def simulate_beam_focusing( z_injection_plane, write_dir ):
"""
Simulate a focusing beam in the boosted frame
Parameters
----------
z_injection_plane: float or None
when this is not None, the injection through a plane is
activated.
write_dir: string
The directory where the boosted diagnostics are written.
"""
# Initialize the simulation object
sim = Simulation( Nz, zmax, Nr, rmax, Nm, dt, zmin=zmin,
gamma_boost=gamma_boost, boundaries='open',
use_cuda=use_cuda, v_comoving=v_comoving )
# Note: no macroparticles get created because we do not pass
# the density and number of particle per cell
# Remove the plasma particles
sim.ptcl = []
# Initialize the bunch, along with its space charge
add_elec_bunch_gaussian( sim, sigma_r, sigma_z, n_emit, gamma0,
sigma_gamma, Q, N, tf=(z_focus-z0)/c, zf=z_focus, boost=boost,
z_injection_plane=z_injection_plane )
# Configure the moving window
sim.set_moving_window( v=c )
# Add a field diagnostic
sim.diags = [
BackTransformedParticleDiagnostic( zmin, zmax, c, dt_snapshot_lab,
Ntot_snapshot_lab, gamma_boost, period=100, fldobject=sim.fld,
species={'bunch':sim.ptcl[0]}, comm=sim.comm, write_dir=write_dir)
]
# Run the simulation
sim.step( N_step )
def run_cpu_gpu_deposition(show=False, particle_shape='cubic'):
# Skip this test if cuda is not installed
if not cuda_installed:
return
# Perform deposition for a few timesteps, with both the CPU and GPU
for hardware in ['cpu', 'gpu']:
if hardware == 'cpu':
use_cuda = False
elif hardware == 'gpu':
use_cuda = True
# Initialize the simulation object
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
zmin=zmin,
use_cuda=use_cuda,
particle_shape=particle_shape)
sim.ptcl = []
# Add an electron bunch (set the random seed first)
np.random.seed(0)
add_elec_bunch_gaussian(sim, sig_r, sig_z, n_emit, gamma0, sig_gamma,
Q, N)
# Add a field diagnostic
sim.diags = [
FieldDiagnostic(diag_period,
sim.fld,
fieldtypes=['rho', 'J'],
comm=sim.comm,
write_dir=os.path.join('tests', hardware))
]
### Run the simulation
sim.step(N_step)
# Check that the results are identical
ts_cpu = OpenPMDTimeSeries('tests/cpu/hdf5')
ts_gpu = OpenPMDTimeSeries('tests/gpu/hdf5')
for iteration in ts_cpu.iterations:
for field, coord in [('rho', ''), ('J', 'x'), ('J', 'z')]:
# Jy is not tested because it is zero
print('Testing %s at iteration %d' % (field + coord, iteration))
F_cpu, info = ts_cpu.get_field(field, coord, iteration=iteration)
F_gpu, info = ts_gpu.get_field(field, coord, iteration=iteration)
tolerance = 1.e-13 * (abs(F_cpu).max() + abs(F_gpu).max())
if not show:
assert np.allclose(F_cpu, F_gpu, atol=tolerance)
else:
if not np.allclose(F_cpu, F_gpu, atol=tolerance):
plot_difference(field, coord, iteration, F_cpu, F_gpu,
info)
# Remove the files used
shutil.rmtree('tests/cpu')
shutil.rmtree('tests/gpu')
if use_restart is False:
# Track electrons if required (species 0 correspond to the electrons)
if track_electrons:
elec.track(sim.comm)
else:
# 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)
# Add diagnostics
sim.diags = [
FieldDiagnostic(diag_period, sim.fld, comm=sim.comm),
ParticleDiagnostic(diag_period, {
"electrons from N": elec_from_N,
"electrons": elec
},
comm=sim.comm),
# Since rho from `FieldDiagnostic` is 0 almost everywhere
# (neutral plasma), it is useful to see the charge density
# of individual particles
ParticleChargeDensityDiagnostic(diag_period, sim, {"electrons": elec})
]
# Add checkpoints
if save_checkpoints:
set_periodic_checkpoint(sim, checkpoint_period)
### Run the simulation
sim.step(N_step)
p_zmin=p_zmin)
