def run_continuous_injection( gamma_boost, dens_func,
p_zmin, p_zmax, show, N_check=3 ):
# Chose the time step
dt = (zmax-zmin)/Nz/c
# Initialize the different structures
sim = Simulation( Nz, zmax, Nr, rmax, Nm, dt,
p_zmin, p_zmax, 0, p_rmax, p_nz, p_nr, p_nt, 0.5*n,
dens_func=dens_func, initialize_ions=False, zmin=zmin,
use_cuda=use_cuda, gamma_boost=gamma_boost, boundaries='open' )
# Add another species with a different number of particles per cell
sim.add_new_species( -e, m_e, 0.5*n, dens_func,
2*p_nz, 2*p_nr, 2*p_nt,
p_zmin, p_zmax, 0, p_rmax )
# Set the moving window, which handles the continuous injection
# The moving window has an arbitrary velocity (0.7*c) so as to check
# that the injection is correct in this case also
sim.set_moving_window( v=c )
# Check that the density is correct after different timesteps
N_step = int( Nz/N_check/2 )
for i in range( N_check ):
sim.step( N_step, move_momenta=False )
check_density( sim, gamma_boost, dens_func, show )
gamma_boost=boost.gamma0,
n_order=n_order,
use_cuda=use_cuda,
boundaries={
'z': 'open',
'r': 'reflective'
})
# 'r': 'open' can also be used, but is more computationally expensive
# Add the plasma electron and plasma ions
plasma_elec = sim.add_new_species(q=-e,
m=m_e,
n=n_e,
dens_func=dens_func,
boost_positions_in_dens_func=True,
p_zmin=p_zmin,
p_zmax=p_zmax,
p_rmax=p_rmax,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt)
plasma_ions = sim.add_new_species(q=e,
m=m_p,
n=n_e,
dens_func=dens_func,
boost_positions_in_dens_func=True,
p_zmin=p_zmin,
p_zmax=p_zmax,
p_rmax=p_rmax,
p_nz=p_nz,
p_nr=p_nr,
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/')
initialize_ions=False,
n_order=n_order,
use_cuda=use_cuda)
# By default the simulation initializes an electron species (sim.ptcl[0])
# Because we did not pass the arguments `n`, `p_nz`, `p_nr`, `p_nz`,
# this electron species does not contain any macroparticles.
# It is okay to just remove it from the list of species.
sim.ptcl = []
# Add the Helium ions (pre-ionized up to level 1),
# the Nitrogen ions (pre-ionized up to level 5)
# and the associated electrons (from the pre-ionized levels)
atoms_He = sim.add_new_species(q=e,
m=4. * m_p,
n=n_He,
dens_func=dens_func,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt,
p_zmin=p_zmin)
atoms_N = sim.add_new_species(q=5 * e,
m=14. * m_p,
n=n_N,
dens_func=dens_func,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt,
p_zmin=p_zmin)
# Important: the electron density from N5+ is 5x larger than that from He+
n_e = n_He + 5 * n_N
elec = sim.add_new_species(q=-e,
m=m_e,
class Simulation(PICMI_Simulation):
# Redefine the `init` method, as required by the picmi `_ClassWithInit`
def init(self, kw):
self.sim_kw = {}
for argname in ['use_ruyten_shapes', 'use_modified_volume']:
if f'fbpic_{argname}' in kw:
self.sim_kw[argname] = kw.pop(f'fbpic_{argname}')
self.step_kw = {}
for argname in [
'correct_currents', 'correct_divE', 'use_true_rho',
'move_positions', 'move_momenta', 'show_progress'
]:
if f'fbpic_{argname}' in kw:
self.step_kw[argname] = kw.pop(f'fbpic_{argname}')
# Get the grid
grid = self.solver.grid
if not type(grid) == PICMI_CylindricalGrid:
raise ValueError('When using fbpic with PICMI, '
'the grid needs to be a CylindricalGrid object.')
# Check rmin and boundary conditions
assert grid.lower_bound[0] == 0.
assert grid.lower_boundary_conditions[
1] == grid.upper_boundary_conditions[1]
if grid.lower_boundary_conditions[1] == 'reflective':
warnings.warn(
"FBPIC does not support reflective boundary condition in z.\n"
"The z boundary condition was automatically converted to 'open'."
)
grid.lower_boundary_conditions[1] = 'open'
grid.upper_boundary_conditions[1] = 'open'
assert grid.upper_boundary_conditions[1] in ['periodic', 'open']
assert grid.upper_boundary_conditions[0] in ['reflective', 'open']
# Determine timestep
if self.solver.cfl is not None:
dz = (grid.upper_bound[1] -
grid.lower_bound[1]) / grid.number_of_cells[1]
dr = (grid.upper_bound[0] -
grid.lower_bound[0]) / grid.number_of_cells[0]
if self.gamma_boost is not None:
beta = np.sqrt(1. - 1. / self.gamma_boost**2)
dr = dr / ((1 + beta) * self.gamma_boost)
dt = self.solver.cfl * min(dz, dr) / c
elif self.time_step_size is not None:
dt = self.time_step_size
else:
raise ValueError('You need to either set the `cfl` of the solver\n'
'or the `timestep_size` of the `Simulation`.')
# Convert API for the smoother
if self.solver.source_smoother is None:
smoother = BinomialSmoother()
else:
if self.solver.source_smoother.n_pass is None:
n_passes = 1
else:
n_passes = {
'r': self.solver.source_smoother.n_pass[0],
'z': self.solver.source_smoother.n_pass[1]
}
if self.solver.source_smoother.compensation is None:
compensator = False
else:
compensator = all(self.solver.source_smoother.compensation)
smoother = BinomialSmoother(n_passes=n_passes,
compensator=compensator)
# Convert verbose level:
verbose_level = self.verbose
if verbose_level is None:
verbose_level = 1
# Order of the stencil for z derivatives in the Maxwell solver
if self.solver.stencil_order is None:
n_order = -1
else:
n_order = self.solver.stencil_order[-1]
# Number of guard cells
if grid.guard_cells is None:
n_guard = None
else:
n_guard = grid.guard_cells[-1]
if self.solver.galilean_velocity is None:
v_comoving = None
else:
v_comoving = self.solver.galilean_velocity[-1]
# Initialize and store the FBPIC simulation object
self.fbpic_sim = FBPICSimulation(Nz=int(grid.number_of_cells[1]),
zmin=grid.lower_bound[1],
zmax=grid.upper_bound[1],
Nr=int(grid.number_of_cells[0]),
rmax=grid.upper_bound[0],
Nm=grid.n_azimuthal_modes,
dt=dt,
use_cuda=True,
smoother=smoother,
n_order=n_order,
boundaries={
'z':
grid.upper_boundary_conditions[1],
'r':
grid.upper_boundary_conditions[0]
},
n_guard=n_guard,
verbose_level=verbose_level,
particle_shape=self.particle_shape,
v_comoving=v_comoving,
gamma_boost=self.gamma_boost,
**self.sim_kw)
# Set the moving window
if grid.moving_window_velocity is not None:
self.fbpic_sim.set_moving_window(grid.moving_window_velocity[-1])
# Redefine the method `add_laser` from the PICMI Simulation class
def add_laser(self, laser, injection_method):
# Call method of parent class
PICMI_Simulation.add_laser(self, laser, injection_method)
# Handle injection method
assert type(injection_method) == PICMI_LaserAntenna
# Handle laser profile method
if type(laser) == PICMI_GaussianLaser:
assert laser.propagation_direction[0] == 0.
