Equilibrium Reconstruction
Equilibrium reconstruction solves for the magnetic configuration that balances plasma pressure against magnetic forces and fits the diagnostics.
Balancing pressure and field
A magnetically confined plasma settles into an equilibrium where the outward push of plasma pressure is balanced by magnetic forces. Equilibrium reconstruction finds the specific configuration, the flux surfaces, current distribution, and pressure profile, that both satisfies this force balance and matches the measured diagnostics. It is the foundational calculation of tokamak state estimation.
The governing relation
In an axisymmetric tokamak the force balance is captured by a single elliptic partial differential equation relating the magnetic flux to the pressure and current profiles. Reconstruction adjusts the free profile functions until the computed magnetic signals match the measured ones, subject to that equation. The classic implementations solve this repeatedly until convergence.
Constraints and inputs
- Magnetic measurements at the boundary from coils and flux loops
- Internal constraints from pressure and current-direction diagnostics when available
- The force-balance equation itself, which sharply limits admissible solutions
- Prior expectations on the smoothness of profiles
Fast reconstruction for control
Standard reconstruction is too slow for the fast control loop, so simplified or surrogate versions are used in real time, with full reconstruction run alongside for accuracy. Turning the reconstruction into a fast surrogate is one of the clearest applications of surrogate modeling in a plasma twin, giving the controller a continuously updated equilibrium within its deadline. See surrogate models.
In the Hyperion breeder
The Hyperion breeder is a spherical tokamak, a compact configuration with a tight aspect ratio, operating at a plasma current of 9.86 mega-amperes with negative triangularity of -0.30 and an on-axis field near 8 tesla, rising to a peak of 16.84 tesla at the coils. Equilibrium reconstruction supplies its shape and internal profiles to the twin and controller. The spherical geometry places specific demands on diagnostic coverage, analyzed through observability studies on the design model today, before hardware exists. See plasma state reconstruction.