#!/usr/bin/env python3 # Copyright 2020 Andrew Myers, Axel Huebl, Luca Fedeli # Remi Lehe # # This file is part of WarpX. # # License: BSD-3-Clause-LBNL # This file is part of the WarpX automated test suite. It is used to test the # injection of a laser pulse from an external binary file. # # - Generate an input binary file with a gaussian laser pulse. # - Run the WarpX simulation for time T, when the pulse is fully injected # - Compute the theory for laser envelope at time T # - Compare theory and simulation, for both envelope and central frequency import glob import os import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt import numpy as np from scipy.signal import hilbert import yt ; yt.funcs.mylog.setLevel(50) #Maximum acceptable error for this test relative_error_threshold = 0.065 #Physical parameters um = 1.e-6 fs = 1.e-15 c = 299792458 #Parameters of the gaussian beam wavelength = 1.*um w0 = 6.*um tt = 10.*fs x_c = 0.*um t_c = 20.*fs foc_dist = 10*um E_max = 1e12 rot_angle = -np.pi/4.0 #Parameters of the tx grid x_l = -12.0*um x_r = 12.0*um x_points = 480 t_l = 0.0*fs t_r = 40.0*fs t_points = 400 tcoords = np.linspace(t_l, t_r, t_points) xcoords = np.linspace(x_l, x_r, x_points) def gauss(T,X,Y,opt): """Compute the electric field for a Gaussian laser pulse. This is used to write the binary input file. """ k0 = 2.0*np.pi/wavelength inv_tau2 = 1./tt/tt osc_phase = k0*c*(T-t_c) diff_factor = 1.0 + 1.0j* foc_dist * 2/(k0*w0*w0) inv_w_2 = 1.0/(w0*w0*diff_factor) pre_fact = np.exp(1.0j * osc_phase) if opt == '3d': pre_fact = pre_fact/diff_factor else: pre_fact = pre_fact/np.sqrt(diff_factor) exp_arg = - (X*X + Y*Y)*inv_w_2 - inv_tau2 * (T-t_c)*(T-t_c) return np.real(pre_fact * np.exp(exp_arg)) # Function for the envelope def gauss_env(T,XX,ZZ): '''Function to compute the theory for the envelope ''' X = np.cos(rot_angle)*XX + np.sin(rot_angle)*ZZ Z = -np.sin(rot_angle)*XX + np.cos(rot_angle)*ZZ inv_tau2 = 1./tt/tt inv_w_2 = 1.0/(w0*w0) exp_arg = - (X*X)*inv_w_2 - inv_tau2 / c/c * (Z-T*c)*(Z-T*c) return E_max * np.real(np.exp(exp_arg)) def write_file(fname, x, y, t, E): """ For a given filename fname, space coordinates x and y, time coordinate t and field E, write a WarpX-compatible input binary file containing the profile of the laser pulse """ with open(fname, 'wb') as file: flag_unif = 0 file.write(flag_unif.to_bytes(1, byteorder='little')) file.write((len(t)).to_bytes(4, byteorder='little', signed=False)) file.write((len(x)).to_bytes(4, byteorder='little', signed=False)) file.write((len(y)).to_bytes(4, byteorder='little', signed=False)) file.write(t.tobytes()) file.write(x.tobytes()) file.write(y.tobytes()) file.write(E.tobytes()) def write_file_unf(fname, x, y, t, E): """ For a given filename fname, space coordinates x and y, time coordinate t and field E, write a WarpX-compatible input binary file containing the profile of the laser pulse. This function should be used in the case of a uniform spatio-temporal mesh """ with open(fname, 'wb') as file: flag_unif = 1 file.write(flag_unif.to_bytes(1, byteorder='little')) file.write((len(t)).to_bytes(4, byteorder='little', signed=False)) file.write((len(x)).to_bytes(4, byteorder='little', signed=False)) file.write((len(y)).to_bytes(4, byteorder='little', signed=False)) file.write(t[0].tobytes()) file.write(t[-1].tobytes()) file.write(x[0].tobytes()) file.write(x[-1].tobytes()) if