# Activate ionization of He ions (for levels above 1).
# Store the created electrons in the species `elec`
atoms_He.make_ionizable('He', target_species=elec, level_start=1)
# Activate ionization of N ions (for levels above 5).
# Store the created electrons in a new dedicated electron species that
# does not contain any macroparticles initially
elec_from_N = sim.add_new_species(q=-e, m=m_e)
atoms_N.make_ionizable('N', target_species=elec_from_N, level_start=5)
# Add a laser to the fields of the simulation
add_laser(sim, a0, w0, ctau, z0, zf=z_foc)
# Configure the moving window
sim.set_moving_window(v=v_window)
# Add a diagnostics
sim.diags = [
FieldDiagnostic(diag_period, sim.fld, comm=sim.comm),
ParticleDiagnostic(diag_period, {
"e- from N": elec_from_N,
"e-": elec
},
comm=sim.comm)
]
### Run the simulation
sim.step(N_step)
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,
p_zmin=0,
p_zmax=0,
p_rmin=0,
p_rmax=0,
p_nz=1,
p_nr=1,
p_nt=1,
n_e=1,
dens_func=None,
zmin=zmin,
boundaries='periodic',
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 = Particles(q=0,
m=0,
n=0,
Npz=1,
zmin=0,
zmax=0,
Npr=1,
rmin=0,
rmax=0,
Nptheta=1,
dt=sim.dt,
ux_m=0.,
uy_m=0.,
uz_m=0.,
ux_th=0.,
uy_th=0.,
uz_th=0.,
dens_func=None,
continuous_injection=False,
grid_shape=sim.fld.interp[0].Ez.shape,
particle_shape='linear',
use_cuda=sim.use_cuda)
sim.ptcl.append(photons)
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.halfpush_x()
elec.handle_elementary_processes(sim.time + 0.5 * sim.dt)
for species in sim.ptcl:
species.halfpush_x()
# 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()
# Load initial fields
# Add a laser to the fields of the simulation
add_laser(sim, a0, w0, ctau, z0)
if use_restart is False:
# Track electrons if required (species 0 correspond to the electrons)
if track_electrons:
sim.ptcl[0].track(sim.comm)
else:
# 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)
# Add diagnostics
sim.diags = [
FieldDiagnostic(diag_period, sim.fld, comm=sim.comm),
ParticleDiagnostic(diag_period, {"electrons": sim.ptcl[0]},
select={"uz": [1., None]},
comm=sim.comm)
]
# Add checkpoints
if save_checkpoints:
set_periodic_checkpoint(sim, checkpoint_period)
### Run the simulation
sim.step(N_step)
print('')
+ LaguerreGaussLaser( 0, 1, 0.5*a0, w0, tau, z0, zf=zf,
lambda0=lambda0, theta_pol=np.pi/2, theta0=np.pi/2 )
# - Mode 1: Use a regular linearly-polarized pulse
profile1 = GaussianLaser(a0=a0,
waist=w0,
tau=tau,
lambda0=lambda0,
z0=z0,
zf=zf)
if not restart:
# Add the profiles to the simulation
add_laser_pulse(sim, profile0)
add_laser_pulse(sim, profile1)
else:
restart_from_checkpoint(sim)
# Calculate the total number of steps
N_step = int(round(L_prop / (c * dt)))
diag_period = int(round(N_step / N_diag))
# Add openPMD diagnostics
sim.diags = [
FieldDiagnostic(diag_period, sim.fld, fieldtypes=["E"], comm=sim.comm)
]
set_periodic_checkpoint(sim, N_step // 2)
# Do only half the steps
sim.step(N_step // 2 + 1)
# Add a field diagnostic
sim.diags = [
FieldDiagnostic(diag_period, sim.fld, sim.comm),
ParticleDiagnostic(diag_period, {
"electrons": sim.ptcl[0],
"bunch": sim.ptcl[2]
