Add Example

docs/source/usage/examples.rst

@@ -70,6 +70,16 @@ Beam Distributions
 
    examples/distgen/README
 
+
+Channels & Rings
+----------------
+
+.. toctree::
+   :maxdepth: 1
+
+   examples/fodo_channel/README.rst
+
+
 Lattice Design & Optimization
 -----------------------------
 

examples/CMakeLists.txt

@@ -219,6 +219,23 @@ add_impactx_test(FODO.py.MPI
     examples/fodo/plot_fodo.py
 )
 
+# FODO Channel ################################################################
+#
+add_impactx_test(FODO_channel
+        examples/fodo_channel/input_fodo.in
+        OFF  # ImpactX MPI-parallel
+        examples/fodo_channel/analysis_fodo.py
+        examples/fodo_channel/plot_fodo.py
+)
+add_impactx_test(FODO_channel.py
+        examples/fodo_channel/run_fodo.py
+        OFF  # ImpactX MPI-parallel
+        examples/fodo_channel/analysis_fodo.py
+        examples/fodo_channel/plot_fodo.py
+)
+label_impactx_test(FODO_channel slow)
+label_impactx_test(FODO_channel.py slow)
+
 # Chicane #####################################################################
 #
 add_impactx_test(chicane

examples/fodo_channel/README.rst

@@ -0,0 +1,74 @@
+.. _examples-fodo-channel:
+
+FODO Channel
+============
+
+A 300m channel of 100 stable FODO cells (3m each) with a zero-current phase advance of 67.8 degrees.
+
+The matched Twiss parameters at entry are:
+
+* :math:`\beta_\mathrm{x} = 2.82161941` m
+* :math:`\alpha_\mathrm{x} = -1.59050035`
+* :math:`\beta_\mathrm{y} = 2.82161941` m
+* :math:`\alpha_\mathrm{y} = 1.59050035`
+
+We use a 2 GeV electron beam with initial unnormalized rms emittance of 2 nm.
+
+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 ``cycle_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 transversal emittance evolution (preserved)

examples/fodo_channel/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/input_fodo.in

@@ -0,0 +1,60 @@
+###############################################################################
+# Particle Beam(s)
+###############################################################################
+beam.npart = 10000
+beam.units = static
+beam.kin_energy = 2.0e3
+beam.charge = 1.0e-9
+beam.particle = electron
+beam.distribution = waterbag_from_twiss
+beam.alphaX = -1.5905003499999992
+beam.alphaY = 1.5905003499999992
+beam.alphaT = 0.0
+beam.betaX = 2.8216194100262637
+beam.betaY = 2.8216194100262637
+beam.betaT = 0.5
+beam.emittX = 2e-09
+beam.emittY = 2e-09
+beam.emittT = 2e-06
+
+
+###############################################################################
+# Beamline: lattice elements and segments
+###############################################################################
+lattice.elements = monitor drift1 quad1 drift2 quad2 drift3
+lattice.nslice = 5
+lattice.periods = 101  # FODO channel of 101 periods
+
+monitor.type = beam_monitor
+monitor.cycle_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