Space charge limited current flow between coaxial cylinders at potentials up to 15 MV

Poisson's equation in cylindrical 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 analytical 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 high-power field-emission diode is considered, with particular reference to the radially pumped ultraviolet laser.