The integro-differential equations for time-dependent space-charge decay currents in media between radially symmetrical electrodes

Abstract

Using a single charge-carrier species with a field-independent mobility model, dimensionless, nonlinear integro-differential equations have been derived whose solutions would exactly predict the time-dependent current produced by the drift and collection of space-charge swarms in media between electrodes with cylindrical and spherical symmetries. The equations are the one-dimensional solutions of the mathematical problems involving arbitrary initial space-charge distributions whose initial currents may or may not be space-charge limited. In principle, if the initial charge distributions were known, the solutions would reduce to first-order, nonlinear differential equations which then could be numerically integrated. The general equations are applied to a specific example of a charge-density distribution which is important in scientific and technological applications.