The equilibrium charge distribution and electric field at a vacuum/dielectric interface

The unique equilibrium electric field configuration for a planar dielectric/vacuum interface subjected to electric stress is found, based on the requirement that the local electric field be inclined to the dielectric surface at the critical angle at which the secondary electron yield of electrons impacting the dielectric surface is unity. The critical angle is independent of the magnitude of the applied field and is a function of material properties. The electric field, potential, and charge distributions are calculated for several orientations of the interface versus the applied stress field. The results show that when the surface is charged, the electric field may be enhanced near either the cathode or the anode depending on whether the angle of the interface is greater or less than the critical angle. This is in contrast to the uncharged case, for which the field is always enhanced near the narrow end of the dielectric independent of the polarity of the applied field. The equilibrium surface charge distribution is not constant over the surface and varies in sign with the orientation of the interface. The magnitude depends on both the critical angle and the relative permittivity of the dielectric. The implications of these results for researchers and designers who are investigating or using high voltage is discussed.