Space charge in insulators with needle-plane geometry

Steady-state space-charge and field distributions in insulators with needle-plane electrodes have been examined theoretically by making use of hyperboloid geometry and a relaxed version of Deutsch's assumption. An analytical solution has been obtained for the conventional space-charge boundary condition of infinite charge and zero field at the surface of the charge injecting needle contact. This solution has been extended to cover a range of injection boundary conditions of both space charge and electrical field magnitudes. It has been found that, in the bulk of the material, the forms of the space charge and field distributions are relatively insensitive to the injection conditions. The distribution of power density dissipated under complete space-charge limited current flow is reported and it has been found that a maximum in the power occurs close to, but not at, the needle tip.