A high-order finite element method for Tokamak plasma equilibria /

A numerical method for the solution of the axisymmetric, free-boundary, Tokamak equilibrium problem is described. The method uses high-order polynomials defined over a mesh of triangular finite elements to solve the magnetohydrodynamic equilibrium (Grad-Shafranov) equation. Arbitrary coil and plasma current configurations can be specified. The formulation incorporates a nonlinear procedure for computing the coil currents required to place the plasma in a desired position. The solution to the nonlinear Grad-Shafranov equation is computed using a modified Newton's method. The inner-most system of sparse, linear equations is solved using a preconditioned, conjugate gradient algorithm. A computer program, PLEQUI (PLasma EQUIlibrium), was written in a portable FORTRAN dialect to implement the method. The method was tested using both fixed-boundary and free-boundary plasma problems. The program was validated by comparing the results to analytic solutions, by examining the flux plots, or by comparing the solution to the output of another finite-element code