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Diffstat (limited to 'Examples/Modules/qed/quantum_synchrotron/analysis.py')
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diff --git a/Examples/Modules/qed/quantum_synchrotron/analysis.py b/Examples/Modules/qed/quantum_synchrotron/analysis.py new file mode 100755 index 000000000..5c2f778a1 --- /dev/null +++ b/Examples/Modules/qed/quantum_synchrotron/analysis.py @@ -0,0 +1,298 @@ +#! /usr/bin/env python + +# Copyright 2019 Luca Fedeli, Maxence Thevenet +# +# This file is part of WarpX. +# +# License: BSD-3-Clause-LBNL + +# -*- coding: utf-8 -*- + +import yt +import numpy as np +import sys +import scipy.special as spe +import scipy.integrate as integ +import scipy.stats as st +sys.path.insert(1, '../../../../warpx/Regression/Checksum/') +import checksumAPI + +import matplotlib.pyplot as plt + +# This script performs detailed checks of the Quantum Synchrotron photon emission process. +# Two electron populations and two positron populations are initialized with different momenta in different +# directions in a background EM field (with non-zero components along each direction). +# Specifically the script checks that: +# +# - The expected number of generated photons n_phot is in agreement with theory. +# The maximum tolerated error is 5*sqrt(n_phot), except for the last 8 points, +# for which a higher tolerance is used (this is due to the fact that the resolution +# of the builtin table is quite limited). +# - The weight of the generated particles is equal to the weight of the photon +# - The generated particles are emitted in the right direction +# - The energy distribution of the generated particles is in agreement with theory +# - The optical depths of the product species are correctly initialized (QED effects are +# enabled for product species too). +# +# More details on the theoretical formulas used in this script can be found in +# the Jupyter notebook picsar/src/multi_physics/QED_tests/validation/validation.ipynb +# +# References: +# 1) R. Duclous et al 2011 Plasma Phys. Control. Fusion 53 015009 +# 2) A. Gonoskov et al. 2015 Phys. Rev. E 92, 023305 +# 3) M. Lobet. PhD thesis "Effets radiatifs et d'electrodynamique +# quantique dans l'interaction laser-matiere ultra-relativiste" +# URL: https://tel.archives-ouvertes.fr/tel-01314224 + + +# Tolerances +tol = 1.e-8 +tol_red = 1.e-2 + +# Physical constants (from CODATA 2018, see: https://physics.nist.gov/cuu/Constants/index.html ) +me = 9.1093837015e-31 #electron mass +c = 299792458 #speed of light +hbar = 6.62607015e-34/(2*np.pi) #reduced Plank constant +fine_structure = 7.2973525693e-3 #fine structure constant +qe = 1.602176634e-19#elementary charge +E_s = (me**2 * c**3)/(qe * hbar) #Schwinger E field +B_s = E_s/c #Schwinger B field + +mec = me*c +mec2 = mec*c +#______________ + +# Initial parameters +spec_names = ["p1", "p2", "p3", "p4"] +spec_names_phot = ["qsp_1", "qsp_2", "qsp_3", "qsp_4"] +initial_momenta = [ + np.array([10.0,0,0])*mec, + np.array([0.0,100.0,0.0])*mec, + np.array([0.0,0.0,1000.0])*mec, + np.array([5773.502691896, 5773.502691896, 5773.502691896])*mec +] +csign = [-1,-1,1,1] +initial_particle_number = 1048576 + +E_f = np.array([-2433321316961438., 973328526784575., 1459992790176863.]) +B_f = np.array([2857142.85714286, 4285714.28571428, 8571428.57142857]) + +NNS = [64,64,64,64] #bins for energy distribution comparison. +#______________ + +def calc_chi_part(p, E, B): + gamma_part = np.sqrt(1.0 + np.dot(p,p)/mec**2) + v = p/(gamma_part*me) + EpvvecB = E + np.cross(v,B) + vdotEoverc = np.dot(v,E)/c + ff = np.sqrt(np.dot(EpvvecB,EpvvecB) - np.dot(vdotEoverc,vdotEoverc)) + return gamma_part*ff/E_s + +#Auxiliary functions +@np.vectorize +def IC_inner_alternative(y): + ff = lambda x : np.exp(-y*(1+(4*x**2)/3)*np.sqrt(1+x*x/3))*(9+36*x**2 + 16*x**4)/(3 + 4*x**2)/np.sqrt(1+(x**2)/3) + return integ.quad(ff, 0, np.inf)[0]/np.sqrt(3) + +def IC_Y(chi_ele, xi): + div = (chi_ele*(1-xi)) + div = np.where(np.logical_and(xi < 1, chi_ele != 0), div, 1.0); + res = (2/3)*np.where(np.logical_and(xi < 1, chi_ele != 0), xi/div, np.inf) + return res + +def IC_S(chi_ele, xi): + Y = IC_Y(chi_ele, xi) + coeff = np.sqrt(3)/2.0/np.pi + first = IC_inner_alternative(Y) + div = np.where(xi == 1, 1.0, 1.0/(1-xi) ) + res = np.where(np.logical_or(xi == 1, xi == 0), 0.0, + coeff*xi*( first + (xi**2 * spe.kv(2./3.,Y)*div ) ) ) + return res + +def IC_SXI(chi_ele, xi): + div = np.where(xi != 0, xi, 1.0) + return np.where(xi != 0, IC_S(chi_ele, xi)/div, np.inf) + +@np.vectorize +def IC_G(chi_ele): + return integ.quad(lambda xi: IC_SXI(chi_ele, xi), 0, 1)[0] + +def small_diff(vv, val): + if(val != 0.0): + return np.max(np.abs((vv - val)/val)) < tol + else: + return np.max(np.abs(vv)) < tol + +def boris(pp, dt, charge_sign): + econst = 0.5*qe*dt*charge_sign/me + u = pp/(me) + u += econst*E_f + inv_gamma = 1/np.sqrt(1 + np.dot(u,u)/c**2) + t = econst*B_f*inv_gamma + s = 2*t/(1 + np.dot(t,t)) + u_p = u + np.cross(u,t) + u += np.cross(u_p, s) + u += econst*E_f + return u *me +#__________________ + +# Quantum Synchrotron total and differential cross sections +def QS_dN_dt(chi_ele, gamma_ele): + coeff_IC = (2./3.) * fine_structure * me*c**2/hbar + return coeff_IC*IC_G(chi_ele)/gamma_ele + +def QS_d2N_dt_dchi(chi, gamma_ele, chi_phot): + coeff_IC = (2./3.) * fine_structure * me*c**2/hbar + return coeff_IC*IC_S(chi, chi_phot/chi)/chi_phot/gamma_ele +#__________________ + +# Get data for a species +def get_spec(ytdata, specname, is_photon): + px = ytdata[specname,"particle_momentum_x"].v + pz = ytdata[specname,"particle_momentum_z"].v + py = ytdata[specname,"particle_momentum_y"].v + + w = ytdata[specname,"particle_weighting"].v + + if (is_photon): + opt = ytdata[specname,"particle_optical_depth_BW"].v + else: + opt = ytdata[specname,"particle_optical_depth_QSR"].v + + return {"px" : px, "py" : py, "pz" : pz, "w" : w, "opt" : opt} + +# Individual tests +def check_number_of_photons(ytdataset, part_name, phot_name, chi_part, gamma_part, dt, particle_number): + dNQS_dt_theo = QS_dN_dt(chi_part, gamma_part) + expected_photons = (1.-np.exp(-dNQS_dt_theo*dt))*particle_number + expected_photons_tolerance = 5.0*np.sqrt(expected_photons) + n_phot = ytdataset.particle_type_counts[phot_name] + assert( np.abs(n_phot-expected_photons) < expected_photons_tolerance) + print(" [OK] generated photons number is within expectations") + return n_phot + +def check_weights(part_data, phot_data): + assert(np.all(part_data["w"] == part_data["w"][0])) + assert(np.all(phot_data["w"] == part_data["w"][0])) + print(" [OK] particles weights are the expected ones") + +def check_momenta(phot_data, p_phot, p0): + pdir = p0/np.linalg.norm(p0) + assert(small_diff(phot_data["px"]/p_phot, pdir[0])) + assert(small_diff(phot_data["py"]/p_phot, pdir[1])) + assert(small_diff(phot_data["pz"]/p_phot, pdir[2])) + print(" [OK] photons move along the initial particle direction") + +def check_opt_depths(part_data, phot_data): + data = (part_data, phot_data) + for dd in data: + loc, scale = st.expon.fit(dd["opt"]) + assert( np.abs(loc - 0) < tol_red ) + assert( np.abs(scale - 