Charge injection and transport in a lossy capacitor stressed by a Marx generator

Injected charge of density q and mobility μ increases the effective ohmic conductivity π to π + | qμ | where q is time and space dependent. Then, open circuit decay curves at moderate voltages can show a dielectric relaxation time that decreases with increasing voltage while at very high voltages the open circuit decay curves can be non-exponential. Such anomalous behavior has been measured in highly purified water¹ and would be present in any material with enough net charge to distort the electric field. A drift dominated conduction model is used to solve for the electric field and charge density distributions and the terminal voltage-current behavior of a lossy capacitor where one electrode injects charge. The capacitor is connected to a Marx capacitor bank so that the injected charge decreases as the Harx voltage decays, the decay rate in turn being in part determined by the injected charge.