def propagate_pulse(Nz,
Nr,
Nm,
zmin,
zmax,
Lr,
L_prop,
zf,
dt,
N_diag,
w0,
ctau,
k0,
E0,
m,
N_show,
n_order,
rtol,
boundaries,
v_window=0,
use_galilean=False,
v_comoving=0,
show=False):
"""
Propagate the beam over a distance L_prop in Nt steps,
and extracts the waist and a0 at each step.
Parameters
----------
show : bool
Wether to show the fields, so that the user can manually check
the agreement with the theory.
If True, this will periodically show the map of the fields (with
a period N_show), as well as (eventually) the evoluation of a0 and w0.
If False, this
N_diag : int
Number of diagnostic points (i.e. measure of waist and a0)
along the propagation
Nz, Nr : int
The number of points on the grid in z and r respectively
Nm : int
The number of modes in the azimuthal direction
zmin, zmax : float
The limits of the box in z
Lr : float
The size of the box in the r direction
(In the case of Lr, this is the distance from the *axis*
to the outer boundary)
L_prop : float
The total propagation distance (in meters)
zf : float
The position of the focal plane of the laser (only works for m=1)
dt : float
The timestep of the simulation
w0 : float
The initial waist of the laser (in meters)
ctau : float
The initial temporal waist of the laser (in meters)
k0 : flat
The central wavevector of the laser (in meters^-1)
E0 : float
The initial E0 of the pulse
m : int
Index of the mode to be tested
For m = 1 : test with a gaussian, linearly polarized beam
For m = 0 : test with an annular beam, polarized in E_theta
n_order : int
Order of the stencil
rtol : float
Relative precision with which the results are tested
boundaries : string
Type of boundary condition
Either 'open' or 'periodic'
v_window : float
Speed of the moving window
v_comoving : float
Velocity at which the currents are assumed to move
use_galilean: bool
Whether to use a galilean frame that moves at the speed v_comoving
Returns
-------
A dictionary containing :
- 'E' : 1d array containing the values of the amplitude
- 'w' : 1d array containing the values of waist
- 'fld' : the Fields object at the end of the simulation.
"""
# Initialize the simulation object
sim = Simulation(Nz,
zmax,
Nr,
Lr,
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.,
n_order=n_order,
zmin=zmin,
use_cuda=use_cuda,
boundaries=boundaries,
v_comoving=v_comoving,
use_galilean=use_galilean)
# Remove the particles
sim.ptcl = []
# Set the moving window object
if v_window != 0:
sim.set_moving_window(v=v_window)
# Initialize the laser fields
z0 = (zmax + zmin) / 2
init_fields(sim, w0, ctau, k0, z0, zf, E0, m)
# Create the arrays to get the waist and amplitude
w = np.zeros(N_diag)
E = np.zeros(N_diag)
# Calculate the number of steps to run between each diagnostic
Ntot_step = int(round(L_prop / (c * dt)))
N_step = int(round(Ntot_step / N_diag))
# Loop over the iterations
print('Running the simulation...')
