A robust, fast, and accurate numerical method is proposed for finding the voltage of the ignition of DC self-sustaining gas discharges in a wide range of conditions. The method is based on physical grounds and builds up from the idea that the ignition of a self-sustaining gas discharge should be associated with a resonance that would occur in a non-self-sustained discharge in the same electrode configuration. Examples of the application of the method are shown for various configurations: parallel-plate discharge, coaxial and wire-to-plane corona discharges, and a discharge along a dielectric surface. The results conform to the conventional Townsend breakdown condition for the parallel-plate configuration and are in good agreement with existing experimental data for the other configurations. The method has the potential of providing a reference point for optimization of the hold-off capability of high-power switchgear operating in low-frequency fields.

提出了一种鲁棒，快速，准确的数值方法，用于在各种条件下寻找直流自持式气体放电的点火电压。该方法基于物理基础，并且基于这样的思想：自持气体放电的点火应与在相同电极配置下非自持放电中发生的共振相关。对于各种配置，显示了该方法的应用示例：平行板放电，同轴和线平面电晕放电以及沿介电表面的放电。结果符合平行板配置的常规Townsend击穿条件，并且与其他配置的现有实验数据高度吻合。