A fusion-modelling and control program: tokamak equilibrium and transport, magneto-inertial confinement, and the control layer that ties them together — each grounded in real experimental validation.
Fusion releases energy by forcing light nuclei together, but the fuel must first be heated to a plasma hotter than the Sun's core — and then held there. No material wall can touch it, so the plasma is confined by magnetic fields or by its own inertia during a fast implosion. The hard part is not reaching fusion temperatures; it is keeping the plasma stable and predicting where it will go microseconds before it gets there. That is a physics-modelling and a real-time control problem at once.
A doughnut-shaped magnetic bottle holds a steady plasma in force balance. The whole design rests on solving for that equilibrium, then predicting how heat leaks across the field (transport) and when the plasma will go unstable (MHD) or abruptly collapse (a disruption). This is the regime of ITER and DIII-D — and of SCPN-Fusion-Core.
Two compact plasmoids are fired together and compressed by a fast external field. There is no steady state — the plasma lives for microseconds and the control loop must fire before a merge instability breaches confinement. That moves the critical decision from software onto FPGA logic, which is the domain of SCPN-MIF-Core.
Both approaches share the same control question: keep the plasma coherent, and act before instability wins. SCPN-Control is the neuro-symbolic control and transport stack that spans them — the same phase-dynamics mathematics drives an FRC merge window and a tokamak transport barrier.
Each panel gives the plain-language idea first, then the equation the code actually solves. Skip the maths or read it — both are here.
Where does the plasma sit? A magnetically confined plasma settles where the outward pressure exactly balances the magnetic pinch. Finding that shape — the nested flux surfaces — is the starting point for everything else.
The axisymmetric Grad-Shafranov equation for the poloidal flux $\psi$, with $\Delta^\ast \equiv R\,\partial_R(R^{-1}\partial_R) + \partial_Z^2$, pressure $p(\psi)$ and poloidal current $F(\psi)=R B_\phi$. SCPN-Fusion-Core solves it free-boundary by nonlinear Picard iteration with Newton-Raphson coil-current acceleration, vacuum contributions from the PF coils computed via a Biot-Savart kernel.
Will two plasmoids merge cleanly, or tear apart? As the compressed plasma rings approach, each rotates at its own rate. Whether they lock into one stable object or drift into instability is a synchronisation problem — the same mathematics that describes coupled oscillators.
A Doppler-Kuramoto model with a time-varying natural frequency $\omega_i(t)$ capturing the accelerating merge frame, phase-lag $\alpha$, and coupling $K_{ij}$. Integrated by RK4 against a closed-form $\theta(t)=\theta_0+\omega_{i0}t+\tfrac12\dot\omega_i t^2$ reference; the merge-window monitor decides fire / no-fire before confinement is lost.
How fast does heat leak, and is the plasma still coherent? Turbulence sets how quickly energy escapes across the field; a single scalar tracks how well the whole plasma stays phase-locked, so a controller can act the moment coherence starts to slip.
A self-contained flux-tube linear gyrokinetic solver (Miller geometry) with mixing-length saturation gives ion/electron heat diffusivities $\chi_i,\chi_e$ and particle diffusivity $D_e$. Control uses a Kuramoto-Sakaguchi phase model with the Lyapunov coherence functional $V(t)$ as the monitored order parameter — zero at perfect lock, rising as the plasma desynchronises.
The models are checked against measured and published plasmas — not only synthetic cases. Negative results are kept executable, not hidden.
g145419.02100 (t = 2100 ms), sourced through the omas package. A measurement-constrained real equilibrium.EFIT reconstructions are measurement-constrained model outputs, not raw truth; validation lanes rerun on every invocation and record honest negatives with runtime provenance.