}, sim.comm),
BoostedFieldDiagnostic(zmin,
zmax,
c,
dt_snapshot_lab,
Ntot_snapshot_lab,
gamma_boost,
period=diag_period,
fldobject=sim.fld,
comm=sim.comm),
BoostedParticleDiagnostic(zmin,
zmax,
c,
dt_snapshot_lab,
Ntot_snapshot_lab,
gamma_boost,
diag_period,
sim.fld,
select={'uz': [0., None]},
species={'electrons': sim.ptcl[2]},
comm=sim.comm)
]
### Run the simulation
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)
# Add a field diagnostic
# Parametric scan: each MPI rank should output its data to a
# different directory
write_dir = 'diags_a0_%.2f' % a0
sim.diags = [
FieldDiagnostic(diag_period,
sim.fld,
comm=sim.comm,
write_dir=write_dir),
ParticleDiagnostic(diag_period, {"electrons": elec},
select={"uz": [1., None]},
comm=sim.comm,
write_dir=write_dir)
]
# Add checkpoints
if save_checkpoints:
set_periodic_checkpoint(sim, checkpoint_period)
# Number of iterations to perform
N_step = int(T_interact / sim.dt)
### Run the simulation
sim.step(N_step)
print('')
def test_boosted_output(gamma_boost=10.):
"""
# TODO
Parameters
----------
gamma_boost: float
The Lorentz factor of the frame in which the simulation is carried out.
"""
# The simulation box
Nz = 500 # Number of gridpoints along z
zmax_lab = 0.e-6 # Length of the box along z (meters)
zmin_lab = -20.e-6
Nr = 10 # Number of gridpoints along r
rmax = 10.e-6 # Length of the box along r (meters)
Nm = 2 # Number of modes used
# Number of timesteps
N_steps = 500
diag_period = 20 # Period of the diagnostics in number of timesteps
dt_lab = (zmax_lab - zmin_lab) / Nz * 1. / c
T_sim_lab = N_steps * dt_lab
# Move into directory `tests`
os.chdir('./tests')
# Initialize the simulation object
sim = Simulation(
Nz,
zmax_lab,
Nr,
rmax,
Nm,
dt_lab,
0,
0, # No electrons get created because we pass p_zmin=p_zmax=0
0,
rmax,
1,
1,
4,
n_e=0,
zmin=zmin_lab,
initialize_ions=False,
gamma_boost=gamma_boost,
v_comoving=-0.9999 * c,
boundaries='open',
use_cuda=use_cuda)
sim.set_moving_window(v=c)
# Remove the electron species
sim.ptcl = []
# Add a Gaussian electron bunch
# Note: the total charge is 0 so all fields should remain 0
# throughout the simulation. As a consequence, the motion of the beam
# is a mere translation.
N_particles = 3000
add_elec_bunch_gaussian(sim,
sig_r=1.e-6,
sig_z=1.e-6,
n_emit=0.,
gamma0=100,
sig_gamma=0.,
Q=0.,
N=N_particles,
zf=0.5 * (zmax_lab + zmin_lab),
boost=BoostConverter(gamma_boost))
sim.ptcl[0].track(sim.comm)
# openPMD diagnostics
sim.diags = [
BackTransformedParticleDiagnostic(zmin_lab,
zmax_lab,
v_lab=c,
dt_snapshots_lab=T_sim_lab / 3.,
Ntot_snapshots_lab=3,
gamma_boost=gamma_boost,
period=diag_period,
fldobject=sim.fld,
species={"bunch": sim.ptcl[0]},
comm=sim.comm)
]
# Run the simulation
sim.step(N_steps)
# Check consistency of the back-transformed openPMD diagnostics:
# Make sure that all the particles were retrived by checking particle IDs
ts = OpenPMDTimeSeries('./lab_diags/hdf5/')
ref_pid = np.sort(sim.ptcl[0].tracker.id)
for iteration in ts.iterations:
pid, = ts.get_particle(['id'], iteration=iteration)
pid = np.sort(pid)
assert len(pid) == N_particles
assert np.all(ref_pid == pid)