len(y) == 1 : file.write(y[0].tobytes()) else : file.write(y[0].tobytes()) file.write(y[-1].tobytes()) file.write(E.tobytes()) def create_gaussian_2d(): T, X, Y = np.meshgrid(tcoords, xcoords, np.array([0.0]), indexing='ij') E_t = gauss(T,X,Y,'2d') write_file("gauss_2d.txye", xcoords, np.array([0.0]), tcoords, E_t) write_file_unf("gauss_2d_unf.txye", xcoords, np.array([0.0]), tcoords, E_t) def do_analysis(fname, compname, steps): ds = yt.load(fname) dt = ds.current_time.to_value()/steps # Define 2D meshes x = np.linspace( ds.domain_left_edge[0], ds.domain_right_edge[0], ds.domain_dimensions[0]).v z = np.linspace( ds.domain_left_edge[ds.dimensionality-1], ds.domain_right_edge[ds.dimensionality-1], ds.domain_dimensions[ds.dimensionality-1]).v X, Z = np.meshgrid(x, z, sparse=False, indexing='ij') # Compute the theory for envelope env_theory = gauss_env(+t_c-ds.current_time.to_value(), X,Z)+gauss_env(-t_c+ds.current_time.to_value(), X,Z) # Read laser field in PIC simulation, and compute envelope all_data_level_0 = ds.covering_grid(level=0,left_edge=ds.domain_left_edge, dims=ds.domain_dimensions) F_laser = all_data_level_0['boxlib', 'Ey'].v.squeeze() env = abs(hilbert(F_laser)) extent = [ds.domain_left_edge[ds.dimensionality-1], ds.domain_right_edge[ds.dimensionality-1], ds.domain_left_edge[0], ds.domain_right_edge[0] ] # Plot results plt.figure(figsize=(8,6)) plt.subplot(221) plt.title('PIC field') plt.imshow(F_laser, extent=extent) plt.colorbar() plt.subplot(222) plt.title('PIC envelope') plt.imshow(env, extent=extent) plt.colorbar() plt.subplot(223) plt.title('Theory envelope') plt.imshow(env_theory, extent=extent) plt.colorbar() plt.subplot(224) plt.title('Difference') plt.imshow(env-env_theory, extent=extent) plt.colorbar() plt.tight_layout() plt.savefig(compname, bbox_inches='tight') relative_error_env = np.sum(np.abs(env-env_theory)) / np.sum(np.abs(env)) print("Relative error envelope: ", relative_error_env) assert(relative_error_env < relative_error_threshold) fft_F_laser = np.fft.fft2(F_laser) freq_rows = np.fft.fftfreq(F_laser.shape[0],dt) freq_cols = np.fft.fftfreq(F_laser.shape[1],dt) pos_max = np.unravel_index(np.abs(fft_F_laser).argmax(), fft_F_laser.shape) freq = np.sqrt((freq_rows[pos_max[0]])**2 + (freq_cols[pos_max[1]]**2)) exp_freq = c/wavelength relative_error_freq = np.abs(freq-exp_freq)/exp_freq print("Relative error frequency: ", relative_error_freq) assert(relative_error_freq < relative_error_threshold) def launch_analysis(executable): create_gaussian_2d() os.system("./" + executable + " inputs.2d_test_txye diag1.file_prefix=diags/plotfiles/plt") do_analysis("diags/plotfiles/plt00250/", "comp_unf.pdf", 250) os.system("sed 's/gauss_2d_unf.txye/gauss_2d.txye/g' inputs.2d_test_txye > inputs.2d_test_txye_non_unf") os.system("./" + executable + " inputs.2d_test_txye_non_unf diag1.file_prefix=diags/plotfiles/plt") do_analysis("diags/plotfiles/plt00250/", "comp_non_unf.pdf", 250) def main() : executables = glob.glob("*.ex") if len(executables) == 1 : launch_analysis(executables[0]) else : assert(False) print('Passed') if __name__ == "__main__": main()