Turn-Dependend Element Changes

10 periods of drift elements, where each drift is a stand-in for a “turn” map. On each turn, the next turn map (drift) is modified based in particle properties.

A 2 GeV electron bunch with normalized transverse rms emittance of 50 pm.

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 as:

  • Python script: python3 run_turn_update.py or

For MPI-parallel runs, prefix these lines with mpiexec -n 4 ... or srun -n 4 ..., depending on the system.

Listing 227 You can copy this file from examples/turn_update/run_turn_update.py.
#!/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.space_charge = False
sim.slice_step_diagnostics = True
sim.tiny_profiler = False

# 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 = 1  # number of slices per ds in the element

bend = [
    monitor,
    elements.Drift(ds=1.0, nslice=ns, name="drift1"),
]

# assign a lattice segment
sim.lattice.extend(bend)
sim.periods = 10


# at the beginning of each period (e.g, turn or channel period), modify the lattice
def hook_before_period(sim):
    turn = sim.tracking_period
    step = sim.tracking_step
    print("- Before turn:")
    print(f"  Updating lattice at turn {turn}, step {step}", flush=True)

    beam = sim.particle_container()
    ref = beam.ref_particle()
    rbc = beam.beam_moments()
    print(
        f"  Beam at s={ref.s:.2f}m, t={ref.t:.2f}s with beta_x={rbc['beta_x']}m",
        flush=True,
    )

    if turn > 0:
        next_ds = 1.0 / ref.s
        print(f"  Updating next drift ds to: {next_ds:.2f}m", flush=True)
        sim.lattice.select(name="drift1")[0].ds = next_ds


def hook_before_element(sim):
    element = sim.tracking_element
    print("- Before element:")
    print(
        f"  Current element name: {element.name} with ds={element.ds:.2f}", flush=True
    )

    if element.name != "monitor":
        print(f"  Drift ds is: {element.ds:.2f}m", flush=True)


sim.hook["before_period"] = hook_before_period
sim.hook["before_element"] = hook_before_element

# run simulation
sim.track_particles()

# clean shutdown
sim.finalize()

Analyze

We run the following script to analyze correctness:

Script analysis_turn_update.py
Listing 228 You can copy this file from examples/turn_update/analysis_turn_update.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()
s_final = series.iterations[last_step].particles["beam"].get_attribute("s_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}"
    f"  s_final={s_final}"
)

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, s_final],
    [
        5.0e-6,
        8.0e-6,
        0.0599584916,
        1.277171100130637e-14,
        1.277171100130637e-14,
        5.396264243e-005,
        4.339439692724345,
    ],
    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],
    [
        5.0e-6,
        8.0e-6,
        0.0599584916,
        1.277171100130637e-14,
        1.277171100130637e-14,
        5.396264243e-005,
    ],
    rtol=rtol,
    atol=atol,
)