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#!/usr/bin/env python3
# Copyright 2022 David Grote
#
# This file is part of WarpX.
#
# License: BSD-3-Clause-LBNL
# This script tests the ion stopping model.
# It uses the same stopping power formula that
# is used in the C++ to check the resulting
# particle energies.
import os
import re
import sys
import numpy as np
from scipy.constants import e, epsilon_0, k, m_e, m_p
import yt
sys.path.insert(1, '../../../../warpx/Regression/Checksum/')
import checksumAPI
# Define constants using the WarpX names for the evals below
q_e = e
kb = k
# Tolerance on the error in the final energy (in eV)
tolerance = 1.e-7
last_filename = sys.argv[1]
# Remove trailing '/' from file name, if necessary
last_filename.rstrip('/')
# Find last iteration in file name, such as 'test_name_plt000001' (last_it = '000001')
last_it = re.search('\d+$', last_filename).group()
# Find output prefix in file name, such as 'test_name_plt000001' (prefix = 'test_name_plt')
prefix = last_filename[:-len(last_it)]
def stopping_from_electrons(ne, Te, Zb, ion_mass):
"""Calculate the coefficient in equation 14.13 from
"Introduction to Plasma Physics", Goldston and Rutherford.
ne: electron density
Te: electron temperature (eV)
Zb: ion charge state
ion_mass: (kg)
"""
vthe = np.sqrt(3.*Te*e/m_e)
wpe = np.sqrt(ne*e**2/(epsilon_0*m_e))
lambdadb = vthe/wpe
loglambda = np.log((12.*np.pi/Zb)*(ne*lambdadb**3))
# Goldston's equation 14.13
dEdt = - np.sqrt(2.)*ne*Zb**2*e**4*np.sqrt(m_e)*loglambda/(6.*np.pi**1.5*epsilon_0**2*ion_mass*(Te*e)**1.5)
return dEdt
def stopping_from_ions(dt, ni, Ti, mi, Zi, Zb, ion_mass, ion_energy):
"""
ni: background ion density
Ti: background ion temperature (eV)
mi: background ion mass
Zi: background ion charge state
Zb: ion charge state
ion_mass: (kg)
ion_energy: (eV)
"""
vthi = np.sqrt(3.*Ti*e/mi)
wpi = np.sqrt(ni*e**2/(epsilon_0*mi))
lambdadb = vthi/wpi
loglambda = np.log((12.*np.pi/Zb)*(ni*lambdadb**3))
alpha = np.sqrt(2.)*ni*Zi**2*Zb**2*e**4*np.sqrt(ion_mass)*loglambda/(8.*np.pi*epsilon_0**2*mi)
f1 = np.clip((ion_energy*e)**(3./2.) - 3./2.*alpha*dt, 0., None)
ion_energy = (f1)**(2./3.)/e
return ion_energy
# Fetch background parameters and inital particle data
ds0 = yt.load(f'{prefix}{len(last_it)*"0"}')
ad0 = ds0.all_data()
Zb = 1. # Ion charge state
ne = float(ds0.parameters['stopping_on_electrons_constant.background_density'])
Te = eval(ds0.parameters['stopping_on_electrons_constant.background_temperature'])*kb/e
ion_mass12 = m_p
mi = eval(ds0.parameters['stopping_on_ions_constant.background_mass'])
Zi = float(ds0.parameters['stopping_on_ions_constant.background_charge_state'])
ni = float(ds0.parameters['stopping_on_ions_constant.background_density'])
Ti = eval(ds0.parameters['stopping_on_ions_constant.background_temperature'])*kb/e
ion_mass34 = 4.*m_p
# For ions1, the background parameters are constants
vx = ad0[('ions1', 'particle_momentum_x')].to_ndarray()/ion_mass12
vy = ad0[('ions1', 'particle_momentum_y')].to_ndarray()/ion_mass12
vz = ad0[('ions1', 'particle_momentum_z')].to_ndarray()/ion_mass12
EE1 = 0.5*ion_mass12*(vx**2 + vy**2 + vz**2)/e
# For ions2, the background parameters are parsed
xx = ad0[('ions2', 'particle_position_x')].to_ndarray()/ion_mass12
yy = ad0[('ions2', 'particle_position_y')].to_ndarray()/ion_mass12
ne2 = np.where(xx > 0., 1.e20, 1.e21)
Te2 = np.where(yy > 0., 1., 2.)