1) < tol_red ) + print(" [OK] optical depth distributions are still exponential") + +def check_energy_distrib(gamma_phot, chi_part, + gamma_part, n_phot, NN, idx, do_plot=False): + gamma_phot_min = 1e-12*gamma_part + gamma_phot_max = gamma_part + h_log_gamma_phot, c_gamma_phot = np.histogram(gamma_phot, bins=np.logspace(np.log10(gamma_phot_min),np.log10(gamma_phot_max),NN+1)) + + cchi_phot_min = chi_part*(gamma_phot_min)/(gamma_part-1) + cchi_phot_max = chi_part*(gamma_phot_max)/(gamma_part-1) + + #Rudimentary integration over npoints for each bin + npoints= 20 + aux_chi = np.logspace(np.log10(cchi_phot_min),np.log10(cchi_phot_max), NN*npoints) + distrib = QS_d2N_dt_dchi(chi_part, gamma_part, aux_chi)*aux_chi + distrib = np.sum(distrib.reshape(-1, npoints),1) + distrib = n_phot*distrib/np.sum(distrib) + + if do_plot : + # Visual comparison of distributions + c_gamma_phot = np.exp(0.5*(np.log(c_gamma_phot[1:])+np.log(c_gamma_phot[:-1]))) + plt.clf() + + fig, (ax1, ax2) = plt.subplots(1, 2) + fig.suptitle("χ_particle = {:f}".format(chi_part)) + ax1.plot(c_gamma_phot, distrib,label="theory") + ax1.loglog(c_gamma_phot, h_log_gamma_phot,label="QSR photons") + ax1.set_xlim(1e-12*(gamma_part-1),gamma_part-1) + ax1.set_ylim(1,1e5) + ax2.plot(c_gamma_phot, distrib,label="theory") + ax2.semilogy(c_gamma_phot, h_log_gamma_phot,label="QSR photons") + ax2.set_ylim(1,1e5) + ax2.set_xlim(1e-12*(gamma_part-1),gamma_part-1) + ax1.set_xlabel("γ_photon") + ax1.set_xlabel("N") + ax2.set_xlabel("γ_photon") + ax2.set_xlabel("N") + plt.legend() + plt.savefig("case_{:d}".format(idx+1)) + + discr = np.abs(h_log_gamma_phot-distrib) + + max_discr = np.sqrt(distrib)*5.0 + # Use a higer tolerance for the last 8 points (this is due to limitations + # of the builtin table) + max_discr[-8:] *= 2.0 + assert(np.all( discr < max_discr )) + + print(" [OK] energy distribution is within expectations") + +#__________________ + +def check(): + filename_end = sys.argv[1] + data_set_end = yt.load(filename_end) + + sim_time = data_set_end.current_time.to_value() + all_data_end = data_set_end.all_data() + + for idx in range(4): + part_name = spec_names[idx] + phot_name = spec_names_phot[idx] + t_pi = initial_momenta[idx] + pm = boris(t_pi,-sim_time*0.5,csign[idx]) + p0 = boris(pm,sim_time*1.0,csign[idx]) + + p2_part = p0[0]**2 + p0[1]**2 + p0[2]**2 + energy_part = np.sqrt(mec2**2 + p2_part*c**2) + gamma_part = energy_part/mec2 + chi_part = calc_chi_part(p0, E_f, B_f) + + print("** Case {:d} **".format(idx+1)) + print(" initial momentum: ", t_pi) + print(" quantum parameter: {:f}".format(chi_part)) + print(" normalized particle energy: {:f}".format(gamma_part)) + print(" timestep: {:f} fs".format(sim_time*1e15)) + + part_data_final = get_spec(all_data_end, part_name, is_photon=False) + phot_data = get_spec(all_data_end, phot_name, is_photon=True) + + p_phot = np.sqrt(phot_data["px"]**2 + phot_data["py"]**2 + phot_data["pz"]**2) + energy_phot = p_phot*c + gamma_phot = energy_phot/mec2 + + n_phot = check_number_of_photons(data_set_end, + part_name, phot_name, + chi_part, gamma_part, sim_time, + initial_particle_number) + + check_weights(part_data_final, phot_data) + + check_momenta(phot_data, p_phot, p0) + + check_energy_distrib(gamma_phot, chi_part, gamma_part, n_phot, NNS[idx], idx) + + check_opt_depths(part_data_final, phot_data) + + print("*************\n") + + test_name = filename_end[:-9] # Could also be os.path.split(os.getcwd())[1] + checksumAPI.evaluate_checksum(test_name, filename_end) + +def main(): + check() + +if __name__ == "__main__": + main() |