def find_rate_equations_steady_state(settings):
""" find the rate equations steady state using a relaxation algorithm """
start_time = time.time()
initialize_logging(settings)
# initialize densities
settings, state = initialize_densities(settings)
# initialize temperatures
state['Ti'] = get_isentrope_temperature(state['n'],
settings,
species='ions')
state['Te'] = get_isentrope_temperature(state['n'],
settings,
species='electrons')
# relaxation algorithm initialization
t_curr = 0
num_time_steps = 0
status_counter = 0
state['termination_criterion_reached'] = False
state['successful_termination'] = False
while t_curr < settings['t_stop']:
state['v_th'] = get_thermal_velocity(state['Ti'],
settings,
species='ions')
state['coulomb_scattering_rate'] = get_coulomb_scattering_rate(
state['n'], state['Ti'], state['Te'], settings, species='ions')
state['mean_free_path'] = calculate_mean_free_path(state['n'],
state['Ti'],
state['Te'],
settings,
state=state,
species='ions')
state['mirror_cell_sizes'] = get_mirror_cell_sizes(state['n'],
state['Ti'],
state['Te'],
settings,
state=state)
state['v_col'], state['flux_E'] = get_collective_velocity(
state, settings)
state['f_above'], state['f_below'] = get_transition_filters(
state['n'], settings) # transition filters
state['v_R'], state['v_L'] = get_transmission_velocities(
state, settings)
state['U'] = get_mmm_velocity(state, settings)
state['alpha_tR'], state['alpha_tL'], state[
'alpha_c'] = define_loss_cone_fractions(state, settings)
state['dn_c_dt'], state['dn_tL_dt'], state[
'dn_tR_dt'] = get_density_time_derivatives(state, settings)
# variables for plots
state[
'transmission_rate_R'] = state['v_R'] / state['mirror_cell_sizes']
state[
'transmission_rate_L'] = state['v_L'] / state['mirror_cell_sizes']
state['mmm_drag_rate'] = state['U'] / state['mirror_cell_sizes']
# print basic run info
if num_time_steps == 0:
print_basic_run_info(state, settings)
logging.info('*** Begin relaxation iterations ***')
# advance step
dt, state = define_time_step(state, settings)
t_curr += dt
num_time_steps += 1
state = advance_densities_time_step(state, dt)
# check if densities are too low and deal with them
state = check_minimal_density(state, settings, dt, t_curr,
num_time_steps)
# boundary conditions
state = enforce_boundary_conditions(state, settings)
# update temperatures
state['Ti'] = get_isentrope_temperature(state['n'],
settings,
species='ions')
state['Te'] = get_isentrope_temperature(state['n'],
settings,
species='electrons')
if check_status_threshold_passed(settings, t_curr, num_time_steps, status_counter) \
or state['termination_criterion_reached']:
# print basic information
if settings['print_time_step_info'] is True:
print_time_step_info(dt, t_curr, num_time_steps)
# print minimal density values for debugging
print_minimal_densities(state)
# define fluxes and check if termination criterion is reached
state = get_fluxes(state, settings)
state = save_fluxes_evolution(state, t_curr)
state = check_termination_criterion_reached(
state, settings, t_curr, num_time_steps, status_counter)
# plot status
if settings['draw_plots'] is True:
plot_relaxation_status(state, settings)
if settings['save_plots_scheme'] == 'status_plots':
save_plots(settings)
status_counter += 1
if state['termination_criterion_reached'] is True:
break
logging.info('*************************************')
logging.info('*** Finished relaxation iterations ***')
if state['successful_termination'] == False:
# print in red color
logging.info('\x1b[5;30;41m' + 'Termination unsuccessful.' + '\x1b[0m')
else:
# print in green color
logging.info('\x1b[5;30;42m' + 'Termination successful.' + '\x1b[0m')
# save the plots
if settings['draw_plots'] is True:
if settings['save_plots_scheme'] == 'status_plots':
save_plots(settings)
elif settings['save_plots_scheme'] == 'only_at_calculation_end':
plot_relaxation_status(state, settings)
save_plots(settings)
else:
raise ValueError(
'draw_plots is True but save_plots_scheme is invalid. '
'save_plots_scheme = ' + str(settings['save_plots_scheme']))
# run time
state['run_time'] = get_simulation_time(start_time)
state['t_end'] = t_curr
state['num_time_steps'] = num_time_steps
# save results
if settings['save_state'] is True:
save_simulation(state, settings)
return state
### Plot fusion and radiation loss parameters settings = define_default_settings() # Z_ion = settings['Z_ion'] Z_ion = 1 # B = 7 # [Tesla] B = 15 # [Tesla] # n0 = settings['n0'] n0 = 2e22 # = ni = ne n_tot = 2 * n0 Ti_0 = settings['Ti_0'] Te_0 = settings['Te_0'] v_th = get_thermal_velocity(Ti_0, settings, species='ions') T_keV_array = np.linspace(0.2, 200, 1000) reactions = [] reactions += ['D_T_to_n_alpha'] reactions += ['D_D_to_p_T_n_He3'] reactions += ['D_He3_to_p_alpha'] # reactions += ['T_T_to_alpha_2n'] reactions += ['p_B_to_3alpha'] # reactions += ['p_D_to_He3_gamma'] # reactions += ['He3_He3_to_alpha_2p'] # reactions += ['p_p_to_D_e_nu'] # colors = ['b', 'g', 'r', 'k', 'm', 'y', 'c', 'b'] colors = cm.rainbow(np.linspace(0, 1, len(reactions)))
species='ions')
Te_isentrope_array = get_isentrope_temperature(n_array,
settings,
species='electrons')
plt.figure(100)
plt.plot(n_array, Ti_isentrope_array / settings['keV'], label='i', color='r')
plt.plot(n_array, Te_isentrope_array / settings['keV'], label='e', color='b')
plt.legend()
plt.xlabel('n [g/cc]')
plt.ylabel('T [keV]')
plt.title('Isentropes')
plt.tight_layout()
plt.grid()
# plot rates
v_th_i = get_thermal_velocity(Ti_isentrope_array, settings, species='ions')
v_th_e = get_thermal_velocity(Te_isentrope_array,
settings,
species='electrons')
mirror_cell_sizes = get_mirror_cell_sizes(n_array, Ti_isentrope_array,
Te_isentrope_array, settings)
# nu_i_trans = get_transmission_rate(v_th_i, mirror_cell_sizes)
# nu_e_trans = get_transmission_rate(v_th_e, mirror_cell_sizes)
nu_i_scat = get_coulomb_scattering_rate(n_array,
Ti_isentrope_array,
Te_isentrope_array,
settings,
species='ions')
nu_e_scat = get_coulomb_scattering_rate(n_array,
Ti_isentrope_array,
Te_isentrope_array,