Control-Oriented Free-Boundary Equilibrium Solver for Tokamaks

TL;DR: A control-oriented free-boundary equilibrium solver for tokamaks was developed using finite difference and Picard iteration methods, enabling forward and inverse modes to solve for magnetic flux and coil currents, validated against analytic and numerical solvers and experimental data.

Abstract: A free-boundary equilibrium solver for an axisymmetric tokamak geometry was developed based on the finite difference method and Picard iteration in a rectangular computational area. The solver can run either in forward mode, where external coil currents are prescribed until the converged magnetic flux function ψ(R,Z) map is achieved, or in inverse mode, where the desired plasma boundary, with or without an X-point, is prescribed to determine the required coil currents. The equilibrium solutions are made consistent with prescribed plasma parameters, such as the total plasma current, poloidal beta, or safety factor at a specified flux surface. To verify the mathematical correctness and accuracy of the solver, the solution obtained using this numerical solver was compared with that from an analytic fixed-boundary equilibrium solver based on the EAST geometry. Additionally, the proposed solver was benchmarked against another numerical solver based on the finite-element and Newton-iteration methods in a triangular-based mesh. Finally, the proposed solver was compared with equilibrium reconstruction results in DIII-D experiments.