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#!/usr/bin/env python3
#
# --- Analysis script for the hybrid-PIC example of ion beam R instability.
import dill
import h5py
import matplotlib
import matplotlib.pyplot as plt
import numpy as np
from pywarpx import picmi
constants = picmi.constants
matplotlib.rcParams.update({'font.size': 20})
# load simulation parameters
with open(f'sim_parameters.dpkl', 'rb') as f:
sim = dill.load(f)
if sim.resonant:
resonant_str = 'resonant'
else:
resonant_str = 'non resonant'
data = np.loadtxt("diags/field_data.txt", skiprows=1)
if sim.dim == 1:
field_idx_dict = {'z': 4, 'By': 8}
else:
field_idx_dict = {'z': 2, 'By': 3}
step = data[:,0]
num_steps = len(np.unique(step))
# get the spatial resolution
resolution = len(np.where(step == 0)[0]) - 1
# reshape to separate spatial and time coordinates
sim_data = data.reshape((num_steps, resolution+1, data.shape[1]))
z_grid = sim_data[1, :, field_idx_dict['z']]
idx = np.argsort(z_grid)[1:]
dz = np.mean(np.diff(z_grid[idx]))
dt = np.mean(np.diff(sim_data[:,0,1]))
data = np.zeros((num_steps, resolution))
for i in range(num_steps):
data[i,:] = sim_data[i,idx,field_idx_dict['By']]
print(f"Data file contains {num_steps} time snapshots.")
print(f"Spatial resolution is {resolution}")
# Create the stack time plot
fig, ax1 = plt.subplots(1, 1, figsize=(10, 5))
max_val = np.max(np.abs(data[:,:]/sim.B0))
extent = [0, sim.Lz/sim.l_i, 0, num_steps*dt*sim.w_ci] # num_steps*dt/sim.t_ci]
im = ax1.imshow(
data[:,:]/sim.B0, extent=extent, origin='lower',
cmap='seismic', vmin=-max_val, vmax=max_val, aspect="equal",
)
# Colorbar
fig.subplots_adjust(right=0.825)
cbar_ax = fig.add_axes([0.85, 0.2, 0.03, 0.6])
fig.colorbar(im, cax=cbar_ax, orientation='vertical', label='$B_y/B_0$')
ax1.set_xlabel("$x/l_i$")
ax1.set_ylabel("$t \Omega_i$ (rad)")
ax1.set_title(f"Ion beam R instability - {resonant_str} case")
plt.savefig(f"diags/ion_beam_R_instability_{resonant_str}_eta_{sim.eta}_substeps_{sim.substeps}.png")
plt.close()
if sim.resonant:
# Plot the 4th, 5th and 6th Fourier modes
field_kt = np.fft.fft(data[:, :], axis=1)
k = 2*np.pi * np.fft.fftfreq(resolution, dz) * sim.l_i
t_grid = np.arange(num_steps)*dt*sim.w_ci
plt.plot(t_grid, np.abs(field_kt[:, 4] / sim.B0), 'r', label=f'm = 4, $kl_i={k[4]:.2f}$')
plt.plot(t_grid, np.abs(field_kt[:, 5] / sim.B0), 'b', label=f'm = 5, $kl_i={k[5]:.2f}$')
plt.plot(t_grid, np.abs(field_kt[:, 6] / sim.B0), 'k', label=f'm = 6, $kl_i={k[6]:.2f}$')
