Analytical Determination of the Three-Dimensional Field in Superconducting Generators

Abstract

Analytical expressions for the three-dimensional field produced by an air-cored turbo-alternator field winding such as might be employed in a superconducting alternator are derived. The analysis is developed for situations where environmental screen surrounds the winding. The environmental screen could be either magnetic or conducting. In developing solutions of the problem using the theory of electromagnetic fields the concept of magnetic vector potential is utilized. A new technique in the mathematical analysis is followed in order to develop a solution of the diffusion or vector Helmholtz equation for the magnetic vector potential in three dimensions which appears in the analysis. The field solutions obtained are relatively simple and constitute a double series sum that is rapidly convergent.