for it in range(N_diag):
print('Diagnostic point %d/%d' % (it, N_diag))
# Fit the fields to find the waist and a0
w[it], E[it] = fit_fields(sim.fld, m)
# Plot the fields during the simulation
if show == True and it % N_show == 0:
plt.clf()
sim.fld.interp[m].show('Et')
plt.show()
# Advance the Maxwell equations
sim.step(N_step, show_progress=False)
# Get the analytical solution
z_prop = c * dt * N_step * np.arange(N_diag)
ZR = 0.5 * k0 * w0**2
if m == 0: # zf is not implemented for m = 0
w_analytic = w0 * np.sqrt(1 + z_prop**2 / ZR**2)
E_analytic = E0 / (1 + z_prop**2 / ZR**2)**(1. / 2)
else:
w_analytic = w0 * np.sqrt(1 + (z_prop - zf)**2 / ZR**2)
E_analytic = E0 / (1 + (z_prop - zf)**2 / ZR**2)**(1. / 2)
# Either plot the results and check them manually
if show is True:
plt.suptitle('Diffraction of a pulse in the mode %d' % m)
plt.subplot(121)
plt.plot(1.e6 * z_prop, 1.e6 * w, 'o', label='Simulation')
plt.plot(1.e6 * z_prop, 1.e6 * w_analytic, '--', label='Theory')
plt.xlabel('z (microns)')
plt.ylabel('w (microns)')
plt.title('Waist')
plt.legend(loc=0)
plt.subplot(122)
plt.plot(1.e6 * z_prop, E, 'o', label='Simulation')
plt.plot(1.e6 * z_prop, E_analytic, '--', label='Theory')
plt.xlabel('z (microns)')
plt.ylabel('E')
plt.legend(loc=0)
plt.title('Amplitude')
plt.show()
# or automatically check that the theoretical and simulated curves
# of w and E are close
else:
assert np.allclose(w, w_analytic, rtol=rtol)
print('The simulation results agree with the theory to %e.' % rtol)
# Return a dictionary of the results
return ({'E': E, 'w': w, 'fld': sim.fld})
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={
'z': 'open',
'r': 'reflective'
},
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_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/')
# Suppress the particles that were intialized by default and add the bunch
sim.ptcl = []
add_elec_bunch(sim,
gamma0,
n_e,
p_zmin,
p_zmax,
p_rmin,
p_rmax,
direction='backward')
# Show the initial fields
plt.figure(0)
sim.fld.interp[0].show('Ez')
plt.figure(1)
sim.fld.interp[0].show('Er')
plt.show()
print('Done')
# Carry out the simulation
for k in range(N_step / N_show):
sim.step(N_show, correct_currents=False, use_true_rho=False)
plt.figure(0)
plt.clf()
sim.fld.interp[0].show('Ez')
plt.figure(1)
plt.clf()
sim.fld.interp[0].show('Er')
plt.show()
import matplotlib.pyplot as plt
plt.subplot(211)
plt.imshow(2 * sim.fld.interp[1].Er.real.T)
plt.colorbar()
if reference_profile is not None:
plt.subplot(212)
plt.imshow(Ex_reference)
plt.colorbar()
plt.show()
if reference_profile is not None:
assert np.allclose(2 * sim.fld.interp[1].Er.real.T,
Ex_reference,
atol=rtol * Ex_reference.max())
# Propagate the pulse
sim.step(1)
# Get pulse energy and peak electric field
if case == 'donut_chirped':
# mode 2 & scale Er by a factor of 2 for correct pulse energy
Er = sim.fld.interp[2].Er.real.T.copy() * 2
else:
# mode 1
Er = sim.fld.interp[1].Er.real.T.copy()
r = sim.fld.interp[1].r
dr = sim.fld.interp[1].dr
dz = sim.fld.interp[1].dz
E_laser_sim = retrieve_pulse_energy(Er, r, dr, dz)
# Check the validity
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/')
p_zmin,
p_zmax,
p_rmin,
p_rmax,
p_nz,
p_nr,
p_nt,
n_e,
n_order=n_order,
boundaries='open')
# 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_file(sim,
filename='test_space_charge_file_data.txt',
Q_tot=1.e-12,
z_off=20.e-6)
# Carry out 100 step, and show the fields
sim.step(100)
plt.figure(0)
sim.fld.interp[0].show('Ez')
plt.figure(1)
sim.fld.interp[0].show('Er')
plt.show()
# 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 )
# 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" : sim.ptcl[0]},
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('')
+ 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)
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_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')
'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(sim, gamma0, n_e, p_zmin, p_zmax, p_rmin, p_rmax)
