Example

docs/source/usage/examples.rst

@@ -83,7 +83,7 @@ Channels & Rings
    :maxdepth: 1
 
    examples/fodo_channel/README.rst
-   examples/fodo_channel_restart/README.rst
+   examples/solenoid_restart/README.rst
 
 
 Lattice Design & Optimization

examples/CMakeLists.txt

@@ -624,6 +624,25 @@ add_impactx_test(solenoid.MADX.py
 )
 
 
+# Ideal, Hard-Edge Solenoid (Restart + 270 degrees) ###########################
+#
+# w/o space charge
+add_impactx_test(solenoid.restart
+    examples/solenoid_restart/input_solenoid.in
+    OFF  # ImpactX MPI-parallel
+    examples/solenoid_restart/analysis_solenoid.py
+    OFF  # no plot script yet
+)
+add_impactx_test(solenoid.restart.py
+    examples/solenoid_restart/run_solenoid.py
+    OFF  # ImpactX MPI-parallel
+    examples/solenoid_restart/analysis_solenoid.py
+    OFF  # no plot script yet
+)
+set_property(TEST solenoid.restart.run APPEND PROPERTY DEPENDS "solenoid.run")
+set_property(TEST solenoid.restart.py.run APPEND PROPERTY DEPENDS "solenoid.py.run")
+
+
 # Pole-face rotation ##########################################################
 #
 # w/o space charge

examples/solenoid_restart/README.rst

@@ -0,0 +1,50 @@
+.. _examples-solenoid-restart:
+
+Solenoid channel (Restart)
+==========================
+
+This is the same example as the :ref:`proton beam undergoing 90 deg X-Y rotation in an ideal solenoid channel <examples-solenoid>`, but it restarts the resulting beam and rotates it another 3 channel periods to the initial X-Y conditions.
+
+The solenoid magnetic field corresponds to B = 2 T.
+
+The second moments of the particle distribution after the solenoid channel are rotated by 90 (start) + 270 = 360 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 :math:`\sigma_x`, :math:`\sigma_y`, :math:`\sigma_t`, :math:`\epsilon_x`, :math:`\epsilon_y`, and :math:`\epsilon_t` must agree with nominal values.
+
+
+Run
+---
+
+This example can be run **either** as:
+
+* **Python** script: ``python3 run_solenoid.py`` or
+* ImpactX **executable** using an input file: ``impactx input_solenoid.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_solenoid.py
+          :language: python3
+          :caption: You can copy this file from ``examples/solenoid_restart/run_solenoid.py``.
+
+   .. tab-item:: Executable: Input File
+
+       .. literalinclude:: input_solenoid.in
+          :language: ini
+          :caption: You can copy this file from ``examples/solenoid_restart/input_solenoid.in``.
+
+
+Analyze
+-------
+
+We run the following script to analyze correctness:
+
+.. dropdown:: Script ``analysis_solenoid.py``
+
+   .. literalinclude:: analysis_solenoid.py
+      :language: python3
+      :caption: You can copy this file from ``examples/solenoid_restart/analysis_solenoid.py``.

examples/solenoid_restart/analysis_solenoid.py

@@ -0,0 +1,96 @@
+#!/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)
+first_step = list(series.iterations)[0]
+last_step = list(series.iterations)[-1]
+initial = series.iterations[first_step].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 = 1.3 * 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,
+)
+
+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 = 2.3 * 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],
+    [
+        1.559531175539e-3,
+        2.205510139392e-3,
+        1.0e-6,
+        2.0e-6,
+        1.0e-6,
+    ],
+    rtol=rtol,
+    atol=atol,
+)

examples/solenoid_restart/input_solenoid.in

@@ -0,0 +1,41 @@
+###############################################################################
+# Reference Particle
+###############################################################################
+beam.kin_energy = 250.0
+beam.particle = proton
+
+# ignored
+beam.charge = 1.0e-9
+beam.units = static
+beam.distribution = empty
+
+
+###############################################################################
+# Beamline: lattice elements and segments
+###############################################################################
+lattice.elements = source monitor sol1 sol1 sol1 monitor
+lattice.nslice = 1
+
+source.type = source
+source.distribution = openPMD
+source.openpmd_path = "../solenoid/diags/openPMD/monitor.h5"
+
+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

examples/solenoid_restart/run_solenoid.py

@@ -0,0 +1,54 @@
+#!/usr/bin/env python3
+#
+# Copyright 2022-2023 ImpactX contributors
+# Authors: Marco Garten, Axel Huebl, Chad Mitchell
+# License: BSD-3-Clause-LBNL
+#
+# -*- coding: utf-8 -*-
+
+from impactx import ImpactX, elements, push
+
+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
+
+#   reference particle
+pc = sim.particle_container()
+ref = pc.ref_particle()
+ref.set_charge_qe(1.0).set_mass_MeV(938.27208816).set_kin_energy_MeV(kin_energy_MeV)
+
+#   load particle bunch from file
+push(pc, elements.Source("openPMD", "../solenoid.py/diags/openPMD/monitor.h5"))
+
+# add beam diagnostics
+monitor = elements.BeamMonitor("monitor", backend="h5")
+
+# design the accelerator lattice
+sol1 = elements.Sol(name="sol1", ds=3.820395, ks=0.8223219329893234)
+sim.lattice.extend(
+    [
+        monitor,
+        sol1,
+        sol1,
+        sol1,
+        monitor,
+    ]
+)
+
+# run simulation
+sim.track_particles()
+
+# clean shutdown
+sim.finalize()