Space-charge-limited bipolar current flow between concentric spherical electrodes

Poisson´s equation in spherical 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 several orders of magnitude. Application to fusion fuel-pellet compression, field-emission microscopy and thermionic-energy conversion is briefly discussed.