Real-Time Equilibrium Reconstruction
Fitting the plasma's magnetic equilibrium every few milliseconds so that shape, position, and profile controllers act on a consistent picture.
The equilibrium problem
A tokamak plasma sits in force balance described by the Grad-Shafranov equation, which relates the poloidal flux to the pressure and current profiles. Equilibrium reconstruction solves the inverse problem: given magnetic measurements (and other diagnostics), find the flux distribution and profiles most consistent with them. Doing this in real time is the backbone of magnetic control.
Offline versus real-time
Offline reconstruction can afford a full, high-resolution nonlinear solve. Real-time reconstruction must finish inside a control cycle - a few milliseconds - so it uses reduced grids, precomputed basis functions or response tables, and constrained fits that trade some accuracy for speed and determinism. The output is a usable equilibrium every cycle, not a perfect one occasionally.
What it delivers
- Boundary shape and gaps to the wall
- Vertical and radial position of the current centroid
- Plasma current and internal inductance
- Flux at chosen isoflux control points
- Where diagnostics allow, the safety-factor and pressure profiles
Constraints and regularization
Magnetic measurements alone under-determine the internal profiles, so reconstruction adds constraints: known coil currents, boundary conditions, and, where available, kinetic diagnostics (motional Stark effect, interferometry, Thomson scattering). Regularization keeps the fit stable against noise. The estimator reports which quantities are well-constrained and which are essentially assumed.
Why real-time matters
Isoflux shape control needs the flux at control points now; vertical control needs position now. A reconstruction that lags or stutters starves these loops. This is why real-time equilibrium is engineered as a hard-real-time service with bounded latency, feeding a single consistent state to every controller above it.