mass = [m_e] boltzmann_constant = k0 charge = [e_e] # Boundary conditions for the density and temperature of left zone, # Setup as initial conditions throughout domain: n_left = 1 * n0 T_left = 1 * T0 plasma_beta = 100 # β = p / (B^2 / 2μ) # Setting magnetic field along x using plasma beta: B1 = np.sqrt(2 * mu * n_left * T_left / plasma_beta) # Velocity, length and time scales: t0 = 1 / time_scales.cyclotron_frequency(B1, e_i, m_i) v0 = velocity_scales.alfven_velocity(B1, n_left, m_i, mu) l0 = v0 * t0 # ion skin depth # Setting permeability: c = 300 * v0 # |c| units(c) eps = 1 / (c**2 * mu) # Setting bulk velocity of left boundary: # Also setup as initial conditions throughout domain: v1_bulk_left = 1 * v0 # Time parameters: N_cfl = 0.1 t_final = 200 * t0
c = 5 * v0
eps = 1 / (c**2 * mu)
# Velocity Scales:
thermal_speed = velocity_scales.thermal_speed(temperature_background, m0, k0)
sound_speed = velocity_scales.sound_speed(temperature_background, k0, gamma)
alfven_velocity = velocity_scales.alfven_velocity(B0, density_background, m0, mu)
# Length scales:
debye_length = length_scales.debye_length(density_background, temperature_background, e0, k0, eps)
skin_depth = length_scales.skin_depth(density_background, e0, c, m0, eps)
gyroradius = length_scales.gyroradius(velocity_scales.thermal_speed(temperature_background, m0, k0), B0, e0, m0)
# Time scales:
plasma_frequency = time_scales.plasma_frequency(density_background, e0, m0, eps)
cyclotron_frequency = time_scales.cyclotron_frequency(B0, e0, m0)
alfven_crossing_time = time_scales.alfven_crossing_time(min(L_x, L_y), B0, density_background, m0, mu)
sound_crossing_time = time_scales.sound_crossing_time(min(L_x, L_y), temperature_background, k0, gamma)
# Setting amplitude and wave number for perturbation:
amplitude = 1e-4
k_q1 = 2 * np.pi / l0
# Time parameters:
N_cfl = 0.006
t_final = 2.43 * t0
PETSc.Sys.Print("==================================================")
PETSc.Sys.Print(" Length Scales of the System ")
PETSc.Sys.Print("==================================================")
PETSc.Sys.Print("Debye Length :", debye_length)
# Charge of electron and positron: e_e = -1 * e0 e_p = 1 * e0 mass = [m_e, m_p] boltzmann_constant = k0 charge = [e_e, e_p] # Background Quantities: density_background = 1 * n0 temperature_background = 0.1 * T0 B1 = 1 # Velocity, length and time scales: t0 = 1 / time_scales.cyclotron_frequency(B1, e0, m0) v0 = velocity_scales.alfven_velocity(B1, density_background, m0, mu) l0 = v0 * t0 # positron skin depth L_x = 1 * l0 L_y = 1.5 * l0 # Setting Maximum Velocity of Phase Space Grid: v_max = 15 * v0 # Calculating Permittivity: c = v_max eps = 1 / (c**2 * mu) # Velocity Scales: thermal_speed = velocity_scales.thermal_speed(temperature_background, m0, k0)