assert laser.propagation_direction[1] == 0.
assert (laser.zeta is None) or (laser.zeta == 0)
assert (laser.beta is None) or (laser.beta == 0)
phi2_chirp = laser.phi2
if phi2_chirp is None:
phi2_chirp = 0
polarization_angle = np.arctan2(laser.polarization_direction[1],
laser.polarization_direction[0])
laser_profile = GaussianLaser(a0=laser.a0,
waist=laser.waist,
z0=laser.centroid_position[-1],
zf=laser.focal_position[-1],
tau=laser.duration,
theta_pol=polarization_angle,
phi2_chirp=phi2_chirp)
else:
raise ValueError('Unknown laser profile: %s' %
type(injection_method))
# Inject the laser
add_laser_pulse(self.fbpic_sim,
laser_profile,
method='antenna',
z0_antenna=injection_method.position[-1],
gamma_boost=self.gamma_boost)
# Redefine the method `add_species` from the PICMI Simulation class
def add_species(self, species, layout, initialize_self_field=False):
# Call method of parent class
PICMI_Simulation.add_species(self, species, layout,
initialize_self_field)
# Call generic method internally
self._add_species_generic(species,
layout,
injection_plane_position=None,
injection_plane_normal_vector=None,
initialize_self_field=initialize_self_field)
def add_species_through_plane(self,
species,
layout,
injection_plane_position,
injection_plane_normal_vector,
initialize_self_field=False):
# Call method of parent class
PICMI_Simulation.add_species_through_plane(
self,
species,
layout,
injection_plane_position,
injection_plane_normal_vector,
initialize_self_field=initialize_self_field)
# Call generic method internally
self._add_species_generic(
species,
layout,
injection_plane_position=injection_plane_position,
injection_plane_normal_vector=injection_plane_normal_vector,
initialize_self_field=initialize_self_field)
def _add_species_generic(self, species, layout, injection_plane_position,
injection_plane_normal_vector,
initialize_self_field):
# Extract list of species
if type(species) == PICMI_Species:
species_instances_list = [species]
elif type(species) == PICMI_MultiSpecies:
species_instances_list = species.species_instances_list
else:
raise ValueError('Unknown type: %s' % type(species))
# Loop over species and create FBPIC species
for s in species_instances_list:
# Get their charge and mass
if s.particle_type is not None:
s.charge = particle_charge[s.particle_type]
s.mass = particle_mass[s.particle_type]
# If `charge_state` is set, redefine the charge and mass
if s.charge_state is not None:
s.charge = s.charge_state * e
s.mass -= s.charge_state * m_e
# Add the species to the FBPIC simulation
fbpic_species = self._create_new_fbpic_species(
s, layout, injection_plane_position,
injection_plane_normal_vector, initialize_self_field)
# Register a pointer to the FBPIC species in the PICMI species itself
# (Useful for particle diagnostics later on)
s.fbpic_species = fbpic_species
# Loop over species and handle ionization
for s in species_instances_list:
for interaction in s.interactions:
assert interaction[0] == 'ionization'
assert interaction[1] == 'ADK'
picmi_target = interaction[2]
if not hasattr(picmi_target, 'fbpic_species'):
raise RuntimeError(
'For ionization with PICMI+FBPIC:\n'
'You need to add the target species to the simulation,'
' before the other species.')
fbpic_target = picmi_target.fbpic_species
fbpic_source = s.fbpic_species
fbpic_source.make_ionizable(element=s.particle_type,
level_start=s.charge_state,
target_species=fbpic_target)
def _create_new_fbpic_species(self, s, layout, injection_plane_position,
injection_plane_normal_vector,
initialize_self_field):
# - For the case of a plasma/beam defined in a gridded layout
if type(layout) == PICMI_GriddedLayout:
# - Uniform distribution
if type(s.initial_distribution) == PICMI_UniformDistribution:
n0 = s.initial_distribution.density
dens_func = None
# - Analytic distribution
elif type(s.initial_distribution) == PICMI_AnalyticDistribution:
import numexpr
density_expression = s.initial_distribution.density_expression
if s.density_scale is not None:
n0 = s.density_scale
else:
n0 = 1.
