Stability Issues in Two-Dimensional Mathematical Models of Plasma Equilibrium in Magnetic Galathea Traps

Galathea traps for confining plasma in a magnetic field created by current-carrying conductors immersed in the plasma volume constitute a promising class of objects for development in the field of controlled thermonuclear fusion. After describing the main properties and quantitative characteristics of the traps, the central problem is to study the stability of equilibrium magnetoplasma configurations. Mathematical modeling and calculations performed in terms of the differential equations of magnetohydrodynamics play an essential role here. These equations are described using the example of a toroidal “Galathea belt” trap straightened into a cylinder. The article presents its plasmastatic model and several approaches to studying the stability of configurations: the convergence of iterative methods for establishing equilibrium in two-dimensional models, a brief survey of the research into the magnetohydrodynamic stability of one-dimensional configurations surrounding a straight current-carrying conductor, and a rigorous study of the stability of configurations with respect to two-dimensional perturbations in the linear approximation. Stability criteria and their relationship to each other are obtained numerically in various approximations. Ways of generalizing the results to three-dimensional perturbations are indicated.