Computation of MHD equilibrium of Tokamak Plasma

Abstract Computation of the MHD equilibrium of a tokamak plasma is reviewed as comprehensively as possible. The basic equation of this problem is the Grad-Shafranov equation. General remarks on this equation and related issues are, first, summarized with historical survey of the MHD equilibrium solution, where some mathematical discussions on the numerical analysis of the problem are also presented. Distinguishing features of this problem are seen in treatment of the boundary condition and constraining conditions and we describe them in a rather detailed manner. In the main part of this review paper we present a concrete description on the numerical procedures of the MHD equilibrium solvers which are classified into two groups, that is, the real space solvers and the inverse equilibrium solvers. We also describe topics on more general equilibrium models, that is, the equilibrium with steady flow, anisotropic equilibria, equilibria with specified current sources, and equilibrium evolution. Brief comments on three-dimensional equilibrium solvers are also presented. As for application of the MHD equilibrium solvers we present only a small part, that is, beta limit optimization, design of external coils, analysis of positional instability, and analysis of experimentally obtained data from electromagnetic measurement. It is concluded that among various kinds of numerical solution methods we can usually find most adequate ones for the present problem.

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