vx = ad0[('ions2', 'particle_momentum_x')].to_ndarray()/ion_mass12
vy = ad0[('ions2', 'particle_momentum_y')].to_ndarray()/ion_mass12
vz = ad0[('ions2', 'particle_momentum_z')].to_ndarray()/ion_mass12
EE2 = 0.5*ion_mass12*(vx**2 + vy**2 + vz**2)/e
# For ions3, the background parameters are constants
vx = ad0[('ions3', 'particle_momentum_x')].to_ndarray()/ion_mass34
vy = ad0[('ions3', 'particle_momentum_y')].to_ndarray()/ion_mass34
vz = ad0[('ions3', 'particle_momentum_z')].to_ndarray()/ion_mass34
EE3 = 0.5*ion_mass34*(vx**2 + vy**2 + vz**2)/e
# For ions4, the background parameters are parsed
xx = ad0[('ions4', 'particle_position_x')].to_ndarray()/ion_mass34
yy = ad0[('ions4', 'particle_position_y')].to_ndarray()/ion_mass34
ni4 = np.where(xx > 0., 1.e20, 1.e21)
Ti4 = np.where(yy > 0., 0.05, 0.10)
vx = ad0[('ions4', 'particle_momentum_x')].to_ndarray()/ion_mass34
vy = ad0[('ions4', 'particle_momentum_y')].to_ndarray()/ion_mass34
vz = ad0[('ions4', 'particle_momentum_z')].to_ndarray()/ion_mass34
EE4 = 0.5*ion_mass34*(vx**2 + vy**2 + vz**2)/e
ds = yt.load(last_filename)
ad = ds.all_data()
dt = ds.current_time.to_value()/int(last_it)
# Step through the same number of time steps
a_EE1 = EE1
a_EE2 = EE2
a_EE3 = EE3
a_EE4 = EE4
for it in range(int(last_it)):
dEdt1 = stopping_from_electrons(ne, Te, Zb, ion_mass12)
a_EE1 *= np.exp(dEdt1*dt)
dEdt2 = stopping_from_electrons(ne2, Te2, Zb, ion_mass12)
a_EE2 *= np.exp(dEdt2*dt)
a_EE3 = stopping_from_ions(dt, ni, Ti, mi, Zi, Zb, ion_mass34, a_EE3)
a_EE4 = stopping_from_ions(dt, ni4, Ti4, mi, Zi, Zb, ion_mass34, a_EE4)
# Fetch the final particle data
vx = ad[('ions1', 'particle_momentum_x')].to_ndarray()/ion_mass12
vy = ad[('ions1', 'particle_momentum_y')].to_ndarray()/ion_mass12
vz = ad[('ions1', 'particle_momentum_z')].to_ndarray()/ion_mass12
EE1 = 0.5*ion_mass12*(vx**2 + vy**2 + vz**2)/e
vx = ad[('ions2', 'particle_momentum_x')].to_ndarray()/ion_mass12
vy = ad[('ions2', 'particle_momentum_y')].to_ndarray()/ion_mass12
vz = ad[('ions2', 'particle_momentum_z')].to_ndarray()/ion_mass12
EE2 = 0.5*ion_mass12*(vx**2 + vy**2 + vz**2)/e
vx = ad[('ions3', 'particle_momentum_x')].to_ndarray()/ion_mass34
vy = ad[('ions3', 'particle_momentum_y')].to_ndarray()/ion_mass34
vz = ad[('ions3', 'particle_momentum_z')].to_ndarray()/ion_mass34
EE3 = 0.5*ion_mass34*(vx**2 + vy**2 + vz**2)/e
vx = ad[('ions4', 'particle_momentum_x')].to_ndarray()/ion_mass34
vy = ad[('ions4', 'particle_momentum_y')].to_ndarray()/ion_mass34
vz = ad[('ions4', 'particle_momentum_z')].to_ndarray()/ion_mass34
EE4 = 0.5*ion_mass34*(vx**2 + vy**2 + vz**2)/e
error1 = np.abs(EE1 - a_EE1)
error2 = np.abs(EE2 - a_EE2)
error3 = np.abs(EE3 - a_EE3)
error4 = np.abs(EE4 - a_EE4)
print('stopping on electrons error with constant = ', error1)
print('stopping on electrons error with parsed = ', error2)
print('stopping on ions error with constant = ', error3)
print('stopping on ions error with parsed = ', error4)
print('tolerance = ', tolerance)
assert np.all(error1 < tolerance)
assert np.all(error2 < tolerance)
assert np.all(error3 < tolerance)
assert np.all(error4 < tolerance)
test_name = os.path.split(os.getcwd())[1]
checksumAPI.evaluate_checksum(test_name, last_filename)
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