Space-charge-limited electron current flow between coaxial cylinders and concentric spheres with ion production at an intermediate radius

The steady-state Poisson equation is formulated in cylindrical and spherical geometries assuming the emission of electrons at zero energy from the cathode and the emission of both ions and electrons, again at zero energy, from an intermediate surface at an arbitrary radius between the electrodes. The equation is solved numerically with the boundary conditions of zero field at the charged particle emitting surfaces to give the maximum electron current. An optimum radius of the intermediate surface is then found corresponding to the overall maximum electron current. The calculations are performed for a ratio of electrode radii ranging from 1 to 400, and, in the case of the external cathode configuration, the increase in electron current afforded by bipolar flow in comparison to unipolar flow can be several orders of magnitude. Application is briefly considered to electron beam pumping of vacuum ultraviolet excimer lasers and to fusion pellet compression by electron beams.