Global stability analysis method to numerically predict precursor of breakdown voltage

This study presents a new method for predicting a precursor of breakdown voltage. This method applies a global linear stability analysis to a drift-diffusion model coupled with the Poisson equation. The instability of the solution of these equations is evaluated with the proposed method and is considered to be the onset of a breakdown. The proposed method is validated in one dimension by using the Townsend theory as a reference. To extend the one-dimensional case and investigate the characteristics of multidimensional eigenmodes, we apply the method to two-dimensional plane-to-plane discharge tubes. To prove an adaptability against complex electrodes geometry, the discharge path and the corresponding breakdown voltage for the well-known corner-to-plane geometry are qualitatively evaluated.