Computation of Electrostatic and Rapidly Pulsed Magnetic Fields

Abstract

It is often required, for example, in the design of some pulsed controlled-thermonuclear-fusion experiments, to calculate electrostatic fields and to calculate magnetic fields in the approximation that flux does not penetrate metal boundaries of the experimental volume. Computation of such magnetic and electric fields by means of the standard relaxation methods is often difficult and very costly, even with high-speed computers. This is because the boundaries of the region of experimental interest are rather arbitrary and because there are generally current- or charge-carrying conductors within the region that make it nonsimply connected. An alternative method of solving the boundary value problems that determine these electric and magnetic fields, which does not involve a difference approximation to the differential equations, has been developed. With this method, an exact analytic solution of the appropriate differential equation is obtained in the region of interest, and this solution is made to approximate the boundary conditions. The method and its application are described in detail. Examples of the application of the method to some controlled-thermonuclear-fusion experiments are given.