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 \(\lambda_x\), \(\lambda_y\), \(\lambda_t\), \(\epsilon_x\), \(\epsilon_y\), 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.
#!/usr/bin/env python3
#
# Copyright 2022-2023 ImpactX contributors
# Authors: Chad Mitchell, Axel Huebl
# License: BSD-3-Clause-LBNL
#
# -*- coding: utf-8 -*-
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 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(
lambdaX=5.0e-6, # 5 um
lambdaY=8.0e-6, # 8 um
lambdaT=0.0599584916, # 200 ps
lambdaPx=2.5543422003e-9, # exn = 50 pm-rad
lambdaPy=1.5964638752e-9, # eyn = 50 pm-rad
lambdaPt=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
sim.finalize()
###############################################################################
# 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.lambdaX = 5.0e-6 #5 um
beam.lambdaY = 8.0e-6 #8 um
beam.lambdaT = 0.0599584916 #200 ps
beam.lambdaPx = 2.5543422003e-9 #exn = 50 pm-rad
beam.lambdaPy = 1.5964638752e-9 #eyn = 50 pm-rad
beam.lambdaPt = 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
#!/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,
)