Simple computation of ignition voltage of self-sustaining gas discharges

Abstract

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.

A practical guide to modeling low-current quasi-stationary gas discharges: Eigenvalue, stationary, and time-dependent solvers

“…The method was introduced and termed the resonance method in the preceding work. 8 Of course, the very idea of finding a real eigenvalue by varying the eigenparameter and searching for this or that kind of resonance is quite obvious. For example, a change of sign of the determinant of the system of algebraic equations obtained by a finite-difference discretization of a boundary-value problem was used in Refs.…”

“…17 However, the problem of ignition of self-sustaining discharges may be solved by accurate mathematical means and this solution is relatively simple. 8 At the ignition, the charged particle densities are very low and the applied electric field is not perturbed by plasma space charge, so the rhs of Eq. ( 3) may be dropped and this equation assumes the form of the Laplace equation,…”

“…Remind that, as discussed in Sec. III A, the plasma space charge is neglected at this step, i.e., the rhs of the Poisson equation ( 3) is dropped or, in other words, the Poisson equation ( 3) is replaced by the Laplace equation (8). Nonlinear processes, such as reactive collisions involving two or more particles produced in the discharge, are neglected as well.…”

“…From the mathematical perspective, the problem of ignition of self-sustaining discharges is an eigenvalue problem. 8 In this work, several methods for its numerical solution are discussed and compared. The method of choice, the so-called resonance method, is physics-based and requires solving a boundary-value problem for steady-state linear partial differential equations, which may be routinely done by means of ready-to-use solvers, including commercial ones.…”

Computational and Experimental Study of Time-Averaged Characteristics of Positive and Negative DC Corona Discharges in Point-Plane Gaps in Atmospheric Air

“…Calculations of the set of solutions describing a wide range of corona voltages/currents for each gap were performed separately for the positive and negative polarities. For each polarity, the first step was to find a solution describing the corona inception, as described in [21]. The second step was a series of computations with the corona current serving as a control parameter and being gradually increased.…”