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SPECTRAX-GK

A differentiable, JAX-based solver for the multispecies Vlasov–Poisson system in 1D1V, supporting Fourier–Hermite and Discontinuous Galerkin (DG) discretizations.

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Why SPECTRAX-GK?

  • Two discretizations: Fourier–Hermite (landau problems) & DG-in-x + Hermite-in-v (robust nonlinearity)
  • Linear & nonlinear physics with multi-species coupling
  • Units-aware inputs: time in \(1/\omega_p\), length in \(\lambda_D\), \(T\) in eV, drift as \(u/c\)
  • Differentiable & JIT-able via JAX
  • Publication-quality diagnostics and example configs
  • Modern workflow: Ruff (lint/format), MyPy (types), pytest (tests), pre-commit, CI/CD, auto docs

👉 New here? Start with the Quickstart.

At a Glance

We solve the Vlasov–Poisson system

\[ \frac{\partial f_s}{\partial t} + v \frac{\partial f_s}{\partial x} + \frac{q_s}{m_s} E(x,t) \frac{\partial f_s}{\partial v} = 0 \]
\[ \frac{\partial E}{\partial x} = \frac{1}{\epsilon_0} \sum_s q_s \int f_s\, dv \]

See the Physics page for the discretizations and normalization.