def dens_func(x, y, z):
d = locals()
d.update(s.initial_distribution.user_defined_kw)
n = numexpr.evaluate(density_expression, local_dict=d)
return n
else:
raise ValueError(
'Unknown combination of layout and distribution')
p_nr = layout.n_macroparticle_per_cell[0]
p_nt = layout.n_macroparticle_per_cell[1]
p_nz = layout.n_macroparticle_per_cell[2]
if initialize_self_field or (injection_plane_position is not None):
assert s.initial_distribution.fill_in != True
if injection_plane_position is None:
z_injection_plane = None
else:
z_injection_plane = injection_plane_position[-1]
gamma0_beta0 = s.initial_distribution.directed_velocity[-1] / c
gamma0 = (1 + gamma0_beta0**2)**.5
dist = s.initial_distribution
fbpic_species = add_particle_bunch(
self.fbpic_sim,
q=s.charge,
m=s.mass,
gamma0=gamma0,
n=n0,
dens_func=dens_func,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt,
p_zmin=dist.lower_bound[-1]
if dist.lower_bound[-1] is not None else -np.inf,
p_zmax=dist.upper_bound[-1]
if dist.upper_bound[-1] is not None else +np.inf,
p_rmin=0,
p_rmax=dist.upper_bound[0]
if dist.upper_bound[0] is not None else +np.inf,
boost=self.fbpic_sim.boost,
z_injection_plane=z_injection_plane,
initialize_self_field=initialize_self_field,
boost_positions_in_dens_func=True)
else:
dist = s.initial_distribution
fbpic_species = self.fbpic_sim.add_new_species(
q=s.charge,
m=s.mass,
n=n0,
dens_func=dens_func,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt,
p_zmin=dist.lower_bound[-1]
if dist.lower_bound[-1] is not None else -np.inf,
p_zmax=dist.upper_bound[-1]
if dist.upper_bound[-1] is not None else +np.inf,
p_rmax=dist.upper_bound[0]
if dist.upper_bound[0] is not None else +np.inf,
continuous_injection=s.initial_distribution.fill_in,
boost_positions_in_dens_func=True)
# - For the case of a Gaussian beam
elif (type(s.initial_distribution)==PICMI_GaussianBunchDistribution) \
and (type(layout) == PICMI_PseudoRandomLayout):
dist = s.initial_distribution
gamma0_beta0 = dist.centroid_velocity[-1] / c
gamma0 = (1 + gamma0_beta0**2)**.5
sig_r = dist.rms_bunch_size[0]
sig_z = dist.rms_bunch_size[-1]
sig_gamma = dist.rms_velocity[-1] / c
sig_vr = dist.rms_velocity[0] / gamma0
if sig_vr != 0:
tf = -sig_r**2 / sig_vr**2 * dist.velocity_divergence[0]
else:
tf = 0.
zf = dist.centroid_position[-1] + \
dist.centroid_velocity[-1]/gamma0 * tf
# Calculate size at focus and emittance
sig_r0 = (sig_r**2 - (sig_vr * tf)**2)**0.5
n_emit = gamma0 * sig_r0 * sig_vr / c
# Get the number of physical particles
n_physical_particles = dist.n_physical_particles
if s.density_scale is not None:
n_physical_particles *= s.density_scale
fbpic_species = add_particle_bunch_gaussian(
self.fbpic_sim,
q=s.charge,
m=s.mass,
gamma0=gamma0,
sig_gamma=sig_gamma,
sig_r=sig_r0,
sig_z=sig_z,
n_emit=n_emit,
n_physical_particles=n_physical_particles,
n_macroparticles=layout.n_macroparticles,
zf=zf,
tf=tf,
boost=self.fbpic_sim.boost,
initialize_self_field=initialize_self_field)
# - For the case of an empty species
elif (s.initial_distribution is None) and (layout is None):
fbpic_species = self.fbpic_sim.add_new_species(q=s.charge,
m=s.mass)
else:
raise ValueError('Unknown combination of layout and distribution')
return fbpic_species
# Redefine the method `add_diagnostic` of the parent class
def add_diagnostic(self, diagnostic):
# Call method of parent class
PICMI_Simulation.add_diagnostic(self, diagnostic)
# Handle iteration_min/max in regular diagnostic
if type(diagnostic) in [
PICMI_FieldDiagnostic, PICMI_ParticleDiagnostic
]:
if diagnostic.step_min is None:
iteration_min = 0
else:
iteration_min = diagnostic.step_min
if diagnostic.step_max is None:
iteration_max = np.inf
else:
iteration_max = diagnostic.step_max
# Register field diagnostic
if type(diagnostic) in [
PICMI_FieldDiagnostic, PICMI_LabFrameFieldDiagnostic
]:
if diagnostic.data_list is None:
data_list = ['rho', 'E', 'B', 'J']
else:
data_list = set() # Use set to avoid redundancy
for data in diagnostic.data_list:
if data in ['Ex', 'Ey', 'Ez', 'E']:
data_list.add('E')
elif data in ['Bx', 'By', 'Bz', 'B']:
data_list.add('B')
elif data in ['Jx', 'Jy', 'Jz', 'J']:
data_list.add('J')
elif data == 'rho':
data_list.add('rho')
data_list = list(data_list)
if type(diagnostic) == PICMI_FieldDiagnostic:
diag = FieldDiagnostic(period=diagnostic.period,
fldobject=self.fbpic_sim.fld,
comm=self.fbpic_sim.comm,
fieldtypes=data_list,
write_dir=diagnostic.write_dir,
iteration_min=iteration_min,
iteration_max=iteration_max)
# Register particle density diagnostic
rho_density_list = []
if diagnostic.data_list is not None:
for data in diagnostic.data_list:
if data.startswith('rho_'):
# particle density diagnostics, rho_speciesname
rho_density_list.append(data)
if rho_density_list:
species_dict = {}
for data in rho_density_list:
sname = data[4:]
for s in self.species:
if s.name == sname:
species_dict[s.name] = s.fbpic_species
pdd_diag = ParticleChargeDensityDiagnostic(
period=diagnostic.period,
sim=self.fbpic_sim,
species=species_dict,
write_dir=diagnostic.write_dir,
iteration_min=iteration_min,
iteration_max=iteration_max)
self.fbpic_sim.diags.append(pdd_diag)
elif type(diagnostic) == PICMI_LabFrameFieldDiagnostic:
diag = BackTransformedFieldDiagnostic(
zmin_lab=diagnostic.grid.lower_bound[1],
zmax_lab=diagnostic.grid.upper_bound[1],
v_lab=c,
dt_snapshots_lab=diagnostic.dt_snapshots,
Ntot_snapshots_lab=diagnostic.num_snapshots,
gamma_boost=self.gamma_boost,
period=100,
fldobject=self.fbpic_sim.fld,
comm=self.fbpic_sim.comm,
fieldtypes=diagnostic.data_list,
write_dir=diagnostic.write_dir)
# Register particle diagnostic
elif type(diagnostic) in [
PICMI_ParticleDiagnostic, PICMI_LabFrameParticleDiagnostic
]:
species_dict = {}
for s in diagnostic.species:
if s.name is None:
raise ValueError('When using a species in a diagnostic, '
'its name must be set.')
