The discharge current induced by the motion of charged particles in time-dependent electric fields; Sato's equation extended

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Abstract
The formula derived by Nobuyasu Sato (1980 J. Phys. D: Appl. Phys. 13 L3-L6), for the current flowing in an external circuit due to the motion of charged particles in a gap is extended to include a time-dependent applied voltage. The effects of negative ions, and electron, positive ion and negative ion diffusion are also included. It is found that Sato's original equation still describes the contribution of charged particle motion to the external circuit current. The total circuit current is determined by adding the displacement current that effectively flows across the gap to the current determined by Sato's equation. Some comments are also made about the interpretation of Sato's equation in three dimensions.

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