Optimal injection of beams in a mirror well

An anisotropic, finite-beta plasma trapped in a mirror well is subject to local hydromagnetic instabilities that depend strongly upon the shape of the angular distribution function of the contained particles. Moreover, the angular distribution is a solution of a diffusion equation that can be significantly modified by appropriate changes in the relative positions and amplitudes of injected beams used to create or maintain the plasma. The question of how to inject beams so that the greatest overall pressure is maintained without the plasma becoming unstable and without inordinate demands upon the technology of beam injection is an application of the theory of continuous games. We examine this problem, and the optimal strategies for a number of games of interest are determined and described.