def run_simulation(gamma_boost, use_separate_electron_species):
"""
Run a simulation with a laser pulse going through a gas jet of ionizable
N5+ atoms, and check the fraction of atoms that are in the N5+ state.
Parameters
----------
gamma_boost: float
The Lorentz factor of the frame in which the simulation is carried out.
use_separate_electron_species: bool
Whether to use separate electron species for each level, or
a single electron species for all levels.
"""
# The simulation box
zmax_lab = 20.e-6 # Length of the box along z (meters)
zmin_lab = 0.e-6
Nr = 3 # Number of gridpoints along r
rmax = 10.e-6 # Length of the box along r (meters)
Nm = 2 # Number of modes used
# The particles of the plasma
p_zmin = 5.e-6 # Position of the beginning of the plasma (meters)
p_zmax = 15.e-6
p_rmin = 0. # Minimal radial position of the plasma (meters)
p_rmax = 100.e-6 # Maximal radial position of the plasma (meters)
n_atoms = 0.2 # The atomic density is chosen very low,
# to avoid collective effects
p_nz = 2 # Number of particles per cell along z
p_nr = 1 # Number of particles per cell along r
p_nt = 4 # Number of particles per cell along theta
# Boosted frame
boost = BoostConverter(gamma_boost)
# Boost the different quantities
beta_boost = np.sqrt(1. - 1. / gamma_boost**2)
zmin, zmax = boost.static_length([zmin_lab, zmax_lab])
p_zmin, p_zmax = boost.static_length([p_zmin, p_zmax])
n_atoms, = boost.static_density([n_atoms])
# Increase the number of particles per cell in order to keep sufficient
# statistics for the evaluation of the ionization fraction
if gamma_boost > 1:
p_nz = int(2 * gamma_boost * (1 + beta_boost) * p_nz)
# The laser
a0 = 1.8 # Laser amplitude
lambda0_lab = 0.8e-6 # Laser wavelength
# Boost the laser wavelength before calculating the laser amplitude
lambda0, = boost.copropag_length([lambda0_lab], beta_object=1.)
# Duration and initial position of the laser
ctau = 10. * lambda0
z0 = -2 * ctau
# Calculate laser amplitude
omega = 2 * np.pi * c / lambda0
E0 = a0 * m_e * c * omega / e
B0 = E0 / c
def laser_func(F, x, y, z, t, amplitude, length_scale):
"""
Function that describes a Gaussian laser with infinite waist
"""
return( F + amplitude * math.cos( 2*np.pi*(z-c*t)/lambda0 ) * \
math.exp( - (z - c*t - z0)**2/ctau**2 ) )
# Resolution and number of timesteps
dz = lambda0 / 16.
dt = dz / c
Nz = int((zmax - zmin) / dz) + 1
N_step = int(
(2. * 40. * lambda0 + zmax - zmin) / (dz * (1 + beta_boost))) + 1
# Get the speed of the plasma
uz_m, = boost.longitudinal_momentum([0.])
v_plasma, = boost.velocity([0.])
# The diagnostics
diag_period = N_step - 1 # Period of the diagnostics in number of timesteps
# Initial ionization level of the Nitrogen atoms
level_start = 2
# Initialize the simulation object, with the neutralizing electrons
# No particles are created because we do not pass the density
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
zmin=zmin,
v_comoving=v_plasma,
use_galilean=False,
boundaries='open',
use_cuda=use_cuda)
# Add the charge-neutralizing electrons
elec = sim.add_new_species(q=-e,
m=m_e,
n=level_start * n_atoms,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt,
p_zmin=p_zmin,
p_zmax=p_zmax,
p_rmin=p_rmin,
p_rmax=p_rmax,
continuous_injection=False,
uz_m=uz_m)
# Add the N atoms
ions = sim.add_new_species(q=0,
m=14. * m_p,
n=n_atoms,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt,
p_zmin=p_zmin,
p_zmax=p_zmax,
p_rmin=p_rmin,
p_rmax=p_rmax,
continuous_injection=False,
uz_m=uz_m)
# Add the target electrons
if use_separate_electron_species:
# Use a dictionary of electron species: one per ionizable level
target_species = {}
level_max = 6 # N can go up to N7+, but here we stop at N6+
for i_level in range(level_start, level_max):
target_species[i_level] = sim.add_new_species(q=-e, m=m_e)
else:
# Use the pre-existing, charge-neutralizing electrons
target_species = elec
level_max = None # Default is going up to N7+
# Define ionization
ions.make_ionizable(element='N',
level_start=level_start,
level_max=level_max,
target_species=target_species)
# Set the moving window
sim.set_moving_window(v=v_plasma)
# Add a laser to the fields of the simulation (external fields)
sim.external_fields = [
ExternalField(laser_func, 'Ex', E0, 0.),
ExternalField(laser_func, 'By', B0, 0.)