# Remove openPMD files
shutil.rmtree('./lab_diags/')
os.chdir('../')
else:
# 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)
# Add diagnostics
sim.diags = [
FieldDiagnostic(dt_period / sim.dt, sim.fld, comm=sim.comm),
ParticleDiagnostic(dt_period / sim.dt, {"electrons": elec},
select={
"ux": [0, None],
"uy": [0, None]
},
comm=sim.comm),
ParticleDiagnostic(dt_period / sim.dt, {"beam": beam},
particle_data=[
"position", "momentum", "weighting", "E", "B",
"gamma"
],
comm=sim.comm)
]
# Add checkpoints
if save_checkpoints:
set_periodic_checkpoint(sim, 50000)
# Number of iterations to perform
N_step = int(T_interact / sim.dt)
### Run the simulation
add_laser(sim, a0, w0, ctau, z0, lambda0=lambda0, zf=zfoc)
if use_restart is False:
# Track electrons if required (species 0 correspond to the electrons)
if track_electrons:
elec.track(sim.comm)
else:
# 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)
# Add diagnostics
sim.diags = [
FieldDiagnostic(dt_period / sim.dt, sim.fld, comm=sim.comm),
ParticleDiagnostic(dt_period / sim.dt, {"electrons": elec},
select={"uz": [1., None]},
comm=sim.comm)
]
# Add checkpoints
if save_checkpoints:
set_periodic_checkpoint(sim, 500000)
# Number of iterations to perform
N_step = int(T_interact / sim.dt)
### Run the simulation
sim.step(N_step)
print('')
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_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/')
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
0,
0,
0,
0,
2,
2,
4,
0.,
zmin=zmin,
n_order=n_order,
boundaries={
'z': 'open',
'r': 'reflective'
})
# Configure the moving window
sim.set_moving_window(v=c)
# Suppress the particles that were intialized by default and add the bunch
sim.ptcl = []
add_elec_bunch_gaussian(sim, sig_r, sig_z, n_emit, gamma0, sig_gamma, Q, N, tf,
zf)
# Set the diagnostics
sim.diags = [FieldDiagnostic(10, sim.fld, comm=sim.comm)]
# Perform one simulation step (essentially in order to write the diags)
sim.step(1)
def run_and_check_laser_antenna(gamma_b,
show,
write_files,
z0,
v=0,
forward_propagating=True):
"""
Generic function, which runs and check the laser antenna for
both boosted frame and lab frame
Parameters
----------
gamma_b: float or None
The Lorentz factor of the boosted frame
show: bool
Whether to show the images of the laser as pop-up windows
write_files: bool
Whether to output openPMD data of the laser
v: float (m/s)
Speed of the laser antenna
"""
# Initialize the simulation object
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
p_zmin=0,
p_zmax=0,
p_rmin=0,
p_rmax=0,
p_nz=2,
p_nr=2,
p_nt=2,
n_e=0.,
zmin=zmin,
use_cuda=use_cuda,
boundaries='open',
gamma_boost=gamma_b)
# Remove the particles
sim.ptcl = []
# Add the laser
add_laser(sim,
a0,
w0,
ctau,
z0,
zf=zf,
method='antenna',
z0_antenna=z0_antenna,
v_antenna=v,
gamma_boost=gamma_b,
fw_propagating=forward_propagating)
# Calculate the number of steps between each output
N_step = int(round(Ntot_step / N_show))
# Add diagnostic
if write_files:
sim.diags = [
FieldDiagnostic(N_step,
sim.fld,
comm=None,
fieldtypes=["rho", "E", "B", "J"])
]
# Loop over the iterations
print('Running the simulation...')
