Space charge limited current flow between concentric spheres at potentials up to 15 MV

Abstract

Poisson's equation in spherical symmetry is solved numerically with the assumptions of zero field and zero electron energy at the cathode surface. The computed current is expressed in terms of an analytic solution obtained for the extreme relativistic case. Internal and external anode configurations are treated, with ratio of electrode radii extending to 10000 and potential difference up to 15 MV. Application of this analysis to the achievement of controlled fusion through pellet compression by charged particles is considered.