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@@ +#!/usr/bin/env python3 +# +# Copyright 2022 ImpactX contributors +# Authors: Axel Huebl, Christopher E. Mayes +# License: BSD-3-Clause-LBNL +# +# Benchmark as in Figure 1 of +# C. E. Mayes, R. D. Ryne, and D. C. Sagan, "3D Space Charge in BMAD," in proc. IPAC2018, +# DOI:10.18429/JACoW-IPAC2018-THPAK085 +# +# -*- coding: utf-8 -*- + +import matplotlib.pyplot as plt +import numpy as np +import pandas as pd + +import amrex.space3d as amr +from impactx import ImpactX, RefPart, distribution, elements + +# theory data from eq. (1) in Mayes, sampled to text files in +theory = pd.read_csv("Ex_Mayes.dat", header=0, sep=r"\s+") +x_theory = theory["x/sigmax"] + + +def run_and_plot(case, r, ax): + """Run ImpactX for a new r and plot + + Parameters + ---------- + case : string + case name + r : Float + aspect ratio = sigma_z / sigma_perp: range 0.1 to 10 + ax : matplotlib.axes + a figure axis to plot into + """ + sim = ImpactX() + + # set numerical parameters and IO control + sim.n_cell = [128, 128, 128] + sim.particle_shape = 2 # B-spline order + sim.space_charge = True + sim.dynamic_size = True + sim.poisson_solver = "fft" + sim.prob_relative = [1.01, 1.01] + + # beam diagnostics + sim.diagnostics = False + sim.slice_step_diagnostics = False + + # domain decomposition & space charge mesh + sim.init_grids() + + # load a cold 10 MeV electron beam + mass_MeV = 0.510998950 # electron mass in MeV/c^2 + energy_MeV = 1.000001 * mass_MeV # reference energy (total) + bunch_charge_C = 1.0e-9 # charge in C + npart = int(10000000) # number of macro particles + + # reference particle (Mayes Fig. 1 is for + charge) + ref = sim.particle_container().ref_particle() + kinetic_MeV = energy_MeV - mass_MeV + ref.set_charge_qe(1.0).set_mass_MeV(mass_MeV).set_kin_energy_MeV(kinetic_MeV) + + # particle bunch + sigma_r = 1.0e-3 # fixed at 1 mm + sigma_z = r * sigma_r + gamma = energy_MeV / mass_MeV + beta = (1.0 - (1.0 / gamma) ** 2) ** 0.5 + c0 = 2.99792458e8 # speed of light in m/s + sigma_t = sigma_z / (beta * gamma) # recall t is implicitly scaled by c0 + print(f"r={r} sigma_t={sigma_t}m") + + distr = distribution.Gaussian( + lambdaX=sigma_r, + lambdaY=sigma_r, + lambdaT=sigma_t, + lambdaPx=0.0, + lambdaPy=0.0, + lambdaPt=0.0, + ) + sim.add_particles(bunch_charge_C, distr, npart) + + # add beam diagnostics + monitor = elements.BeamMonitor("monitor", backend="h5") + + # design the accelerator lattice + sim.lattice.extend([monitor]) + + # run simulation + sim.evolve() + + # plotting + + # simulation data + F_x = sim.space_charge_field(lev=0, comp="x") # [V/m] in the lab frame + + gm = sim.Geom(lev=0) + dr = gm.data().CellSize() + dV = np.prod(dr) + + half_x, half_y, half_z = [n // 2 for n in sim.n_cell] # order: x,y,z + + # plot theory + p = ax.plot(x_theory, theory[case], label=case) # E_x(sigma_r) [MV/m] + line_color = p[0].get_color() + + # plot data slices + ng = F_x.n_grow_vect + q_e = -1.602176634e-19 + for mfi in F_x: + bx = mfi.validbox() + rbx = amr.RealBox(bx, dr, gm.ProbLo()) + + arr_np = F_x.array(mfi).to_numpy(copy=True) # indices: x, y, z, comp + + # crop off guard cells + arr_np = arr_np[ng[0] : -ng[0], ng[1] : -ng[1], ng[2] : -ng[2]] + + # shift box to zero-based local mfi index space + half_y_local = half_y - bx.lo_vect[1] + half_z_local = half_z - bx.lo_vect[2] + + # check if the current tile contains the half-y plane + if half_y_local < 0 or half_y >= bx.hi_vect[1]: + continue + # check if the current tile contains the half-z plane + if half_z_local < 0 or half_z >= bx.hi_vect[2]: + continue + + comp = 0 + lineout = arr_np[..., half_y_local, half_z_local, comp] # w/o guard, N + E_x = lineout / gamma / 1.0e6 # E_x(x[m]) [MV/m] + ax.plot( + np.linspace(rbx.lo(0) / sigma_r, rbx.hi(0) / sigma_r, E_x.shape[0]), + E_x, + "o", + markersize=2, + color=line_color, + ) + + # clean shutdown + del sim + + +f = plt.figure() +ax = f.gca() + +run_and_plot("r=0.1", 0.1, ax) +run_and_plot("r=0.2", 0.2, ax) +run_and_plot("r=0.5", 0.5, ax) +run_and_plot("r=1", 1, ax) +run_and_plot("r=10", 10, ax) + + +# Charge density (Gaussian, normalized) +def gauss(x): + return np.exp(-(x**2) / 2) + + +ax2 = ax.twinx() +ax2.fill_between(x_theory, 0, gauss(x_theory), color="gray", alpha=0.2) + +xmin = -6.0 +xmax = 6.0 +ymin = -6.0 +ymax = 6.0 +ax.set_xlim([xmin, xmax]) +ax.set_ylim([ymin, ymax]) +ax2.set_ylim([-1.2, 1.2]) +ax2.set_yticks([0, 0.5, 1.0]) + +# ax2.spines['right'].set_color('gray') +ax2.yaxis.label.set_color("gray") +ax2.tick_params(colors="gray", which="both") + +ax.set_xlabel(r"$x$ [$\sigma_x$]") +ax.set_ylabel(r"$E_x$ [MV/m]") +ax2.set_ylabel(r"charge density [arb. u.]") +ax.legend(loc="upper left") +plt.show() + +# clean shutdown +amr.finalize()