]
# Add a particle diagnostic
sim.diags = [
ParticleDiagnostic(
diag_period,
{"ions": ions},
particle_data=["position", "gamma", "weighting", "E", "B"],
# Test output of fields and gamma for standard
# (non-boosted) particle diagnostics
write_dir='tests/diags',
comm=sim.comm)
]
if gamma_boost > 1:
T_sim_lab = (2. * 40. * lambda0_lab + zmax_lab - zmin_lab) / c
sim.diags.append(
BackTransformedParticleDiagnostic(zmin_lab,
zmax_lab,
v_lab=0.,
dt_snapshots_lab=T_sim_lab / 2.,
Ntot_snapshots_lab=3,
gamma_boost=gamma_boost,
period=diag_period,
fldobject=sim.fld,
species={"ions": ions},
comm=sim.comm,
write_dir='tests/lab_diags'))
# Run the simulation
sim.step(N_step, use_true_rho=True)
# Check the fraction of N5+ ions at the end of the simulation
w = ions.w
ioniz_level = ions.ionizer.ionization_level
# Get the total number of N atoms/ions (all ionization levels together)
ntot = w.sum()
# Get the total number of N5+ ions
n_N5 = w[ioniz_level == 5].sum()
# Get the fraction of N5+ ions, and check that it is close to 0.32
N5_fraction = n_N5 / ntot
print('N5+ fraction: %.4f' % N5_fraction)
assert ((N5_fraction > 0.30) and (N5_fraction < 0.34))
# When different electron species are created, check the fraction of
# each electron species
if use_separate_electron_species:
for i_level in range(level_start, level_max):
n_N = w[ioniz_level == i_level].sum()
assert np.allclose(target_species[i_level].w.sum(), n_N)
# Check consistency in the regular openPMD diagnostics
ts = OpenPMDTimeSeries('./tests/diags/hdf5/')
last_iteration = ts.iterations[-1]
w, q = ts.get_particle(['w', 'charge'],
species="ions",
iteration=last_iteration)
# Check that the openPMD file contains the same number of N5+ ions
n_N5_openpmd = np.sum(w[(4.5 * e < q) & (q < 5.5 * e)])
assert np.isclose(n_N5_openpmd, n_N5)
# Remove openPMD files
shutil.rmtree('./tests/diags/')
# Check consistency of the back-transformed openPMD diagnostics
if gamma_boost > 1.:
ts = OpenPMDTimeSeries('./tests/lab_diags/hdf5/')
last_iteration = ts.iterations[-1]
w, q = ts.get_particle(['w', 'charge'],
species="ions",
iteration=last_iteration)
# Check that the openPMD file contains the same number of N5+ ions
n_N5_openpmd = np.sum(w[(4.5 * e < q) & (q < 5.5 * e)])
assert np.isclose(n_N5_openpmd, n_N5)
# Remove openPMD files
shutil.rmtree('./tests/lab_diags/')
def __init__(self,
interp,
comm,
dt,
ptcl,
v,
p_nz,
time,
ux_m=0.,
uy_m=0.,
uz_m=0.,
ux_th=0.,
uy_th=0.,
uz_th=0.,
gamma_boost=None):
"""
Initializes a moving window object.
Parameters
----------
interp: a list of Interpolation objects
Contains the positions of the boundaries
comm: a BoundaryCommunicator object
Contains information about the MPI decomposition
and about the longitudinal boundaries
dt: float
The timestep of the simulation.
ptcl: a list of Particle objects
Needed in order to infer the position of injection
of the particles by the moving window.
v: float (meters per seconds), optional
The speed of the moving window
p_nz: int
Number of macroparticles per cell along the z direction
time: float (seconds)
The time (in the simulation) at which the moving
window was initialized
ux_m, uy_m, uz_m: floats (dimensionless)
Normalized mean momenta of the injected particles in each direction
ux_th, uy_th, uz_th: floats (dimensionless)
Normalized thermal momenta in each direction
gamma_boost : float, optional
When initializing the laser in a boosted frame, set the
value of `gamma_boost` to the corresponding Lorentz factor.
