Physics Solvers

Grad-Shafranov equilibrium, five-tier gyrokinetic transport, MHD stability criteria, edge/pedestal models, and neoclassical transport. Publication-accurate implementations.

Equilibrium & Geometry

Grad-Shafranov SolverProduction
Fixed + free-boundary equilibrium. Three iteration methods: Jacobi, SOR (successive over-relaxation), and multigrid. Picard nonlinear iteration. Convergence to ε<10-8.
JAX-Differentiable GSStable
Full Grad-Shafranov solve under JAX autodiff. JIT-compiled. GPU-accelerated. Gradient through complete equilibrium reconstruction for optimisation loops.
Neural Equilibrium SurrogateStable
PCA + MLP architecture. 1000× faster than iterative GS. Trained on 50K equilibria. Input: pressure/current profiles. Output: ψ(R,Z) flux surface geometry.
GEQDSK I/OProduction
Read/write EFIT GEQDSK format. Compatible with ITER, JET, DIII-D, NSTX-U equilibrium files. Automatic grid interpolation.
Tokamak ConfigurationsProduction
Pre-configured geometries: ITER (R=6.2m, a=2.0m), NSTX-U (R=0.93m, ST), SPARC (R=1.85m, B=12.2T). Parameterised Millerised flux surfaces.
VMEC-lite StellaratorExperimental
Simplified 3D equilibrium for stellarator geometry. Fourier decomposition of flux surfaces. Not a full VMEC replacement — educational/prototyping use.

5-Tier Gyrokinetic Transport

TierModelFidelitySpeedDescription
1 Critical-Gradient Low <1 ms Threshold model: χ=0 below R/LT,crit, stiff above. Fast controller inner-loop.
2 QLKNN-10D MLP Medium <5 ms 10-dimensional neural network surrogate trained on QuaLiKiz database. Ion + electron channels.
3 Native Linear Eigenvalue High ~100 ms Electromagnetic ITG/TEM/ETG eigenvalue solver. Ballooning representation. Miller geometry.
4 Native TGLF-Equivalent High ~1 s SAT0, SAT1, SAT2 saturation rules. Spectral-shift model. Zonal flow shear. Multi-scale.
5 Nonlinear δf GK Highest ~hours 5D Vlasov equation. Orszag 2/3 dealiasing. Dimits shift verified. Research-grade. GPU recommended.

MHD Stability

Five Stability CriteriaProduction
Mercier interchange, ideal ballooning, Kruskal-Shafranov (q>1), Troyon β-limit (βN<2.8), NTM onset threshold. All evaluated per flux surface.
Ballooning EigenvalueStable
s-α ballooning equation ODE solver. Shooting method with Frobenius boundary conditions. Extended ballooning angle θk.
Sawtooth ModelsStable
Porcelli trigger criterion (three branches). Kadomtsev full reconnection. q-profile evolution. Sawtooth period estimation.
NTM PhysicsStable
Modified Rutherford equation (MRE). Bootstrap drive, curvature stabilisation, polarisation current. Island width evolution δw/δt.
Tearing & Locked ModesStable
Classical tearing mode Δ′ calculation. Locked mode torque balance. Error field penetration threshold.
ELM ModelsExperimental
Peeling-ballooning stability boundary. Type-I ELM trigger. ELM energy loss ΔWELM/Wped. ELM-free QH-mode proxy.

Edge & Pedestal

EPED ModelStable
Pedestal height/width prediction. KBM constraint + peeling-ballooning limit intersection. Snyder et al. formulation.
SOL Two-Point ModelProduction
Scrape-off layer parallel transport. Upstream-to-target mapping. Sheath boundary conditions. Power decay length λq.
L-H TransitionStable
Martin 2008 power threshold scaling. PLH = 0.0488 ne0.717 BT0.803 S0.941. Hysteresis model for H-L back-transition.
MARFE ModelExperimental
Multifaceted Asymmetric Radiation From the Edge. Radiation collapse criterion. Impurity concentration threshold. Poloidal asymmetry.
Plasma-Wall InteractionExperimental
Sputtering yield (Eckstein formula), recycling coefficients, impurity influx, tungsten erosion/redeposition estimates.

Transport

Neoclassical (Sauter)Production
Sauter et al. 1999 neoclassical conductivity and bootstrap current. Banana, plateau, Pfirsch-Schlüter regimes. Collisionality-dependent.
Momentum TransportStable
Toroidal rotation evolution. Momentum pinch, residual stress, NBI torque source. Prandtl number χφ/χi.
Impurity TransportStable
Hirshman-Sigmar multi-species formulation. Neoclassical impurity screening/accumulation. Trace and non-trace regimes.
Orbit-FollowingExperimental
Guiding-centre orbit integrator. Banana orbit width. Finite-orbit-width corrections. Fast ion loss estimation.
Pellet InjectionExperimental
Négrier ablation model. Cloud drift (grad-B). Pellet penetration depth. Density profile perturbation. Fuelling efficiency.