Numerical methods for solving some problems of the theory of plasma equilibrium in toroidal configurations

Abstract

The author develops numerical methods based on the virtual-casing principle for solving some problems relating to the equilibrium of plasma in axially symmetric toroidal configurations with a transverse cross-section of arbitrary shape. Methods are presented for calculating maintaining magnetic fields on the basis of a known equilibrium field at the plasma boundary, for extending numerically the equilibrium magnetic field beyond the plasma boundary, and for solving the direct equilibrium problem in the case of a quasi-uniform current. A method for obtaining some non-linear solutions of the equilibrium equations is discussed. The paper also goes into the question of calculating an iron-free inductor and the question of determining the inductance of a toroidal superconductor of arbitrary transverse cross-section. The methods described are illustrated by magnetic-field calculations for configurations of the “finger-ring” Tokamak type and the “Ohkawa doublet” type.