(uz_m is to be given in the lab frame ; for the moment, this
will not work if any of ux_th, uy_th, uz_th, ux_m, uy_m is nonzero)
"""
# Check that the boundaries are open
if ((comm.rank == comm.size-1) and (comm.right_proc is not None)) \
or ((comm.rank == 0) and (comm.left_proc is not None)):
raise ValueError(
'The simulation is using a moving window, but '
'the boundaries are periodic.\n Please select open '
'boundaries when initializing the Simulation object.')
# Momenta parameters
self.ux_m = ux_m
self.uy_m = uy_m
self.uz_m = uz_m
self.ux_th = ux_th
self.uy_th = uy_th
self.uz_th = uz_th
# When running the simulation in boosted frame, convert the arguments
if gamma_boost is not None:
boost = BoostConverter(gamma_boost)
self.uz_m, = boost.longitudinal_momentum([self.uz_m])
# Attach moving window speed and period
self.v = v
# Get the positions of the global physical domain
zmin_global_domain, zmax_global_domain = comm.get_zmin_zmax(
local=False, with_damp=False, with_guard=False)
# Attach reference position of moving window (only for the first proc)
# (Determines by how many cells the window should be moved)
if comm.rank == 0:
self.zmin = zmin_global_domain
# Attach injection position and speed (only for the last proc)
if comm.rank == comm.size - 1:
self.v_end_plasma = \
c * self.uz_m / np.sqrt(1 + ux_m**2 + uy_m**2 + self.uz_m**2)
# Initialize plasma *ahead* of the right *physical* boundary of
# the box so, after `exchange_period` iterations
# (without adding new plasma), there will still be plasma
# inside the physical domain. ( +3 takes into account that 3 more
# cells need to be filled w.r.t the left edge of the physical box
# such that the last cell inside the box is always correct for
# 1st and 3rd order shape factor particles after the moving window
# shifted by exchange_period cells. )
self.z_inject = zmax_global_domain + 3*comm.dz + \
comm.exchange_period * (v-self.v_end_plasma) * dt
# Try to detect the position of the end of the plasma:
# Find the maximal position of the particles which are
# continously injected.
self.z_end_plasma = None
for species in ptcl:
if species.continuous_injection and species.Ntot != 0:
# Add half of the spacing between particles (the injection
# function itself will add a half-spacing again)
self.z_end_plasma = species.z.max() + 0.5 * comm.dz / p_nz
break
# Default value in the absence of continuously-injected particles
if self.z_end_plasma is None:
self.z_end_plasma = zmax_global_domain
self.nz_inject = 0
self.p_nz = p_nz
# Attach time of last move
self.t_last_move = time - dt
def __init__(self,
interp,
comm,
ptcl,
v,
p_nz,
time,
ux_m=0.,
uy_m=0.,
uz_m=0.,
ux_th=0.,
uy_th=0.,
uz_th=0.,
gamma_boost=None):
"""
Initializes a moving window object.
Parameters
----------
interp: a list of Interpolation objects
Contains the positions of the boundaries
comm: a BoundaryCommunicator object
Contains information about the MPI decomposition
and about the longitudinal boundaries
ptcl: a list of Particle objects
Needed in order to infer the position of injection
of the particles by the moving window.
v: float (meters per seconds), optional
The speed of the moving window
p_nz: int
Number of macroparticles per cell along the z direction
time: float (seconds)
The time (in the simulation) at which the moving
window was initialized
ux_m, uy_m, uz_m: floats (dimensionless)
Normalized mean momenta of the injected particles in each direction
ux_th, uy_th, uz_th: floats (dimensionless)
Normalized thermal momenta in each direction
gamma_boost : float, optional
When initializing the laser in a boosted frame, set the
value of `gamma_boost` to the corresponding Lorentz factor.
(uz_m is to be given in the lab frame ; for the moment, this
will not work if any of ux_th, uy_th, uz_th, ux_m, uy_m is nonzero)
"""
# Check that the boundaries are open
if ((comm.rank == comm.size-1) and (comm.right_proc is not None)) \
or ((comm.rank == 0) and (comm.left_proc is not None)):
raise ValueError(
'The simulation is using a moving window, but '
'the boundaries are periodic.\n Please select open '
'boundaries when initializing the Simulation object.')