species_dict[s.name] = s.fbpic_species
if diagnostic.data_list is None:
data_list = ['position', 'momentum', 'weighting']
else:
data_list = diagnostic.data_list
if type(diagnostic) == PICMI_ParticleDiagnostic:
diag = ParticleDiagnostic(period=diagnostic.period,
species=species_dict,
comm=self.fbpic_sim.comm,
particle_data=data_list,
write_dir=diagnostic.write_dir,
iteration_min=iteration_min,
iteration_max=iteration_max)
else:
diag = BackTransformedParticleDiagnostic(
zmin_lab=diagnostic.grid.lower_bound[1],
zmax_lab=diagnostic.grid.upper_bound[1],
v_lab=c,
dt_snapshots_lab=diagnostic.dt_snapshots,
Ntot_snapshots_lab=diagnostic.num_snapshots,
gamma_boost=self.gamma_boost,
period=100,
fldobject=self.fbpic_sim.fld,
species=species_dict,
comm=self.fbpic_sim.comm,
particle_data=data_list,
write_dir=diagnostic.write_dir)
# Add it to the FBPIC simulation
self.fbpic_sim.diags.append(diag)
# Redefine the method `add_diagnostic` of the parent class
def add_applied_field(self, applied_field):
# Call method of parent class
PICMI_Simulation.add_applied_field(self, applied_field)
if type(applied_field) == PICMI_Mirror:
assert applied_field.z_front_location is not None
mirror = Mirror(z_lab=applied_field.z_front_location,
n_cells=applied_field.number_of_cells,
gamma_boost=self.fbpic_sim.boost.gamma0)
self.fbpic_sim.mirrors.append(mirror)
elif type(applied_field) == PICMI_ConstantAppliedField:
# TODO: Handle bounds
for field_name in ['Ex', 'Ey', 'Ez', 'Bx', 'By', 'Bz']:
field_value = getattr(applied_field, field_name)
if field_value is None:
continue
def field_func(F, x, y, z, t, amplitude, length_scale):
return (F + amplitude * field_value)
# Pass it to FBPIC
self.fbpic_sim.external_fields.append(
ExternalField(field_func, field_name, 1., 0.))
elif type(applied_field) == PICMI_AnalyticAppliedField:
# TODO: Handle bounds
for field_name in ['Ex', 'Ey', 'Ez', 'Bx', 'By', 'Bz']:
# Extract expression and execute it inside a function definition
expression = getattr(applied_field, field_name + '_expression')
if expression is None:
continue
fieldfunc = None
define_function_code = \
"""def fieldfunc( F, x, y, z, t, amplitude, length_scale ):\n return( F + amplitude * %s )""" %expression
# Take into account user-defined variables
for k in applied_field.user_defined_kw:
define_function_code = \
"%s = %s\n" %(k,applied_field.user_defined_kw[k]) \
+ define_function_code
exec(define_function_code, globals())
# Pass it to FBPIC
self.fbpic_sim.external_fields.append(
ExternalField(fieldfunc, field_name, 1., 0.))
else:
raise ValueError("Unrecognized `applied_field` type.")
# Redefine the method `step` of the parent class
def step(self, nsteps=None):
if nsteps is None:
nsteps = self.max_steps
self.fbpic_sim.step(nsteps, **self.step_kw)
class Simulation(PICMI_Simulation):
# Redefine the `init` method, as required by the picmi `_ClassWithInit`
def init(self, kw):
# Get the grid
grid = self.solver.grid
if not type(grid) == PICMI_CylindricalGrid:
raise ValueError('When using fbpic with PICMI, '
'the grid needs to be a CylindricalGrid object.')
# Check rmin and boundary conditions
assert grid.rmin == 0.
assert grid.bc_zmin == grid.bc_zmax
assert grid.bc_zmax in ['periodic', 'open']
assert grid.bc_rmax in ['reflective', 'open']
# Determine timestep
if self.solver.cfl is not None:
dz = (grid.zmax - grid.zmin) / grid.nz
dt = self.solver.cfl * dz / c
elif self.time_step_size is not None:
dt = self.time_step_size
else:
raise ValueError('You need to either set the `cfl` of the solver\n'
'or the `timestep_size` of the `Simulation`.')
# Convert API for the smoother
if self.solver.source_smoother is None:
smoother = BinomialSmoother()
else:
smoother = BinomialSmoother(
n_passes=self.solver.source_smoother.n_pass,
compensator=self.solver.source_smoother.compensation)
# Initialize and store the FBPIC simulation object
self.fbpic_sim = FBPICSimulation(Nz=int(grid.nz),
zmin=grid.zmin,
zmax=grid.zmax,
Nr=int(grid.nr),
rmax=grid.rmax,
Nm=grid.n_azimuthal_modes,
dt=dt,
use_cuda=True,
smoother=smoother,
n_order=32,
boundaries={
'z': grid.bc_zmax,
'r': grid.bc_rmax
})
# Set the moving window
if grid.moving_window_zvelocity is not None:
self.fbpic_sim.set_moving_window(grid.moving_window_zvelocity)
# Redefine the method `add_laser` from the PICMI Simulation class
def add_laser(self, laser, injection_method):
# Call method of parent class
PICMI_Simulation.add_laser(self, laser, injection_method)
# Handle injection method
assert type(injection_method) == PICMI_LaserAntenna
# Handle laser profile method
if type(laser) == PICMI_GaussianLaser:
assert laser.propagation_direction[0] == 0.
assert laser.propagation_direction[1] == 0.
assert (laser.zeta is None) or (laser.zeta == 0)
assert (laser.beta is None) or (laser.beta == 0)
phi2_chirp = laser.phi2
if phi2_chirp is None:
phi2_chirp = 0
polarization_angle = np.arctan2(laser.polarization_direction[1],
laser.polarization_direction[0])
laser_profile = GaussianLaser(a0=laser.a0,
waist=laser.waist,
z0=laser.centroid_position[-1],
zf=laser.focal_position[-1],
tau=laser.duration,
theta_pol=polarization_angle,
phi2_chirp=phi2_chirp)
else:
raise ValueError('Unknown laser profile: %s' %
type(injection_method))
# Inject the laser
add_laser_pulse(self.fbpic_sim,
laser_profile,
method='antenna',
z0_antenna=injection_method.position[-1])
# Redefine the method `add_species` from the PICMI Simulation class
def add_species(self, species, layout, initialize_self_field=False):
# Call method of parent class
PICMI_Simulation.add_species(self, species, layout,
initialize_self_field)
# Extract list of species
if type(species) == PICMI_Species:
species_instances_list = [species]
elif type(species) == PICMI_MultiSpecies:
species_instances_list = species.species_instances_list
else:
raise ValueError('Unknown type: %s' % type(species))
# Loop over species and create FBPIC species
for s in species_instances_list:
# Get their charge and mass
if s.particle_type is not None:
s.charge = particle_charge[s.particle_type]
s.mass = particle_mass[s.particle_type]
# If `charge_state` is set, redefine the charge and mass
if s.charge_state is not None:
s.charge = s.charge_state * e
s.mass -= s.charge_state * m_e
# Add the species to the FBPIC simulation
fbpic_species = self._create_new_fbpic_species(
s, layout, initialize_self_field)
# Register a pointer to the FBPIC species in the PICMI species itself
# (Useful for particle diagnostics later on)
s.fbpic_species = fbpic_species
# Loop over species and handle ionization
for s in species_instances_list:
for interaction in s.interactions:
assert interaction[0] == 'ionization'
assert interaction[1] == 'ADK'
picmi_target = interaction[2]
if not hasattr(picmi_target, 'fbpic_species'):
raise RuntimeError(
'For ionization with PICMI+FBPIC:\n'
'You need to add the target species to the simulation,'
' before the other species.')
