Physics Solvers — SCPN-Fusion-Core

The equilibrium problem

Everything a tokamak model computes starts from magnetostatic force balance — the shape the plasma settles into. SCPN-Fusion-Core solves this free-boundary, then layers transport, stability, and disruption physics on top.

Grad-Shafranov equation

$$\Delta^* \psi \;=\; -\mu_0\, R^2\, p'(\psi) \;-\; F(\psi)\,F'(\psi)$$

Poloidal flux $\psi$ with the operator $\Delta^\ast \equiv R\,\partial_R(R^{-1}\partial_R)+\partial_Z^2$, pressure $p(\psi)$, and poloidal current $F(\psi)=R B_\phi$. Solved by nonlinear Picard iteration with Newton-Raphson coil-current acceleration; free-boundary vacuum field from the PF coils via a Biot-Savart kernel. Fixed and free-boundary lanes, SOR and multigrid, GEQDSK I/O.

Normalised flux & magnetic shear

$$\psi_N(r)=\frac{\psi(r)-\psi(0)}{\psi(R_s)-\psi(0)}, \qquad s=\frac{1}{R_s}\int_0^{R_s}\frac{r}{\rho_i(r)}\,dr$$

Normalised poloidal flux and the magnetic shear integral used across the transport and stability closures.

Density & line-integrated density

$$n(r)=\frac{p(r)}{(T_i+T_e)e}, \qquad N_{\rm line}=\int_0^{R_s} n(r)\,2\pi r\,dr$$

Profile density from pressure and temperatures, and the line-integrated density a real interferometer measures — a directly comparable validation observable.

Core Physics (118 modules)

Domain	Capability
Grad-Shafranov equilibrium	Fixed and free-boundary solve; SOR and multigrid; vacuum field; GEQDSK I/O; native same-case profile-source metrics
Transport (1.5D)	Radial transport with QLKNN-10D and FNO neural surrogates; operator-source checks
Gyrokinetic (three-path)	External-code bridges, native GK research solver, and neural surrogates — see below
MHD stability	7 criteria: Mercier, ballooning, Troyon, kink, RWM, tearing, vertical stability
Neoclassical transport	Bootstrap current, neoclassical conductivity and flux contracts
Disruption chain	Disruption prediction and mitigation chain; pellet/SPI injection models
Edge & pedestal	ELM, MARFE, and L-H transition models
Runaway electrons	Runaway-electron contracts (fail-closed against DREAM kinetic parity)
Impurity transport	Impurity contracts (fail-closed against independent Aurora/STRAHL validation)
Plasma-wall interaction	PWI erosion and wall-interaction contracts
3D equilibrium	3D equilibrium research operators (external coupling required for full nonlinear MHD)

Gyrokinetic Three-Path Architecture

Three transport lanes are exposed with explicit fidelity limits. Lane A defers to external codes; lane B is a bounded native research solver; lane C uses neural surrogates.

Lane	Scope	Performance / fidelity
A: External codes	GENE, CGYRO, GS2 same-case bridges	Full nonlinear 5D parity stays fail-closed until public same-case evidence exists
B: Native GK	Linear transport plus nonlinear 5D operator contracts	~0.3 s/surface for linear eigenvalue; bounded NumPy/JAX research solver with explicit invariant benchmarks
C: Surrogates	QLKNN-10D transport, FNO turbulence	QLKNN test rel_L2 = 0.094; FNO val rel_L2 = 0.055

Free-Boundary Equilibrium

The public operator-source GEQDSK gate passes and the FreeGS public-example vacuum comparison passes. Native same-case profile-source metrics, finite signed-q sanity, and machine-readable strict threshold checks are published, and free-boundary strict parity is accepted for the public FreeGS same-case lane. EFIT-grade profile-source / free-boundary reconstruction remains an open evidence gate with row-level debug traces.