On the structure of the steady state space-charge-limited boundary layer in one dimension

The authors study the external SGEMP boundary layer in one Cartesian dimension in the steady-state limit. Dimensional arguments backed by explicit calculations show the surface charge density to be independent of the electron charge, and show that the characteristic potential and dipole moment of the layer are practically independent of fluence. The general equation of motion is shown to imply that the electrostatic energy density is everywhere twice the density of kinetic energy stored in the normal component of electron motion. Detailed solutions are given for several electron energy spectra including an exponential energy spectrum with a cos theta angular emission spectrum. Estimates are given for the times at which the steady-state solution should be applicable.