EFIT-Class Equilibrium Reconstruction
Reconstruction codes fit a Grad-Shafranov equilibrium to magnetic and kinetic measurements, giving the best-estimate flux map of a real discharge.
The reconstruction problem
Forward equilibrium solvers take profiles and coil currents and predict the flux map. Reconstruction does the inverse: given a set of experimental measurements, find the equilibrium that best reproduces them while still satisfying the Grad-Shafranov equation. EFIT (Equilibrium FITting) is the archetype and gives its name to a whole class of codes.
Inputs and outputs
- Inputs: magnetic probe signals, flux loop voltages, coil and vessel currents, plasma current, and optionally kinetic profiles (pressure, current) from other diagnostics
- Outputs: psi(R,Z), plasma boundary and X-point location, q profile, stored energy, plasma beta, and internal inductance
Method
The free functions p(psi) and F dF/dpsi are expanded in basis functions (often polynomials or splines) with unknown coefficients. The code linearizes the response of each measurement to those coefficients, then solves a constrained least-squares problem, iterating the nonlinear Grad-Shafranov solve inside the fit. A chi-squared metric reports how well the reconstruction matches the diagnostics.
Kinetic vs magnetic reconstruction
A purely magnetic reconstruction constrains the boundary and integral quantities well but leaves the internal current profile poorly determined. Adding kinetic constraints (Thomson scattering pressure, motional Stark effect for the internal magnetic pitch angle, and measured current) pins down the interior, producing a kinetic EFIT used for transport and stability analysis.
Practical notes
Reconstruction is used both between shots for analysis and, in fast simplified form, in real time for plasma shape control. Real-time variants trade basis-function richness for speed, running inside the control cycle on dedicated hardware.
Reliable reconstruction depends on a well-calibrated diagnostic set and an accurate model of the conducting structures surrounding the plasma, since eddy currents in the vessel modify the measured fields.