Development of an auto-convergent free-boundary axisymmetric equilibrium solver

Improvements upon the calculation of the magnetic flux for a given current profile in axisymmetric toroidal plasmas using an iterative, modular algorithm coupled with a fast, direct elliptic solver for the Grad-Shafranov equation to reconstruct a free boundary equilibrium solution are implemented and analyzed. The equilibrium algorithm is modified with the application of the von Hagenow method for determining the flux on the computational boundary, greatly reducing the time cost from $O(N^4)$ to $O(N^2 \ln N)$ machine operations. These improvements allow the grid resolution to be increased efficiently and automatically to reduce the maximum Grad-Shafranov error to values needed for accurate stability calculations on a more effective time scale.