Equilibrium of field reversed configurations with rotation. III. Two space dimensions and one type of ion

Abstract

A two-dimensional equilibrium model for field reversed configurations (FRCs) with rotation is presented. In a previous paper [N. Rostoker and A. Qerushi, Phys. Plasmas 9, 3057 (2002)] it was shown that a complete description of equilibria for FRCs with rotation is provided by a generalized Grad–Shafranov equation for the plasma flux function. In this paper it is shown how to solve that fundamental equation for the case of two space dimensions and one type of ion. Periodic boundary conditions and a Green’s function are used to convert the original differential equation to an equivalent integral equation. The integral equation is solved by iteration. An iteration algorithm is described which converges to a solution of the generalized Grad–Shafranov equation starting with a one-dimensional trial function. Analytic one-dimensional solutions are shown to be a limiting case of two-dimensional solutions when the applied magnetic field is constant. In addition to rapid convergence for a complex nonlinear problem, the Green’s function method guarantees that the boundary conditions are satisfied in every iteration.