Real-Time Equilibrium Reconstruction
Equilibrium reconstruction infers the plasma shape, position, and internal fields from magnetic and other measurements, fast enough for control.
The reconstruction problem
The plasma's shape and internal field distribution are not measured directly. They are inferred by solving the equation that balances plasma pressure against magnetic forces, constrained to match the sensor readings. This is equilibrium reconstruction, and doing it fast enough to feed control loops is real-time reconstruction.
Inputs
- Magnetic pickup coils and flux loops around the vessel
- Coil currents driving the field
- Optional internal constraints from interferometry or polarimetry
- Pressure information from kinetic profile measurements
The speed constraint
A full offline reconstruction can take a long time. Real-time versions use fixed grids, pre-computed matrices, and bounded iteration counts to guarantee they finish inside the control cycle. They trade some accuracy for determinism, and the accuracy they keep is concentrated in the quantities control needs: boundary shape, position, and safety factor.
Feeding the controllers
The reconstructed equilibrium supplies the shape control points, the vertical position, and the q-profile estimate that current-profile control needs. It also locates rational surfaces for tearing-mode control to aim at. Because so many loops depend on it, the reconstruction is a shared service that must be both fast and reliable.
In the Kronos program
For the Hyperion breeder, real-time equilibrium reconstruction must resolve the negative-triangularity boundary and the elongated shape accurately enough for shape and vertical control, and must locate the surfaces used by tearing-mode and sawtooth control. As a spherical tokamak, its geometry requires reconstruction tuned to low aspect ratio. The method is validated in simulation before operation.