Mathematical model of the Galathea-belt toroidal magnetic trap

Abstract

We consider a mathematical model of equilibrium configurations of plasma, magnetic field, and electric field in a toroidal trap with two ring conductors with current loaded into plasma. We present the mathematical apparatus of the model based on the numerical solution of boundary value problems for the Grad–Shafranov equation (a differential equation of elliptic type for the magnetic flux function), solution methods for these problems, and numerically obtained properties of equilibrium configurations. We indicate the differences in configurations in the toroidal trap and in its analog straightened into a cylinder.