Comparison of Sato's equation and Pedersen's theory to obtain gas discharge current

Sato's equation has been employed to calculate the pulse current caused by dielectric barrier discharge (DBD). However, it was derived from the gas discharge in a gap between both metallic electrodes. Hence, due to the existence of surface charges, the applicability of Sato's equation to DBD needs to be clarified. In this paper, the models about gas discharge in a gap between electrodes, one electrode and one layer of barrier dielectric, and between two layers of barrier dielectric are established. And the discharge current for each circumstance is obtained by Sato's equation and by Pedersen's theory simultaneously. The latter was used to explain the mechanism of pulse current method which considers the effect of surface charges. It's found that Sato's current in the gap between both electrodes is consistent with that obtained by Pedersen's theory, which results from the equivalence of the two methods where charge diffusion is neglected. Besides, in the gap between one electrode and one layer of barrier dielectric, the current obtained by the two methods is consistent under positive polarity of applied voltage, while it's inconsistent under the negative one. Moreover, the inconsistency in the gap between two layers of barrier dielectric appears under both polarities of applied voltage. These simulation results show that using Sato's equation to calculate pulse current may be not suitable for DBD or PD, which ignores the accumulation of surface charge.