Evaluation of discharge current employing generalized energy method and integral ohm's law using finite element method

The terminal current in voltage driven systems is an essential role for characterizing the pattern of electric discharge such as corona, breakdown, etc. Until now, to evaluate this terminal current, Sato's equation has been widely used in areas of high voltage and plasma discharge. Basically Sato's equation was derived by using the energy balance equation and its final form described physical meaning explicitly. To give more general abilities in Sato's equation, we present a generalized approach by directly using the Poynting's theorem incorporating the finite element method. When the magnetic field effect or the time-dependent voltage source is considered, this generalized energy method can be easily applicable to those problems with any dielectric media such as gas, fluid, and solid. As an alternative approach, the integral Ohm's law resulting in small numerical errors has an ability to be applied to multi-port systems. To test the generalized energy method and integral Ohm's law, first, the results from two prosed methods were compared to those from Sato's approach and an analytic solution in parallel plane electrodes. After verification, the generalized method was applied to the tip-sphere electrodes for evaluating the terminal current with three carriers and the Fowler-Nordheim field emission condition. From these results, we concluded that the generalized energy method can be a consistent technique for evaluating the discharge current with various dielectric materials or large magnetic field.