# Show the initial fields
plt.figure(0)
plt.imshow(sim.fld.interp[0].Ez.real)
plt.figure(1)
plt.imshow(sim.fld.interp[0].Er.real)
plt.show()
print('Done')
# Carry out the simulation
for k in range(round(N_step / N_show)):
sim.step(N_show)
plt.figure(0)
plt.clf()
plt.imshow(sim.fld.interp[0].Ez.real)
plt.figure(1)
plt.clf()
plt.imshow(sim.fld.interp[0].Er.real)
plt.show()
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)
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)
# 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]
# 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=n_order,
boundaries={
'z': grid.bc_zmax,
'r': grid.bc_rmax
})
# 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])
# 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(layout) == PICMI_GriddedLayout:
assert initialize_self_field == False
# - 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(z, r):
n = numexpr.evaluate(density_expression)
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]
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=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:
if diagnostic.data_list is None:
data_list = ['rho', 'E', 'B', 'J']
else:
data_list = diagnostic.data_list
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 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
if diagnostic.data_list is None:
data_list = ['position', 'momentum', 'weighting']
else:
data_list = diagnostic.data_list
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)
# Add it to the FBPIC simulation
self.fbpic_sim.diags.append(diag)
# 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)
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 = [
BoostedParticleDiagnostic(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('../')
def test_cherenkov_instability(show=False):
"""
Run a simulation with the standard and Galilean scheme respectively
and check that the first one is unstable while the second one is stable
"""
# Dictionary to record the final value of E
slope_Erms = {}
for scheme in ['standard', 'galilean', 'pseudo-galilean']:
# Choose the correct parameters for the scheme
if scheme == 'standard':
v_comoving = 0.
use_galilean = False
else:
v_comoving = 0.9999 * c
if scheme == 'galilean':
use_galilean = True
else:
use_galilean = False
# 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,
initialize_ions=True,
v_comoving=v_comoving,
use_galilean=use_galilean,
boundaries='periodic',
use_cuda=use_cuda)
# Give a relativistic velocity to the particle, with some noise
sim.ptcl[0].uz[:] = uz_m
sim.ptcl[0].inv_gamma[:] = 1. / np.sqrt(1 + sim.ptcl[0].uz**2)
sim.ptcl[1].uz[:] = uz_m
sim.ptcl[1].inv_gamma[:] = 1. / np.sqrt(1 + sim.ptcl[1].uz**2)
# Perform the simulation;
# record the rms electric field every 50 timestep
Er_rms = np.zeros(int(N_step / 30) + 1)
t = np.zeros(int(N_step / 30 + 1))
Er_rms[0] = get_Er_rms(sim)
t[0] += sim.time
for i in range(int(N_step / 30)):
sim.step(30, show_progress=False)
print('Checkpoint %d' % i)
Er_rms[i + 1] = get_Er_rms(sim)
t[i + 1] += sim.time
print('Calculated RMS')
# Check/plot the results
if show:
import matplotlib.pyplot as plt
# Add a plot
plt.semilogy(t, Er_rms, '-', label=scheme)
plt.ylabel('RMS(Er)')
plt.xlabel('Time')
else:
# Registed the final value of the slope of the electric field
slope_Erms[scheme] = np.log(Er_rms[-1]) - np.log(Er_rms[-2])
if show:
# Show the plot
plt.legend(loc=0)
plt.show()
else:
# Check that, in the standard case, the electric field is
# growing much faster, due to the Cherenkov instability
assert slope_Erms['standard'] > 3.5 * slope_Erms['galilean']
assert slope_Erms['standard'] > 3.5 * slope_Erms['pseudo-galilean']
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={
'z': 'periodic',
'r': 'reflective'
},
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 test_linear_wakefield(Nm=1, show=False):
"""
Run a simulation of linear laser-wakefield and compare the fields
with the analytical solution.
