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Outputs & Diagnostics

Running a simulation produces structured outputs (NumPy/JAX arrays) plus plots & animations.

🔹 Raw backend output

  • Fourier mode solver: python { "C_kSnt": (Nk, S, N, nt), # Hermite-Fourier coefficients "Ek_kt": (Nk, nt), # Electric field Fourier modes "k": (Nk,) # Wavenumber array }

  • DG solver:

{
  "C_St": (S, N, Nx, nt),  # Hermite coefficients per cell
  "E_xt": (Nx, nt),        # Electric field in real space
  "x": (Nx,)               # Spatial grid
}

🔹 Plots & diagnostics

The plotting suite automatically produces publication-quality figures:

  1. Energy panel

  2. Kinetic energy per species

  3. Field energy
  4. Total energy (check conservation)

  5. Log scale for dynamic range

  6. Electric field

  7. Heatmap of \(E(x,t)\)

  8. Shows wave growth, damping, nonlinear saturation

  9. Per-species diagnostics

  10. Hermite spectrum: phase-mixing, \(\log |c_n(t)|\) vs time

  11. Distribution function: animated \(f(x,v,t)\) reconstruction

🔹 Example: Plot configuration

In the TOML file:

[plot]
nv = 257           # velocity grid for reconstruction
vmin_c = -0.3      # min velocity in units of c
vmax_c = 0.3       # max velocity in units of c
fig_width = 10.0   # inches
fig_row_height = 2.2
fps = 30           # animation frames per second
dpi = 150
# save_anim = "out.mp4"  # enable to save video

🔹 How to interpret results

  • Energy panel

  • Landau damping: field energy decays, kinetic increases slightly.

  • Two-stream instability: field energy grows exponentially, then saturates.

  • Hermite spectrum

  • Diagonal ridges = phase mixing.

  • Broadening = nonlinear cascade in velocity space.

  • Distribution function

  • Flattening of slopes = quasilinear diffusion.

  • Phase-space holes/clumps = BGK modes.

📝 Tips

  • Always compare total energy: drift should be <1% for well-resolved runs.
  • Use vmin_c / vmax_c to zoom in on relevant phase-space region.
  • For movies, keep fps=30 and dpi=150 for smooth, high-quality output.
  • Outputs are NumPy arrays → you can load them directly for further analysis.