for it in range(N_show):
print('Diagnostic point %d/%d' % (it, N_show))
# Advance the Maxwell equations
sim.step(N_step, show_progress=False)
# Plot the fields during the simulation
if show == True:
show_fields(sim.fld.interp[1], 'Er')
# Finish the remaining iterations
sim.step(Ntot_step - N_show * N_step, show_progress=False)
# Check the transverse E and B field
Nz_half = int(sim.fld.interp[1].Nz / 2) + 2
z = sim.fld.interp[1].z[Nz_half:-(sim.comm.n_guard+sim.comm.n_damp+\
sim.comm.n_inject)]
r = sim.fld.interp[1].r
# Loop through the different fields
for fieldtype, info_in_real_part, factor in [ ('Er', True, 2.), \
('Et', False, 2.), ('Br', False, 2.*c), ('Bt', True, 2.*c) ]:
# factor correspond to the factor that has to be applied
# in order to get a value which is comparable to an electric field
# (Because of the definition of the interpolation grid, the )
field = getattr(sim.fld.interp[1], fieldtype)\
[Nz_half:-(sim.comm.n_guard+sim.comm.n_damp+\
sim.comm.n_inject)]
print('Checking %s' % fieldtype)
check_fields(factor * field, z, r, info_in_real_part, z0, gamma_b,
forward_propagating)
print('OK')
def test_cpu_gpu_deposition(show=False):
"Function that is run by py.test, when doing `python setup.py test`"
# Skip this test if cuda is not installed
if not cuda_installed:
return
# Perform deposition for a few timesteps, with both the CPU and GPU
for hardware in ['cpu', 'gpu']:
if hardware == 'cpu':
use_cuda = False
elif hardware == 'gpu':
use_cuda = True
# Initialize the simulation object
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
p_zmin,
p_zmax,
p_rmin,
p_rmax,
p_nz,
p_nr,
p_nt,
n_e,
zmin=zmin,
use_cuda=use_cuda)
# Tweak the velocity of the electron bunch
gamma0 = 10.
sim.ptcl[0].ux = sim.ptcl[0].x
sim.ptcl[0].uy = sim.ptcl[0].y
sim.ptcl[0].uz = np.sqrt(gamma0**2 - sim.ptcl[0].ux**2 -
sim.ptcl[0].uy**2 - 1)
sim.ptcl[0].inv_gamma = 1. / gamma0 * np.ones_like(sim.ptcl[0].x)
sim.ptcl[0].m = 1e10
# Add a field diagnostic
sim.diags = [
FieldDiagnostic(diag_period,
sim.fld,
fieldtypes=['rho', 'J'],
comm=sim.comm,
write_dir=os.path.join('tests', hardware))
]
### Run the simulation
sim.step(N_step)
# Check that the results are identical
ts_cpu = OpenPMDTimeSeries('tests/cpu/hdf5')
ts_gpu = OpenPMDTimeSeries('tests/gpu/hdf5')
for iteration in ts_cpu.iterations:
for field, coord in [('rho', ''), ('J', 'x'), ('J', 'z')]:
# Jy is not tested because it is zero
print('Testing %s at iteration %d' % (field + coord, iteration))
F_cpu, info = ts_cpu.get_field(field, coord, iteration=iteration)
F_gpu, info = ts_gpu.get_field(field, coord, iteration=iteration)
tolerance = 1.e-13 * (abs(F_cpu).max() + abs(F_gpu).max())
if not show:
assert np.allclose(F_cpu, F_gpu, atol=tolerance)
else:
if not np.allclose(F_cpu, F_gpu, atol=tolerance):
plot_difference(field, coord, iteration, F_cpu, F_gpu,
info)
# Remove the files used
shutil.rmtree('tests/cpu')
shutil.rmtree('tests/gpu')
sim.diags = [
# Diagnostics in the boosted frame
FieldDiagnostic(dt_period=dt_boosted_diag_period,
fldobject=sim.fld,
comm=sim.comm),
ParticleDiagnostic(dt_period=dt_boosted_diag_period,
species={
"electrons": plasma_elec,
"bunch": bunch
},
comm=sim.comm),
# Diagnostics in the lab frame (back-transformed)
BackTransformedFieldDiagnostic(zmin,
zmax,
v_window,
dt_lab_diag_period,
N_lab_diag,
boost.gamma0,
fieldtypes=['rho', 'E', 'B'],
period=write_period,
fldobject=sim.fld,
comm=sim.comm),
BackTransformedParticleDiagnostic(zmin,
zmax,
v_window,
dt_lab_diag_period,
N_lab_diag,
boost.gamma0,
write_period,
sim.fld,
select={'uz': [0., None]},
species={'bunch': bunch},
comm=sim.comm)
]
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/')