Parameters
----------
Nm: int
The number of azimuthal modes used in the simulation (Use 1, 2 or 3)
This also determines the profile of the driving laser:
- Nm=1: azimuthally-polarized annular laser
(laser in mode m=0, wakefield in mode m=0)
- Nm=2: linearly-polarized Gaussian laser
(laser in mode m=1, wakefield in mode m=0)
- Nm=3: linearly-polarized Laguerre-Gauss laser
(laser in mode m=0 and m=2, wakefield in mode m=0 and m=2,
show: bool
Whether to have pop-up windows show the comparison between
analytical and simulated results
"""
# Automatically choose higher number of macroparticles along theta
p_nt = 2 * Nm
# 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,
use_cuda=use_cuda,
boundaries='open')
# Create the relevant laser profile
if Nm == 1:
# Build an azimuthally-polarized pulse from 2 Laguerre-Gauss profiles
profile = LaguerreGaussLaser( 0, 1, a0=a0, waist=w0, tau=tau, z0=z0,
theta_pol=np.pi/2, theta0=0. ) \
+ LaguerreGaussLaser( 0, 1, a0=a0, waist=w0, tau=tau, z0=z0,
theta_pol=0., theta0=-np.pi/2 )
elif Nm == 2:
profile = GaussianLaser(a0=a0,
waist=w0,
tau=tau,
z0=z0,
theta_pol=np.pi / 2)
elif Nm == 3:
profile = LaguerreGaussLaser(0,
1,
a0=a0,
waist=w0,
tau=tau,
z0=z0,
theta_pol=np.pi / 2)
add_laser_pulse(sim, profile)
# Configure the moving window
sim.set_moving_window(v=c)
# Add diagnostics
if write_fields:
sim.diags.append(FieldDiagnostic(diag_period, sim.fld, sim.comm))
if write_particles:
sim.diags.append(
ParticleDiagnostic(diag_period, {'electrons': sim.ptcl[0]},
sim.comm))
# Prevent current correction for MPI simulation
if sim.comm.size > 1:
correct_currents = False
else:
correct_currents = True
# Run the simulation
sim.step(N_step, correct_currents=correct_currents)
# Compare the fields
compare_fields(sim, Nm, show)
def test_external_laser_field(show=False):
"Function that is run by py.test, when doing `python setup.py test`"
# Initialize the simulation
sim = Simulation(Nz,
zmax,
Nr,
rmax,
Nm,
dt,
p_zmin,
p_zmax,
0,
p_rmax,
p_nz,
p_nr,
p_nt,
n,
initialize_ions=False,
zmin=zmin,
use_cuda=use_cuda,
boundaries='periodic')
# Add the external fields
sim.external_fields = [
ExternalField(laser_func, 'Ex', a0 * m_e * c**2 * k0 / e, lambda0),
ExternalField(laser_func, 'By', a0 * m_e * c * k0 / e, lambda0)
]
# 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))
uz = np.zeros((N_step, Nptcl))
uy = np.zeros((N_step, Nptcl))
# Prepare the particles with proper transverse and longitudinal momentum
sim.ptcl[0].ux = a0 * np.sin(k0 * sim.ptcl[0].z)
sim.ptcl[0].uz[:] = 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 = 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(k0 * (z[i, :] - c * t[i]))
uz_analytical[i, :] = 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_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={
'z': 'open',
'r': 'reflective'
},
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.nz_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.nz_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')
# Add a laser to the fields of the simulation
add_laser(sim, a0, w0, ctau, z0)
# Configure the moving window
sim.set_moving_window(v=c)
# Add diagnostics
if write_fields:
sim.diags.append(FieldDiagnostic(diag_period, sim.fld, sim.comm))
sim.diags.append(
FieldDiagnostic(diag_period,
sim.fld,
None,
write_dir='proc%d' % sim.comm.rank))
if write_particles:
sim.diags.append(
ParticleDiagnostic(diag_period, {'electrons': sim.ptcl[0]}, sim.comm))
if __name__ == '__main__':
# Prevent current correction for MPI simulation
if sim.comm.size > 1:
correct_currents = False
else:
correct_currents = True
# Run the simulation
sim.step(N_step, correct_currents=correct_currents)
# Plot the fields
compare_fields(sim)
