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_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')
p_rmax, p_nz, p_nr, p_nt, n_e, n_order=n_order, v_comoving=-0.999999 * c, use_galilean=True) # Configure the moving window #sim.moving_win = MovingWindow( sim.fld.interp[0], # ncells_damp=2, # ncells_zero=2 ) # 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()
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')
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()
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, initialize_ions=False, v_comoving=v_plasma, use_galilean=False, boundaries='open', use_cuda=use_cuda) sim.ptcl = [] # Add the charge-neutralizing electrons elec = sim.add_new_species(q=-e, m=m_e, n=level_start * n_atoms, p_nz=p_nz, p_nr=p_nr, p_nt=p_nt, p_zmin=p_zmin, p_zmax=p_zmax, p_rmin=p_rmin, p_rmax=p_rmax, continuous_injection=False, uz_m=uz_m) # Add the N atoms ions = sim.add_new_species(q=0, m=14. * m_p, n=n_atoms, p_nz=p_nz, p_nr=p_nr, p_nt=p_nt, p_zmin=p_zmin, p_zmax=p_zmax, p_rmin=p_rmin, p_rmax=p_rmax, continuous_injection=False, uz_m=uz_m) # Add the target electrons if use_separate_electron_species: # Use a dictionary of electron species: one per ionizable level target_species = {} level_max = 6 # N can go up to N7+, but here we stop at N6+ for i_level in range(level_start, level_max): target_species[i_level] = sim.add_new_species(q=-e, m=m_e) else: # Use the pre-existing, charge-neutralizing electrons target_species = elec level_max = None # Default is going up to N7+ # Define ionization ions.make_ionizable(element='N', level_start=level_start, level_max=level_max, target_species=target_species) # Set the moving window sim.set_moving_window(v=v_plasma) # Add a laser to the fields of the simulation (external fields) sim.external_fields = [ ExternalField(laser_func, 'Ex', E0, 0.), ExternalField(laser_func, 'By', B0, 0.) ] # Add a particle diagnostic sim.diags = [ ParticleDiagnostic( diag_period, {"ions": ions}, particle_data=["position", "gamma", "weighting", "E", "B"], # Test output of fields and gamma for standard # (non-boosted) particle diagnostics write_dir='tests/diags', comm=sim.comm) ] if gamma_boost > 1: T_sim_lab = (2. * 40. * lambda0_lab + zmax_lab - zmin_lab) / c sim.diags.append( BackTransformedParticleDiagnostic(zmin_lab, zmax_lab, v_lab=0., dt_snapshots_lab=T_sim_lab / 2., Ntot_snapshots_lab=3, gamma_boost=gamma_boost, period=diag_period, fldobject=sim.fld, species={"ions": ions}, comm=sim.comm, write_dir='tests/lab_diags')) # Run the simulation sim.step(N_step, use_true_rho=True) # Check the fraction of N5+ ions at the end of the simulation w = ions.w ioniz_level = ions.ionizer.ionization_level # Get the total number of N atoms/ions (all ionization levels together) ntot = w.sum() # Get the total number of N5+ ions n_N5 = w[ioniz_level == 5].sum() # Get the fraction of N5+ ions, and check that it is close to 0.32 N5_fraction = n_N5 / ntot print('N5+ fraction: %.4f' % N5_fraction) assert ((N5_fraction > 0.30) and (N5_fraction < 0.34)) # When different electron species are created, check the fraction of # each electron species if use_separate_electron_species: for i_level in range(level_start, level_max): n_N = w[ioniz_level == i_level].sum() assert np.allclose(target_species[i_level].w.sum(), n_N) # Check consistency in the regular openPMD diagnostics ts = OpenPMDTimeSeries('./tests/diags/hdf5/') last_iteration = ts.iterations[-1] w, q = ts.get_particle(['w', 'charge'], species="ions", iteration=last_iteration) # Check that the openPMD file contains the same number of N5+ ions n_N5_openpmd = np.sum(w[(4.5 * e < q) & (q < 5.5 * e)]) assert np.isclose(n_N5_openpmd, n_N5) # Remove openPMD files shutil.rmtree('./tests/diags/') # Check consistency of the back-transformed openPMD diagnostics if gamma_boost > 1.: ts = OpenPMDTimeSeries('./tests/lab_diags/hdf5/') last_iteration = ts.iterations[-1] w, q = ts.get_particle(['w', 'charge'], species="ions", iteration=last_iteration) # Check that the openPMD file contains the same number of N5+ ions n_N5_openpmd = np.sum(w[(4.5 * e < q) & (q < 5.5 * e)]) assert np.isclose(n_N5_openpmd, n_N5) # Remove openPMD files shutil.rmtree('./tests/lab_diags/')
def 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, exchange_period=1, 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: import matplotlib.pyplot as plt plt.clf() sim.fld.interp[m].show('Er') 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 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: import matplotlib.pyplot as plt 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) assert np.allclose(E, E_analytic, rtol=5.e-3) 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 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('../')
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)