# Momenta parameters
self.ux_m = ux_m
self.uy_m = uy_m
self.uz_m = uz_m
self.ux_th = ux_th
self.uy_th = uy_th
self.uz_th = uz_th
# When running the simulation in boosted frame, convert the arguments
if gamma_boost is not None:
boost = BoostConverter(gamma_boost)
self.uz_m, = boost.longitudinal_momentum([self.uz_m])
# Attach moving window speed and period
self.v = v
self.exchange_period = comm.exchange_period
# Attach reference position of moving window (only for the first proc)
# (Determines by how many cells the window should be moved)
if comm.rank == 0:
self.zmin = interp[0].zmin
# Attach injection position and speed (only for the last proc)
if comm.rank == comm.size - 1:
ng = comm.n_guard
self.z_inject = interp[0].zmax - ng / 2 * interp[0].dz
# Try to detect the position of the end of the plasma:
# Find the maximal position of the particles which are
# continously injected.
self.z_end_plasma = None
for species in ptcl:
if species.continuous_injection and species.Ntot != 0:
# Add half of the spacing between particles (the injection
# function itself will add a half-spacing again)
self.z_end_plasma = species.z.max(
) + 0.5 * interp[0].dz / p_nz
break
# Default value in the absence of continuously-injected particles
if self.z_end_plasma is None:
self.z_end_plasma = self.z_inject
self.v_end_plasma = \
c * self.uz_m / np.sqrt(1 + ux_m**2 + uy_m**2 + self.uz_m**2)
self.nz_inject = 0
self.p_nz = p_nz
# Attach time of last move
self.t_last_move = time
def run_simulation(gamma_boost):
"""
Run a simulation with a laser pulse going through a gas jet of ionizable
N5+ atoms, and check the fraction of atoms that are in the N5+ state.
Parameters
----------
gamma_boost: float
The Lorentz factor of the frame in which the simulation is carried out.
"""
# The simulation box
zmax_lab = 20.e-6 # Length of the box along z (meters)
zmin_lab = 0.e-6
Nr = 3 # Number of gridpoints along r
rmax = 10.e-6 # Length of the box along r (meters)
Nm = 2 # Number of modes used
# The particles of the plasma
p_zmin = 5.e-6 # Position of the beginning of the plasma (meters)
p_zmax = 15.e-6
p_rmin = 0. # Minimal radial position of the plasma (meters)
p_rmax = 100.e-6 # Maximal radial position of the plasma (meters)
n_e = 1. # The plasma density is chosen very low,
# to avoid collective effects
p_nz = 2 # Number of particles per cell along z
p_nr = 1 # Number of particles per cell along r
p_nt = 4 # Number of particles per cell along theta
# Boosted frame
boost = BoostConverter(gamma_boost)
# Boost the different quantities
beta_boost = np.sqrt(1. - 1. / gamma_boost**2)
zmin, zmax = boost.static_length([zmin_lab, zmax_lab])
p_zmin, p_zmax = boost.static_length([p_zmin, p_zmax])
n_e, = boost.static_density([n_e])
# Increase the number of particles per cell in order to keep sufficient
# statistics for the evaluation of the ionization fraction
if gamma_boost > 1:
p_nz = int(2 * gamma_boost * (1 + beta_boost) * p_nz)
# The laser
a0 = 1.8 # Laser amplitude
lambda0_lab = 0.8e-6 # Laser wavelength
# Boost the laser wavelength before calculating the laser amplitude
lambda0, = boost.copropag_length([lambda0_lab], beta_object=1.)
# Duration and initial position of the laser
ctau = 10. * lambda0
z0 = -2 * ctau
# Calculate laser amplitude
omega = 2 * np.pi * c / lambda0
E0 = a0 * m_e * c * omega / e
B0 = E0 / c
def laser_func(F, x, y, z, t, amplitude, length_scale):
"""
Function that describes a Gaussian laser with infinite waist
"""
return( F + amplitude * math.cos( 2*np.pi*(z-c*t)/lambda0 ) * \
math.exp( - (z - c*t - z0)**2/ctau**2 ) )
# Resolution and number of timesteps
dz = lambda0 / 16.
dt = dz / c
Nz = int((zmax - zmin) / dz) + 1
N_step = int(
(2. * 40. * lambda0 + zmax - zmin) / (dz * (1 + beta_boost))) + 1
# Get the speed of the plasma
uz_m, = boost.longitudinal_momentum([0.])
v_plasma, = boost.velocity([0.])