# The theoretical growth rates for the 4th, 5th and 6th Foruier modes of
# the By-field was obtained from Fig. 12a of Munoz et al.
# Note the rates here are gamma / w_ci
gamma4 = 0.1915611861780133
gamma5 = 0.20087036355662818
gamma6 = 0.17123024228396777
# Draw the line of best fit with the theoretical growth rate (slope) in the
# window t*w_ci between 10 and 40
idx = np.where((t_grid > 10) & (t_grid < 40))
t_points = t_grid[idx]
A4 = np.exp(np.mean(np.log(np.abs(field_kt[idx, 4] / sim.B0)) - t_points*gamma4))
plt.plot(t_points, A4*np.exp(t_points*gamma4), 'r--', lw=3)
A5 = np.exp(np.mean(np.log(np.abs(field_kt[idx, 5] / sim.B0)) - t_points*gamma5))
plt.plot(t_points, A5*np.exp(t_points*gamma5), 'b--', lw=3)
A6 = np.exp(np.mean(np.log(np.abs(field_kt[idx, 6] / sim.B0)) - t_points*gamma6))
plt.plot(t_points, A6*np.exp(t_points*gamma6), 'k--', lw=3)
plt.grid()
plt.legend()
plt.yscale('log')
plt.ylabel('$|B_y/B_0|$')
plt.xlabel('$t\Omega_i$ (rad)')
plt.tight_layout()
plt.savefig(f"diags/ion_beam_R_instability_{resonant_str}_eta_{sim.eta}_substeps_{sim.substeps}_low_modes.png")
plt.close()
# check if the growth rate matches expectation
m4_rms_error = np.sqrt(np.mean(
(np.abs(field_kt[idx, 4] / sim.B0) - A4*np.exp(t_points*gamma4))**2
))
m5_rms_error = np.sqrt(np.mean(
(np.abs(field_kt[idx, 5] / sim.B0) - A5*np.exp(t_points*gamma5))**2
))
m6_rms_error = np.sqrt(np.mean(
(np.abs(field_kt[idx, 6] / sim.B0) - A6*np.exp(t_points*gamma6))**2
))
print("Growth rate RMS errors:")
print(f" m = 4: {m4_rms_error:.3e}")
print(f" m = 5: {m5_rms_error:.3e}")
print(f" m = 6: {m6_rms_error:.3e}")
if not sim.test:
with h5py.File('diags/Python_hybrid_PIC_plt/openpmd_004000.h5', 'r') as data:
timestep = str(np.squeeze([key for key in data['data'].keys()]))
z = np.array(data['data'][timestep]['particles']['ions']['position']['z'])
vy = np.array(data['data'][timestep]['particles']['ions']['momentum']['y'])
w = np.array(data['data'][timestep]['particles']['ions']['weighting'])
fig, ax1 = plt.subplots(1, 1, figsize=(10, 5))
im = ax1.hist2d(
z/sim.l_i, vy/sim.M/sim.vA, weights=w, density=True,
range=[[0, 250], [-10, 10]], bins=250, cmin=1e-5
)
# Colorbar
fig.subplots_adjust(bottom=0.15, right=0.815)
cbar_ax = fig.add_axes([0.83, 0.2, 0.03, 0.6])
fig.colorbar(im[3], cax=cbar_ax, orientation='vertical', format='%.0e', label='$f(z, v_y)$')
ax1.set_xlabel("$x/l_i$")
ax1.set_ylabel("$v_{y}/v_A$")
ax1.set_title(f"Ion beam R instability - {resonant_str} case")
plt.savefig(f"diags/ion_beam_R_instability_{resonant_str}_eta_{sim.eta}_substeps_{sim.substeps}_core_phase_space.png")
plt.close()
with h5py.File('diags/Python_hybrid_PIC_plt/openpmd_004000.h5', 'r') as data:
timestep = str(np.squeeze([key for key in data['data'].keys()]))
z = np.array(data['data'][timestep]['particles']['beam_ions']['position']['z'])
vy = np.array(data['data'][timestep]['particles']['beam_ions']['momentum']['y'])
w = np.array(data['data'][timestep]['particles']['beam_ions']['weighting'])
fig, ax1 = plt.subplots(1, 1, figsize=(10, 5))
im = ax1.hist2d(
z/sim.l_i, vy/sim.M/sim.vA, weights=w, density=True,
range=[[0, 250], [-10, 10]], bins=250, cmin=1e-5
)
# Colorbar
fig.subplots_adjust(bottom=0.15, right=0.815)
cbar_ax = fig.add_axes([0.83, 0.2, 0.03, 0.6])
fig.colorbar(im[3], cax=cbar_ax, orientation='vertical', format='%.0e', label='$f(z, v_y)$')
ax1.set_xlabel("$x/l_i$")
ax1.set_ylabel("$v_{y}/v_A$")
ax1.set_title(f"Ion beam R instability - {resonant_str} case")
plt.savefig(f"diags/ion_beam_R_instability_{resonant_str}_eta_{sim.eta}_substeps_{sim.substeps}_beam_phase_space.png")
plt.show()
if sim.test:
# physics based check - these error tolerances are not set from theory
# but from the errors that were present when the test was created. If these
# assert's fail, the full benchmark should be rerun (same as the test but
# without the `--test` argument) and the growth rates (up to saturation)
# compared to the theoretical ones to determine if the physics test passes.
# At creation, the full test had the following errors when ran on 8 procs:
# m4_rms_error = 4.476; m5_rms_error = 9.211; m6_rms_error = 3.252
assert m4_rms_error < 1.55
assert m5_rms_error < 0.75
assert m6_rms_error < 0.40
# checksum check
import os
import sys
sys.path.insert(1, '../../../../warpx/Regression/Checksum/')
import checksumAPI
# this will be the name of the plot file
fn = sys.argv[1]
test_name = os.path.split(os.getcwd())[1]
checksumAPI.evaluate_checksum(test_name, fn)
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