Python Restart Test

examples/CMakeLists.txt

@@ -303,6 +303,18 @@ label_impactx_test(FODO_channel slow)
 label_impactx_test(FODO_channel.py slow)
 
 
+# FODO Channel Restart ########################################################
+#
+add_impactx_test(FODO_channel_restart.py
+    examples/fodo_channel_restart/run_fodo.py
+    OFF  # ImpactX MPI-parallel
+    examples/fodo_channel_restart/analysis_fodo.py
+    examples/fodo_channel_restart/plot_fodo.py
+)
+label_impactx_test(FODO_channel.py slow)
+set_property(TEST FODO_channel_restart.py.run APPEND PROPERTY DEPENDS "FODO_channel.py.run")
+
+
 # Chicane #####################################################################
 #
 add_impactx_test(chicane

examples/fodo_channel_restart/README.rst

@@ -0,0 +1,65 @@
+.. _examples-fodo-channel-restart:
+
+FODO Channel Restart
+====================
+
+This example takes the last output of the :ref:`FODO Channel <examples-fodo-channel>` example, loads the beam back into a new simulation and continues the simulation for another 100 FODO periods.
+
+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 :math:`\lambda_x`, :math:`\lambda_y`, :math:`\lambda_t`, :math:`\epsilon_x`, :math:`\epsilon_y`, and :math:`\epsilon_t` must agree with nominal values.
+This test also demonstrates the ``period_sample_intervals`` capability of our beam monitor diagnostics, only creating output every 10th FODO cell
+
+
+Run
+---
+
+This example can be run **either** as:
+
+* **Python** script: ``python3 run_fodo.py`` or
+* ImpactX **executable** using an input file: ``impactx input_fodo.in``
+
+For `MPI-parallel <https://www.mpi-forum.org>`__ runs, prefix these lines with ``mpiexec -n 4 ...`` or ``srun -n 4 ...``, depending on the system.
+
+.. tab-set::
+
+   .. tab-item:: Python: Script
+
+       .. literalinclude:: run_fodo.py
+          :language: python3
+          :caption: You can copy this file from ``examples/fodo/run_fodo.py``.
+
+   .. tab-item:: Executable: Input File
+
+       .. literalinclude:: input_fodo.in
+          :language: ini
+          :caption: You can copy this file from ``examples/fodo/input_fodo.in``.
+
+
+Analyze
+-------
+
+We run the following script to analyze correctness:
+
+.. dropdown:: Script ``analysis_fodo.py``
+
+   .. literalinclude:: analysis_fodo.py
+      :language: python3
+      :caption: You can copy this file from ``examples/fodo/analysis_fodo.py``.
+
+
+Visualize
+---------
+
+You can run the following script to visualize the beam evolution over time:
+
+.. dropdown:: Script ``plot_fodo.py``
+
+   .. literalinclude:: plot_fodo.py
+      :language: python3
+      :caption: You can copy this file from ``examples/fodo/plot_fodo.py``.
+
+.. figure:: https://gist.githubusercontent.com/ax3l/8ae7dcb9e07c361e002fa56d6b16cb16/raw/cc952670bb946cd7a62282bc7aa3f03f3d5faa16/fodo_channel.png
+   :alt: preserved emittance in the FODO channel.
+
+   FODO transverse emittance evolution (preserved)

examples/fodo_channel_restart/analysis_fodo.py

@@ -0,0 +1,105 @@
+#!/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)
+
+# compare beamline length: 300m
+assert np.isclose(
+    300.0, series.iterations[last_step].particles["beam"].get_attribute("z_ref")
+)
+# compare beam monitor outputs: 10 (every 10th FODO element + 1)
+assert len(series.iterations) == 11
+
+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 = 2.2 * 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 = 2.2 * 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,
+)

examples/fodo_channel_restart/input_fodo.in

@@ -0,0 +1,59 @@
+###############################################################################
+# Reference Particle
+###############################################################################
+beam.kin_energy = 2.0e3
+beam.particle = electron
+
+# ignored
+beam.charge = 1.0e-9
+beam.units = static
+beam.distribution = empty
+
+
+###############################################################################
+# Beamline: lattice elements and segments
+###############################################################################
+lattice.elements = source line
+lattice.nslice = 5
+
+source.type = source
+source.distribution = openPMD
+source.openpmd_path = "../FODO.channel/diags/openPMD/monitor.h5"
+
+line.type = line
+line.repeat = 101  # FODO channel of 101 periods
+line.elements = monitor drift1 quad1 drift2 quad2 drift3
+
+monitor.type = beam_monitor
+monitor.period_sample_intervals = 10
+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 = false

examples/fodo_channel_restart/plot_fodo.py

@@ -0,0 +1,132 @@
+#!/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
+import openpmd_api as io
+import pandas as pd
+from matplotlib.ticker import MaxNLocator
+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, 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)
+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_emittance_x = ax1.plot(z, emittance_x, ".-", label=r"$\epsilon_x$")
+im_emittance_y = ax1.plot(z, emittance_y, ".-", label=r"$\epsilon_y$")
+
+ax1.legend()
+ax1.set_xlabel(r"$z$ [m]")
+ax1.set_ylabel(r"$\epsilon_{x,y}$ [nm]")
+ax1.set_ylim([1.98, 2.03])
+ax1.xaxis.set_major_locator(MaxNLocator(integer=True))
+plt.tight_layout()
+if args.save_png:
+    plt.savefig("fodo_lambda.png")
+else:
+    plt.show()