fbpic_target = picmi_target.fbpic_species
fbpic_source = s.fbpic_species
fbpic_source.make_ionizable(element=s.particle_type,
level_start=s.charge_state,
target_species=fbpic_target)
def _create_new_fbpic_species(self, s, layout, initialize_self_field):
# - For the case of a plasma defined in a gridded layout
if (type(s.initial_distribution)==PICMI_AnalyticDistribution) and \
(type(layout) == PICMI_GriddedLayout):
assert initialize_self_field == False
import numexpr
density_expression = s.initial_distribution.density_expression
if s.density_scale is not None:
density_expression = "%f*(%s)" \
%(s.density_scale, density_expression)
def dens_func(z, r):
n = numexpr.evaluate(density_expression)
return n
p_nr = layout.n_macroparticle_per_cell[0]
p_nt = layout.n_macroparticle_per_cell[1]
p_nz = layout.n_macroparticle_per_cell[2]
fbpic_species = self.fbpic_sim.add_new_species(
q=s.charge,
m=s.mass,
n=1.,
dens_func=dens_func,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt,
p_zmin=s.initial_distribution.lower_bound[-1],
p_zmax=s.initial_distribution.upper_bound[-1],
continuous_injection=s.initial_distribution.fill_in)
# - For the case of a Gaussian beam
elif (type(s.initial_distribution)==PICMI_GaussianBunchDistribution) \
and (type(layout) == PICMI_PseudoRandomLayout):
dist = s.initial_distribution
gamma0_beta0 = dist.centroid_velocity[-1] / c
gamma0 = (1 + gamma0_beta0**2)**.5
sig_r = dist.rms_bunch_size[0]
sig_z = dist.rms_bunch_size[-1]
sig_gamma = dist.rms_velocity[-1] / c
sig_vr = dist.rms_velocity[0] / gamma0
if sig_vr != 0:
tf = -sig_r**2 / sig_vr**2 * dist.velocity_divergence[0]
else:
tf = 0.
zf = dist.centroid_position[-1] + \
dist.centroid_velocity[-1]/gamma0 * tf
# Calculate size at focus and emittance
sig_r0 = (sig_r**2 - (sig_vr * tf)**2)**0.5
n_emit = gamma0 * sig_r0 * sig_vr / c
# Get the number of physical particles
n_physical_particles = dist.n_physical_particles
if s.density_scale is not None:
n_physical_particles *= s.density_scale
fbpic_species = add_particle_bunch_gaussian(
self.fbpic_sim,
q=s.charge,
m=s.mass,
gamma0=gamma0,
sig_gamma=sig_gamma,
sig_r=sig_r0,
sig_z=sig_z,
n_emit=n_emit,
n_physical_particles=n_physical_particles,
n_macroparticles=layout.n_macroparticles,
zf=zf,
tf=tf,
initialize_self_field=initialize_self_field)
# - For the case of an empty species
elif (s.initial_distribution is None) and (layout is None):
fbpic_species = self.fbpic_sim.add_new_species(q=s.charge,
m=s.mass)
else:
raise ValueError('Unknown combination of layout and distribution')
return fbpic_species
# Redefine the method `add_diagnostic` of the parent class
def add_diagnostic(self, diagnostic):
# Call method of parent class
PICMI_Simulation.add_diagnostic(self, diagnostic)
# Handle diagnostic
if diagnostic.step_min is None:
iteration_min = 0
else:
iteration_min = diagnostic.step_min
if diagnostic.step_max is None:
iteration_max = np.inf
else:
iteration_max = diagnostic.step_max
# Register field diagnostic
if type(diagnostic) == PICMI_FieldDiagnostic:
diag = FieldDiagnostic(period=diagnostic.period,
fldobject=self.fbpic_sim.fld,
comm=self.fbpic_sim.comm,
fieldtypes=diagnostic.data_list,
write_dir=diagnostic.write_dir,
iteration_min=iteration_min,
iteration_max=iteration_max)
# Register particle diagnostic
elif type(diagnostic) == PICMI_ParticleDiagnostic:
species_dict = {}
for s in diagnostic.species:
if s.name is None:
raise ValueError('When using a species in a diagnostic, '
'its name must be set.')
species_dict[s.name] = s.fbpic_species
diag = ParticleDiagnostic(period=diagnostic.period,
species=species_dict,
comm=self.fbpic_sim.comm,
particle_data=diagnostic.data_list,
write_dir=diagnostic.write_dir,
iteration_min=iteration_min,
iteration_max=iteration_max)
# Add it to the FBPIC simulation
self.fbpic_sim.diags.append(diag)
# Redefine the method `step` of the parent class
def step(self, nsteps):
self.fbpic_sim.step(nsteps)
dt,
zmin=zmin,
boundaries={
'z': 'open',
'r': 'reflective'
},
n_order=n_order,
use_cuda=use_cuda,
use_all_mpi_ranks=False)
# Create the plasma electrons
elec = sim.add_new_species(q=-e,
m=m_e,
n=n_e,
dens_func=dens_func,
p_zmin=p_zmin,
p_zmax=p_zmax,
p_rmax=p_rmax,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt)
# Load initial fields
# Add a laser to the fields of the simulation
add_laser(sim, a0, w0, ctau, z0)
if use_restart is True:
# Load the fields and particles from the latest checkpoint file
restart_from_checkpoint(sim)
# Configure the moving window
sim.set_moving_window(v=v_window)
def run_external_laser_field_simulation(show, gamma_boost=None):
"""
Runs a simulation with a set of particles whose motion corresponds
to that of a particle that is initially at rest (in the lab frame)
before being reached by a plane wave (propagating to the right)
In the lab frame, the motion is given by
ux = a0 sin ( k0(z-ct) )
uz = ux^2 / 2 (from the conservation of gamma - uz)
In the boosted frame, the motion is given by
ux = a0 sin ( k0 gamma0 (1-beta0) (z-ct) )
uz = - gamma0 beta0 + gamma0 (1-beta0) ux^2 / 2
"""
# Time parameters
dt = lambda0 / c / 200 # 200 points per laser period
N_step = 400 # Two laser periods
# Initialize BoostConverter object
if gamma_boost is None:
boost = BoostConverter(gamma0=1.)