# The diagnostics
diag_period = N_step - 1 # Period of the diagnostics in number of timesteps
# Initialize the simulation object
sim = Simulation(
Nz,
zmax,
Nr,
rmax,
Nm,
dt,
p_zmax,
p_zmax, # No electrons get created because we pass p_zmin=p_zmax
p_rmin,
p_rmax,
p_nz,
p_nr,
p_nt,
n_e,
zmin=zmin,
initialize_ions=False,
v_comoving=v_plasma,
use_galilean=False,
boundaries='open',
use_cuda=use_cuda)
sim.set_moving_window(v=v_plasma)
# Add the N atoms
p_zmin, p_zmax, Npz = adapt_to_grid(sim.fld.interp[0].z, p_zmin, p_zmax,
p_nz)
p_rmin, p_rmax, Npr = adapt_to_grid(sim.fld.interp[0].r, p_rmin, p_rmax,
p_nr)
sim.ptcl.append(
Particles(q=e,
m=14. * m_p,
n=0.2 * n_e,
Npz=Npz,
zmin=p_zmin,
zmax=p_zmax,
Npr=Npr,
rmin=p_rmin,
rmax=p_rmax,
Nptheta=p_nt,
dt=dt,
use_cuda=use_cuda,
uz_m=uz_m,
grid_shape=sim.fld.interp[0].Ez.shape,
continuous_injection=False))
sim.ptcl[1].make_ionizable(element='N',
level_start=0,
target_species=sim.ptcl[0])
# Add a laser to the fields of the simulation (external fields)
sim.external_fields = [
ExternalField(laser_func, 'Ex', E0, 0.),
ExternalField(laser_func, 'By', B0, 0.)
]
# Add a field diagnostic
sim.diags = [
ParticleDiagnostic(diag_period, {"ions": sim.ptcl[1]},
write_dir='tests/diags',
comm=sim.comm)
]
if gamma_boost > 1:
T_sim_lab = (2. * 40. * lambda0_lab + zmax_lab - zmin_lab) / c
sim.diags.append(
BoostedParticleDiagnostic(zmin_lab,
zmax_lab,
v_lab=0.,
dt_snapshots_lab=T_sim_lab / 2.,
Ntot_snapshots_lab=3,
gamma_boost=gamma_boost,
period=diag_period,
fldobject=sim.fld,
species={"ions": sim.ptcl[1]},
comm=sim.comm,
write_dir='tests/lab_diags'))
# Run the simulation
sim.step(N_step, use_true_rho=True)
# Check the fraction of N5+ ions at the end of the simulation
w = sim.ptcl[1].w
ioniz_level = sim.ptcl[1].ionizer.ionization_level
# Get the total number of N atoms/ions (all ionization levels together)
ntot = w.sum()
# Get the total number of N5+ ions
n_N5 = w[ioniz_level == 5].sum()
# Get the fraction of N5+ ions, and check that it is close to 0.32
N5_fraction = n_N5 / ntot
print('N5+ fraction: %.4f' % N5_fraction)
assert ((N5_fraction > 0.30) and (N5_fraction < 0.34))
# Check consistency in the regular openPMD diagnostics
ts = OpenPMDTimeSeries('./tests/diags/hdf5/')
last_iteration = ts.iterations[-1]
w, q = ts.get_particle(['w', 'charge'],
species="ions",
iteration=last_iteration)
# Check that the openPMD file contains the same number of N5+ ions
n_N5_openpmd = np.sum(w[(4.5 * e < q) & (q < 5.5 * e)])
assert np.isclose(n_N5_openpmd, n_N5)
# Remove openPMD files
shutil.rmtree('./tests/diags/')
# Check consistency of the back-transformed openPMD diagnostics
if gamma_boost > 1.:
ts = OpenPMDTimeSeries('./tests/lab_diags/hdf5/')
last_iteration = ts.iterations[-1]
w, q = ts.get_particle(['w', 'charge'],
species="ions",
iteration=last_iteration)
# Check that the openPMD file contains the same number of N5+ ions
n_N5_openpmd = np.sum(w[(4.5 * e < q) & (q < 5.5 * e)])
assert np.isclose(n_N5_openpmd, n_N5)
# Remove openPMD files
shutil.rmtree('./tests/lab_diags/')