, bz, dx=0, dy=0, rotation=0, nslice=1)

Acceleration in a uniform field Ez, with a uniform solenoidal field Bz.

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) = (charge * electric field Ez in V/m) / (m*c^2)

  • bz – magnetic field strength in m^(-1) = (charge * magnetic field Bz in T) / (m*c)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

property ez

electric field strength in 1/m

property bz

magnetic field strength in 1/m

class impactx.elements.RFCavity(ds, escale, freq, phase, dx=0, dy=0, rotation=0, mapsteps=1, nslice=1)

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 float 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

  • cos_coefficients – array of float 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

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • mapsteps – 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, dx=0, dy=0, rotation=0, nslice=1)

An ideal sector bend.

Parameters

  • ds – Segment length in m.

  • rc – Radius of curvature in m.

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

class impactx.elements.ExactSbend(ds, phi, B, dx=0, dy=0, rotation=0, 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:

      1. Bruhwiler et al, in Proc. of EPAC 98, pp. 1171-1173 (1998).

    1. Forest et al, Part. Accel. 45, pp. 65-94 (1994).

Parameters

  • ds – Segment length in m.

  • phi – Bend angle in degrees.

  • 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.

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

class impactx.elements.Buncher(V, k, dx=0, dy=0, rotation=0)

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

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

class impactx.elements.ShortRF(V, freq, phase, dx=0, dy=0, rotation=0)

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)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

class impactx.elements.ChrUniformAcc(ds, k, dx=0, dy=0, rotation=0, 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)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • nslice – number of slices used for the application of space charge

class impactx.elements.SoftSolenoid(ds, bscale, cos_coefficients, sin_coefficients, dx=0, dy=0, rotation=0, mapsteps=1, 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 float cosine coefficients in Fourier expansion of on-axis magnetic field Bz (optional); default is a thin-shell model from DOI:10.1016/J.NIMA.2022.166706

  • sin_coefficients – array of float sine coefficients in Fourier expansion of on-axis magnetic field Bz (optional); default is a thin-shell model from DOI:10.1016/J.NIMA.2022.166706

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • mapsteps – 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, dx=0, dy=0, rotation=0, 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)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • 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

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

class impactx.elements.Aperture(xmax, ymax, shape='rectangular', dx=0, dy=0, rotation=0)

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"

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

property shape

aperture type (rectangular, elliptical)

property xmax

maximum horizontal coordinate

property ymax

maximum vertical coordinate

class impactx.elements.SoftQuadrupole(ds, gscale, cos_coefficients, sin_coefficients, dx=0, dy=0, rotation=0, mapsteps=1, 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 float cosine 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.pdf

  • sin_coefficients – array of float sine 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.pdf

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

  • mapsteps – 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, dx=0, dy=0, rotation=0)

A general thin dipole element.

Parameters

  • theta – Bend angle (degrees)

  • rc – Effective curvature radius (meters)

  • dx – horizontal translation error in m

  • dy – vertical translation error in m

  • rotation – rotation error in the transverse plane [degrees]

Reference:

    1. 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 –

impactx.coordinate_transformation(pc, direction)

Function to transform the coordinates of the particles in a particle container either to fixed \(t\) or to fixed \(s\).

Parameters

  • pc – impactx.particle_container whose particle coordinates are to be transformed.

  • direction – enumerated type impactx.TransformationDirection, indicates whether to transform to fixed \(s\) or fixed \(t\).