else:
boost = BoostConverter(gamma_boost)
# Reduce time resolution, for the case of a boosted simulation
if gamma_boost is not None:
dt = dt * (1. + boost.beta0) / boost.gamma0
# Initialize the simulation
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
initialize_ions=False,
zmin=zmin,
use_cuda=use_cuda,
boundaries='periodic',
gamma_boost=gamma_boost)
# Add electrons
sim.ptcl = []
sim.add_new_species(-e,
m_e,
n=n,
p_rmax=p_rmax,
p_nz=p_nz,
p_nr=p_nr,
p_nt=p_nt)
# Add the external fields
sim.external_fields = [
ExternalField(laser_func,
'Ex',
a0 * m_e * c**2 * k0 / e,
lambda0,
gamma_boost=gamma_boost),
ExternalField(laser_func,
'By',
a0 * m_e * c * k0 / e,
lambda0,
gamma_boost=gamma_boost)
]
# Prepare the arrays for the time history of the pusher
Nptcl = sim.ptcl[0].Ntot
x = np.zeros((N_step, Nptcl))
y = np.zeros((N_step, Nptcl))
z = np.zeros((N_step, Nptcl))
ux = np.zeros((N_step, Nptcl))
uy = np.zeros((N_step, Nptcl))
uz = np.zeros((N_step, Nptcl))
# Prepare the particles with proper transverse and longitudinal momentum,
# at t=0 in the simulation frame
k0p = k0 * boost.gamma0 * (1. - boost.beta0)
sim.ptcl[0].ux = a0 * np.sin(k0p * sim.ptcl[0].z)
sim.ptcl[0].uz[:] = -boost.gamma0*boost.beta0 \
+ boost.gamma0*(1-boost.beta0)*0.5*sim.ptcl[0].ux**2
# Push the particles over N_step and record the corresponding history
for i in range(N_step):
# Record the history
x[i, :] = sim.ptcl[0].x[:]
y[i, :] = sim.ptcl[0].y[:]
z[i, :] = sim.ptcl[0].z[:]
ux[i, :] = sim.ptcl[0].ux[:]
uy[i, :] = sim.ptcl[0].uy[:]
uz[i, :] = sim.ptcl[0].uz[:]
# Take a simulation step
sim.step(1)
# Compute the analytical solution
t = sim.dt * np.arange(N_step)
# Conservation of ux
ux_analytical = np.zeros((N_step, Nptcl))
uz_analytical = np.zeros((N_step, Nptcl))
for i in range(N_step):
ux_analytical[i, :] = a0 * np.sin(k0p * (z[i, :] - c * t[i]))
uz_analytical[i,:] = -boost.gamma0*boost.beta0 \
+ boost.gamma0*(1-boost.beta0)*0.5*ux_analytical[i,:]**2
# Show the results
if show:
import matplotlib.pyplot as plt
plt.figure(figsize=(10, 5))
plt.subplot(211)
plt.plot(t, ux_analytical, '--')
plt.plot(t, ux, 'o')
plt.xlabel('t')
plt.ylabel('ux')
plt.subplot(212)
plt.plot(t, uz_analytical, '--')
plt.plot(t, uz, 'o')
plt.xlabel('t')
plt.ylabel('uz')
plt.show()
else:
assert np.allclose(ux, ux_analytical, atol=5.e-2)
assert np.allclose(uz, uz_analytical, atol=5.e-2)
def run_fbpic(job: Job) -> None:
"""
This ``signac-flow`` operation runs a ``fbpic`` simulation.
:param job: the job instance is a handle to the data of a unique statepoint
"""
from fbpic.main import Simulation
from fbpic.lpa_utils.laser import add_laser_pulse, GaussianLaser
from fbpic.openpmd_diag import FieldDiagnostic, ParticleDiagnostic
# The density profile
def dens_func(z: np.ndarray, r: np.ndarray) -> np.ndarray:
"""Returns relative density at position z and r.
