Space-charge-limited bipolar current flow between coaxial cylindrical electrodes

Abstract

Poisson's equation in cylindrical symmetry is solved numerically assuming that at each electrode there is an unlimited supply of charges of zero energy; positive charges at the positive electrode and negative charges at the negative electrode. A solution is obtained corresponding to zero electric field at each electrode surface; this defines the maximum possible current flow of each charge polarity. The numerical technique is based on a perturbation of the solution appropriate to parallel-plane geometry and is carried out for a ratio of electrode radii ranging from 1 to 400. In the case of the external emitter configuration, the increase in charged-particle current afforded by bipolar flow in comparison to unipolar flow can be significant. Application to the electron-beam pumping of vacuum ultraviolet excimer lasers is briefly considered.