Local synthesis of 3D magnetic surfaces

Abstract

Local synthesis of nested 3D toroidal magnetic surfaces is carried out on the basis of the general theory of surfaces by using magnetic coordinates (generally unknown a priori). An equilibrium magnetic surface is calculated by specifying two functions on the surface (the absolute value of the magnetic field and the distance to the nearest magnetic surface) and three parameters (the rotational transform, pressure gradient, and poloidal current). The choice of the parameters is restricted by the requirement that the surface should be closed toroidally. A method of synthesis of a closed magnetic surface is proposed when two functions—the absolute value of the magnetic field and the major radius—are specified. A set of harmonics of a new type of poloidally preudosymmetric configuration (a toroidal mirror with a large mirror ratio and small rotational transform) is obtained.