:param z: longitudinal positions, 1d array
:param r: radial positions, 1d array
:return: a 1d array ``n`` containing the density (between 0 and 1) at the given positions (z, r)
"""
# Allocate relative density
n = np.ones_like(z)
# Make linear ramp
n = np.where(
z < job.sp.ramp_start + job.sp.ramp_length,
(z - job.sp.ramp_start) / job.sp.ramp_length,
n,
)
# Supress density before the ramp
n = np.where(z < job.sp.ramp_start, 0.0, n)
return n
# plot density profile for checking
all_z = np.linspace(job.sp.zmin, job.sp.p_zmax, 1000)
dens = dens_func(all_z, 0.0)
width_inch = job.sp.p_zmax / 1e-5
major_locator = pyplot.MultipleLocator(10)
minor_locator = pyplot.MultipleLocator(5)
major_locator.MAXTICKS = 10000
minor_locator.MAXTICKS = 10000
def mark_on_plot(*, ax, parameter: str, y=1.1):
ax.annotate(s=parameter,
xy=(job.sp[parameter] * 1e6, y),
xycoords="data")
ax.axvline(x=job.sp[parameter] * 1e6, linestyle="--", color="red")
return ax
fig, ax = pyplot.subplots(figsize=(width_inch, 4.8))
ax.plot(all_z * 1e6, dens)
ax.set_xlabel(r"$%s \;(\mu m)$" % "z")
ax.set_ylim(-0.1, 1.2)
ax.set_xlim(job.sp.zmin * 1e6 - 20, job.sp.p_zmax * 1e6 + 20)
ax.set_ylabel("Density profile $n$")
ax.xaxis.set_major_locator(major_locator)
ax.xaxis.set_minor_locator(minor_locator)
mark_on_plot(ax=ax, parameter="zmin")
mark_on_plot(ax=ax, parameter="zmax")
mark_on_plot(ax=ax, parameter="p_zmin", y=0.9)
mark_on_plot(ax=ax, parameter="z0", y=0.8)
mark_on_plot(ax=ax, parameter="zf", y=0.6)
mark_on_plot(ax=ax, parameter="ramp_start", y=0.7)
mark_on_plot(ax=ax, parameter="L_interact")
mark_on_plot(ax=ax, parameter="p_zmax")
ax.annotate(s="ramp_start + ramp_length",
xy=(job.sp.ramp_start * 1e6 + job.sp.ramp_length * 1e6, 1.1),
xycoords="data")
ax.axvline(x=job.sp.ramp_start * 1e6 + job.sp.ramp_length * 1e6,
linestyle="--",
color="red")
ax.fill_between(all_z * 1e6, dens, alpha=0.5)
fig.savefig(job.fn("check_density.png"))
# redirect stdout to "stdout.txt"
orig_stdout = sys.stdout
f = open(job.fn("stdout.txt"), "w")
sys.stdout = f
# Initialize the simulation object
sim = Simulation(
job.sp.Nz,
job.sp.zmax,
job.sp.Nr,
job.sp.rmax,
job.sp.Nm,
job.sp.dt,
n_e=None, # no electrons
zmin=job.sp.zmin,
boundaries={
"z": "open",
"r": "reflective"
},
n_order=-1,
use_cuda=True,
verbose_level=2,
)
# Create a Gaussian laser profile
laser_profile = GaussianLaser(a0=job.sp.a0,
waist=job.sp.w0,
tau=job.sp.ctau / c_light,
z0=job.sp.z0,
zf=job.sp.zf,
theta_pol=0.,
lambda0=job.sp.lambda0,
cep_phase=0.,
phi2_chirp=0.,
propagation_direction=1)
# Add it to the simulation
add_laser_pulse(sim,
laser_profile,
gamma_boost=None,
method='direct',
z0_antenna=None,
v_antenna=0.)
# Create the plasma electrons
elec = sim.add_new_species(q=-q_e,
m=m_e,
n=job.sp.n_e,
dens_func=dens_func,
p_zmin=job.sp.p_zmin,
p_zmax=job.sp.p_zmax,
p_rmax=job.sp.p_rmax,
p_nz=job.sp.p_nz,
p_nr=job.sp.p_nr,
p_nt=job.sp.p_nt)
# Track electrons, useful for betatron radiation
# elec.track(sim.comm)
# Configure the moving window
sim.set_moving_window(v=c_light)
# Add diagnostics
write_dir = os.path.join(job.ws, "diags")
sim.diags = [
FieldDiagnostic(job.sp.diag_period,
sim.fld,
comm=sim.comm,
write_dir=write_dir,
fieldtypes=["rho", "E"]),
ParticleDiagnostic(job.sp.diag_period, {"electrons": elec},
select={"uz": [1., None]},
comm=sim.comm,
write_dir=write_dir,
particle_data=["momentum", "weighting"]),
]
# Plot the Ex component of the laser
# Get the fields in the half-plane theta=0 (Sum mode 0 and mode 1)
gathered_grids = [
sim.comm.gather_grid(sim.fld.interp[m]) for m in range(job.sp.Nm)
]
rgrid = gathered_grids[0].r
zgrid = gathered_grids[0].z
# construct the Er field for theta=0
Er = gathered_grids[0].Er.T.real
for m in range(1, job.sp.Nm):
# There is a factor 2 here so as to comply with the convention in
# Lifschitz et al., which is also the convention adopted in Warp Circ
Er += 2 * gathered_grids[m].Er.T.real
e0 = electric_field_amplitude_norm(lambda0=job.sp.lambda0)
fig = pyplot.figure(figsize=(8, 8))
sliceplots.Plot2D(
fig=fig,
arr2d=Er / e0,
h_axis=zgrid * 1e6,
v_axis=rgrid * 1e6,
zlabel=r"$E_r/E_0$",
xlabel=r"$z \;(\mu m)$",
ylabel=r"$r \;(\mu m)$",
extent=(
zgrid[0] * 1e6, # + 40
zgrid[-1] * 1e6, # - 20
rgrid[0] * 1e6,
rgrid[-1] * 1e6, # - 15,
),
cbar=True,
vmin=-3,
vmax=3,
hslice_val=0.0, # do a 1D slice through the middle of the simulation box
)
fig.savefig(job.fn('check_laser.png'))
# set deterministic random seed
np.random.seed(0)
# Run the simulation
sim.step(job.sp.N_step, show_progress=False)
# redirect stdout back and close "stdout.txt"
sys.stdout = orig_stdout
f.close()
def run_continuous_injection(gamma_boost,
ramp,
p_zmin,
p_zmax,
show,
N_check=2):
# Chose the time step
dt = (zmax - zmin) / Nz / c
def dens_func(z, r):
dens = np.ones_like(z)
# Make the density smooth at rmax
dens = np.where(r > rmax - smooth_r,
np.cos(0.5 * np.pi * (r - smooth_r) / smooth_r)**2,
dens)
# Make the density 0 below p_zmin
dens = np.where(z < p_zmin, 0., dens)
# Make a linear ramp
dens = np.where((z >= p_zmin) & (z < p_zmin + ramp),
(z - p_zmin) / ramp * dens, dens)
return (dens)
# Initialize the different structures
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
p_zmin,
p_zmax,
0,
p_rmax,
p_nz,
p_nr,
p_nt,
0.5 * n,
dens_func=dens_func,
initialize_ions=False,
zmin=zmin,
use_cuda=use_cuda,
gamma_boost=gamma_boost,
boundaries='open')
# Add another species with a different number of particles per cell
# and with a finite temperature
uth = 0.0001
sim.add_new_species(-e,
m_e,
0.5 * n,
dens_func,
2 * p_nz,
2 * p_nr,
2 * p_nt,
p_zmin,
p_zmax,
0,
p_rmax,
ux_th=uth,
uy_th=uth,
uz_th=uth)
# Set the moving window, which handles the continuous injection
# The moving window has an arbitrary velocity (0.7*c) so as to check
# that the injection is correct in this case also
sim.set_moving_window(v=c)
# Check that the density is correct after different timesteps
N_step = int(Nz / N_check / 2)
for i in range(N_check):
sim.step(N_step, move_momenta=False)
check_density(sim, gamma_boost, dens_func, show)
def run_simulation( gamma_boost, show ):
"""
Run a simulation with a relativistic electron bunch crosses a laser
Parameters
----------
gamma_boost: float
The Lorentz factor of the frame in which the simulation is carried out.
