spectrax._model

Hermite–Fourier model operators for the Vlasov–Maxwell system.

This module contains the spectral Ampère–Maxwell current operator (plasma_current()) and the right-hand side of the Hermite–Fourier moment equations (Hermite_Fourier_system()).

Functions

plasma_current(qs, alpha_s, u_s, Ck, Nn, Nm, Np, Ns)

Compute the spectral Ampère-Maxwell current from Hermite-Fourier coefficients.

Hermite_Fourier_system(Ck, C, F, kx_grid, ky_grid, ...)

Evaluate the right-hand side of the coupled Hermite-Fourier moment equations.

Module Contents

spectrax._model.plasma_current(qs, alpha_s, u_s, Ck, Nn, Nm, Np, Ns)

Compute the spectral Ampère-Maxwell current from Hermite-Fourier coefficients.

Parameters:

  • qs (jnp.ndarray, shape (Ns,)) – Charges of the species.

  • alpha_s (jnp.ndarray, shape (3 * Ns,)) – Velocity scaling factors for each species.

  • u_s (jnp.ndarray, shape (3 * Ns,)) – Velocity shift for each species.

  • Ck (jnp.ndarray, shape (Ns * Np * Nm * Nn, Ny, Nx, Nz)) – Hermite-Fourier coefficients for all species stacked along the first axis.

  • Nn (int) – Number of Hermite modes in x, y, and z respectively.

  • Nm (int) – Number of Hermite modes in x, y, and z respectively.

  • Np (int) – Number of Hermite modes in x, y, and z respectively.

  • Ns (int) – Number of species.

Returns:

The total Ampère-Maxwell current components (Jx, Jy, Jz).

Return type:

jnp.ndarray, shape (3, Ny, Nx, Nz)

spectrax._model.Hermite_Fourier_system(Ck, C, F, kx_grid, ky_grid, kz_grid, k2_grid, col, sqrt_n_plus, sqrt_n_minus, sqrt_m_plus, sqrt_m_minus, sqrt_p_plus, sqrt_p_minus, Lx, Ly, Lz, nu, D, alpha_s, u_s, qs, Omega_cs, Nn, Nm, Np, Ns, mask23)

Evaluate the right-hand side of the coupled Hermite-Fourier moment equations.

Parameters:

  • Ck (jnp.ndarray) – Hermite-Fourier coefficients with shape (Ns * Np * Nm * Nn, Ny, Nx, Nz).

  • C (jnp.ndarray) – Configuration-space Hermite coefficients (i.e., inverse FFT of Ck), with shape (Ns * Np * Nm * Nn, Ny, Nx, Nz). The array is reshaped internally to separate the species and Hermite indices.

  • F (jnp.ndarray) – Configuration-space electromagnetic fields with shape (6, Ny, Nx, Nz) ordered as (Ex, Ey, Ez, Bx, By, Bz).

  • kx_grid (jnp.ndarray) – Fourier wave-number grids scaled to the physical domain length.

  • ky_grid (jnp.ndarray) – Fourier wave-number grids scaled to the physical domain length.

  • kz_grid (jnp.ndarray) – Fourier wave-number grids scaled to the physical domain length.

  • k2_grid (jnp.ndarray) – Squared magnitude of the wave number.

  • col (jnp.ndarray) – Precomputed collision coefficients.

  • sqrt_* (jnp.ndarray) – Square-root ladder coefficients for the Hermite recurrences along each axis.

  • Lx (float) – Domain lengths in each spatial direction.

  • Ly (float) – Domain lengths in each spatial direction.

  • Lz (float) – Domain lengths in each spatial direction.

  • nu (float) – Collision frequency.

  • D (float) – Hyper-diffusion coefficient.

  • alpha_s (jnp.ndarray) – Thermal scaling parameters and drift velocities per species.

  • u_s (jnp.ndarray) – Thermal scaling parameters and drift velocities per species.

  • qs (jnp.ndarray) – Species charges.

  • Omega_cs (jnp.ndarray) – Cyclotron frequencies per species.

  • Nn (int) – Number of Hermite modes and species.

  • Nm (int) – Number of Hermite modes and species.

  • Np (int) – Number of Hermite modes and species.

  • Ns (int) – Number of Hermite modes and species.

  • mask23 (jnp.ndarray) – Boolean mask implementing the 2/3 de-aliasing rule in Fourier space.

Returns:

Time derivative dCk/dt with shape (Ns, Np, Nm, Nn, Ny, Nx, Nz).

Return type:

jnp.ndarray