Relation Between Circuit Current and Plasma Current Density in Plasma Discharges with Dielectric Media

The theoretical derivation of the relation between moving charges in the plasma and external circuit current was first established on a firm basis by Sato [J. Phys. D 13, L3 (1980)] for the case of a discharge with constant applied voltage between bare electrodes. The generalization to time varying applied voltages was established by Morrow and Sato [J. Phys. D 32, L20 (1999)], still considering bare electrodes. In the present work, we extend the latter derivation to include general devices with arbitrarily arranged linear dielectric media, and multiple electrodes with time dependent voltages, of interest, for instance, for a Dielectric Barrier Discharge (DBD). In particular, the present derivation determines a general, practical expression for the reactive term present in the Morrow and Sato formula. Using the expression derived, we show how in simple DBD geometries usual circuit approximations of the plasma discharge can be obtained and its validity was justified. Also, we consider the determination of the internal plasma current from the measurement of the external circuit current for a cylindrical DBD operated with helium at atmospheric pressure. Finally, we apply the theory to a three-electrode device in order to relate electric measurements to volume integrals on the plasma that were shown to be useful in order to quantify species production by electron impact.