show: bool
Whether to show a plot of the angular distribution
"""
# Boosted frame
boost = BoostConverter(gamma_boost)
# The simulation timestep
diag_period = 100
N_step = 101 # Number of iterations to perform
# Calculate timestep to resolve the interaction with enough points
laser_duration_boosted, = boost.copropag_length(
[laser_duration], beta_object=-1 )
bunch_sigma_z_boosted, = boost.copropag_length(
[bunch_sigma_z], beta_object=1 )
dt = (4*laser_duration_boosted + bunch_sigma_z_boosted/c)/N_step
# Initialize the simulation object
zmax, zmin = boost.copropag_length( [zmax_lab, zmin_lab], beta_object=1. )
sim = Simulation( Nz, zmax, Nr, rmax, Nm, dt,
dens_func=None, zmin=zmin, boundaries={'z':'periodic', 'r':'reflective'},
use_cuda=use_cuda )
# Remove particles that were previously created
sim.ptcl = []
print( 'Initialized simulation' )
# Add electron bunch (automatically converted to boosted-frame)
add_elec_bunch_gaussian( sim, sig_r=1.e-6, sig_z=bunch_sigma_z,
n_emit=0., gamma0=gamma_bunch_mean, sig_gamma=gamma_bunch_rms,
Q=Q_bunch, N=N_bunch, tf=0.0, zf=0.5*(zmax+zmin), boost=boost )
elec = sim.ptcl[0]
print( 'Initialized electron bunch' )
# Add a photon species
photons = sim.add_new_species( q=0, m=0 )
print( 'Initialized photons' )
# Activate Compton scattering for electrons of the bunch
elec.activate_compton( target_species=photons,
laser_energy=laser_energy, laser_wavelength=laser_wavelength,
laser_waist=laser_waist, laser_ctau=laser_ctau,
laser_initial_z0=laser_initial_z0, ratio_w_electron_photon=50,
boost=boost )
print( 'Activated Compton' )
# Add diagnostics
if write_hdf5:
sim.diags = [ ParticleDiagnostic( diag_period,
species={'electrons': elec, 'photons': photons}, comm=sim.comm ) ]
# Get initial total momentum
initial_total_elec_px = (elec.w*elec.ux).sum() * m_e * c
initial_total_elec_py = (elec.w*elec.uy).sum() * m_e * c
initial_total_elec_pz = (elec.w*elec.uz).sum() * m_e * c
### Run the simulation
for species in sim.ptcl:
species.send_particles_to_gpu()
for i_step in range( N_step ):
for species in sim.ptcl:
species.push_x( 0.5*sim.dt )
elec.handle_elementary_processes( sim.time + 0.5*sim.dt )
for species in sim.ptcl:
species.push_x( 0.5*sim.dt )
# Increment time and run diagnostics
sim.time += sim.dt
sim.iteration += 1
for diag in sim.diags:
diag.write( sim.iteration )
# Print fraction of photons produced
if i_step%10 == 0:
for species in sim.ptcl:
species.receive_particles_from_gpu()
simulated_frac = photons.w.sum()/elec.w.sum()
for species in sim.ptcl:
species.send_particles_to_gpu()
print( 'Iteration %d: Photon fraction per electron = %f' \
%(i_step, simulated_frac) )
for species in sim.ptcl:
species.receive_particles_from_gpu()
# Check estimation of photon fraction
check_photon_fraction( simulated_frac )
# Check conservation of momentum (is only conserved )
if elec.compton_scatterer.ratio_w_electron_photon == 1:
check_momentum_conservation( gamma_boost, photons, elec,
initial_total_elec_px, initial_total_elec_py, initial_total_elec_pz )
# Transform the photon momenta back into the lab frame
photon_u = 1./photons.inv_gamma
photon_lab_pz = boost.gamma0*( photons.uz + boost.beta0*photon_u )
photon_lab_p = boost.gamma0*( photon_u + boost.beta0*photons.uz )
# Plot the scaled angle and frequency
if show:
import matplotlib.pyplot as plt
# Bin the photons on a grid in frequency and angle
freq_min = 0.5
freq_max = 1.2
N_freq = 500
gammatheta_min = 0.
gammatheta_max = 1.
N_gammatheta = 100
hist_range = [[freq_min, freq_max], [gammatheta_min, gammatheta_max]]
extent = [freq_min, freq_max, gammatheta_min, gammatheta_max]
fundamental_frequency = 4*gamma_bunch_mean**2*c/laser_wavelength
photon_scaled_freq = photon_lab_p*c / (h*fundamental_frequency)
gamma_theta = gamma_bunch_mean * np.arccos(photon_lab_pz/photon_lab_p)
grid, freq_bins, gammatheta_bins = np.histogram2d(
photon_scaled_freq, gamma_theta, weights=photons.w,
range=hist_range, bins=[ N_freq, N_gammatheta ] )
# Normalize by solid angle, frequency and number of photons
dw = (freq_bins[1]-freq_bins[0]) * 2*np.pi * fundamental_frequency
dtheta = ( gammatheta_bins[1]-gammatheta_bins[0] )/gamma_bunch_mean
domega = 2.*np.pi*np.sin( gammatheta_bins/gamma_bunch_mean )*dtheta
grid /= dw * domega[np.newaxis, 1:] * elec.w.sum()
grid = np.where( grid==0, np.nan, grid )
plt.imshow( grid.T, origin='lower', extent=extent,
cmap='gist_earth', aspect='auto', vmax=1.8e-16 )
plt.title('Particles, $d^2N/d\omega \,d\Omega$')
plt.xlabel('Scaled energy ($\omega/4\gamma^2\omega_\ell$)')
plt.ylabel(r'$\gamma \theta$' )
plt.colorbar()
# Plot theory
plt.plot( 1./( 1 + gammatheta_bins**2), gammatheta_bins, color='r' )
plt.show()
plt.clf()
