Literature and code context¶
MHX is positioned between validated plasma/MHD solvers and differentiable JAX research workflows.
Differentiable JAX ecosystem¶
JAX documentation motivates pure array programs that compose with
jit,vmap,grad, and accelerator execution.Diffrax adjoints document checkpointed discrete adjoints and continuous/backsolve adjoints for differentiable time integration.
Lineax provides JAX-native matrix-free linear solves, useful for implicit diffusion, projection, and elliptic pieces.
JAX-Fluids is a current reference for differentiable CFD implementation and performance discipline in JAX.
Plasma and MHD validation targets¶
The first validation sequence will cover FKR/Coppi tearing growth, plasmoid instability, ideal tearing, GEM-style Hall reconnection, and generalized Ohm’s law terms. Extended-MHD examples will be added only with explicit assumptions, equations, tests, and limitations.
For the active tearing validation gates:
Furth, Killeen & Rosenbluth (1963), finite-resistivity sheet-pinch instabilities is the classical constant-\(\psi\) resistive tearing reference.
MacTaggart (2019), The tearing instability of resistive magnetohydrodynamics gives the 1D reduced-MHD normal-mode equations and reference growth-rate values used by
mhx benchmark linear-tearing-eigenvalue.MacTaggart & Stewart (2017), Optimal energy growth in current sheets discusses the discrete generalized eigenproblem, the unique unstable tearing eigenvalue near \(0.0131\) for \(S=1000\), \(k=0.5\), and the non-normal spectrum.
Rutherford (1973), nonlinear growth of the tearing mode is the nonlinear island-growth reference behind the MHX island-width proxy and duration audit; MHX does not yet claim to reproduce this regime with the PDE solver.
McClements et al. (2022), triggering tearing in a forming current sheet gives a modern discussion of FKR versus Coppi regime separation and hyper-resistive tearing scalings.
Loureiro, Schekochihin & Cowley (2007), instability of current sheets and formation of plasmoid chains is the Sweet-Parker plasmoid-scaling target used in the README schematic: \(\gamma_{\max}\tau_A\sim S^{1/4}\) and \(k_{\max}L\sim S^{3/8}\).
Pucci & Velli (2014), reconnection of quasi-singular current sheets motivates the ideal-tearing aspect-ratio scaling used in the analytic validation roadmap.
Orszag & Tang (1979), small-scale structure of two-dimensional MHD turbulence is the classic vortex test adapted in MHX as an incompressible reduced-MHD nonlinear media and cascade gate.
For generalized Ohm’s law and collisionless/two-fluid reconnection context:
Birn et al. (2001), GEM magnetic reconnection challenge compares resistive tearing, anisotropic pressure, and Hall effects in a common Harris-sheet setup.
Shay et al. (2001), Alfvénic collisionless reconnection and the Hall term is a standard reference for Hall-mediated fast reconnection in the GEM challenge family.
Rogers et al. (2001), Role of dispersive waves in collisionless reconnection connects Hall/two-fluid terms with whistler/kinetic-Alfvén dispersive physics.
Liu et al. (2024), Ohm’s law and reconnection rate provides a modern review of the generalized Ohm’s-law terms that break frozen-in flux in collisionless reconnection.
External comparison codes¶
MHX will document comparison workflows against public or widely used codes: