Mathematical Model of Equilibrium Plasma Configurations in Magnetic Traps and Their Stability Analysis

The paper presents a review of numerical investigations of a special class of magnetic field-based plasma confinement traps in which current-carrying conductors are immersed in plasma. These traps are referred to as Galatea traps, as proposed by A. I. Morozov. The investigations are presented as applied to a cylinder with two conductors parallel to the axis, which is a straightened analog of a toroidal Galatea-belt trap. The mathematical model of equilibrium is based on a boundary value problem for the two-dimensional elliptic Grad–Shafranov equation, which is solved numerically. Of main interest are various approaches to the stability analysis of magnetoplasma configurations in a trap and the dependence of stability on the geometry and parameters of the problem. We analyze the linear-approximation stability of one-dimensional configurations surrounding a conductor and of two-dimensional configurations in a Galatea-belt trap. The main result of calculations in various problem statements is that the ratio of the characteristic gas and magnetic pressures under which stability occurs is bounded from above. We give a brief account of the main results published in recent years and present new results obtained recently.