Computing Different Modes on Cathodes of DC Glow and High‐Pressure Arc Discharges: Time‐Dependent Versus Stationary Solvers

Abstract

Complex behavior can appear in the modeling of gas discharges even in apparently simple steady‐state situations. Time‐dependent solvers may fail to deliver essential information in such cases. One of such cases considered in this work is the 1D DC discharge. The other case is represented by multiple multidimensional solutions existing in the theory of DC discharges and describing modes of current transfer with different patterns of spots on the cathodes. It is shown that, although some of the solutions, including those describing beautiful self‐organized patterns, can be computed by means of a time‐dependent solver, in most examples results of time‐dependent modeling are at best incomplete. In most examples, numerical stability of the time‐dependent solver was not equivalent to physical stability.

Simple computation of ignition voltage of self-sustaining gas discharges

“…Appropriate tools for the modelling of quasi-stationary gas discharges are stationary solvers, which, in particular, are not subject to the Courant-Friedrichs-Lewy criterion or analogous limitations on the mesh element size. Although most of the popular ready-to-use codes for gas discharge simulation employ time-dependent solvers, e.g., nonPDPSIM [10] and Plasma module of COMSOL Multiphysics, stationary solvers for gas discharge modelling are provided by Plasimo [11]; COMSOL Multiphysics provides stationary solvers for general partial differential equations; although the Plasma module of COMSOL is intended to work with time-dependent solvers, it can still be used with stationary solvers [12]. Several examples of gas discharge modelling where stationary solvers offer important advantages compared to time-dependent solvers can be found in [12].…”

Nonsteady-state processes in a low-current discharge in airflow and formation of a plasma jet

“…The discharge is initiated at the instant t 0 so that the spark channel with a metal vapour cathode spot arises [19,[43][44][45][46]. The discharge burning voltage in the spark regime is practically equal to zero value.…”

“…The mechanism of transition is associated with the development of the so-called explosive emission instability in the cathode layer of glow discharge [3,47]. The arising metal vapour cathode spot bridges the cathode fall of the glow discharge [44][45][46]. Then we see the sharp decrease in the discharge burning voltage up to approximately 50 V. The subsequent sharp increases and decreases in the discharge burning voltage at the temporal stage up the instant t 3 are just related to the extinctions of the spots and to the new glow-to-spark transitions.…”

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

“…Several such examples referring to the modeling of glow discharges and thermionic arc discharges can be found in Ref. 5.…”

“…Although most of the popular ready-to-use toolkits for gas discharge simulation employ time-dependent solvers, e.g., nonPDPSIM 6 and Plasma module of commercial software COMSOL Multiphysics®, stationary solvers for gas discharge modeling are provided by Plasimo; 7 COMSOL Multiphysics® provides stationary solvers for general partial differential equations; and although the Plasma module of COMSOL Multiphysics® is intended to work with time-dependent solvers, it can still be used with stationary solvers. 5 This work is concerned with modeling of low-current discharges, including the Townsend and corona discharges, the aim being to develop an integrated approach suitable for the computation of the whole range of existence of a quasi-stationary discharge from its inception to a non-stationary transition to another discharge form, such as the transition from the Townsend discharge to a normal glow discharge or the corona-to-streamer transition. It is convenient to divide the task into three steps: (i) modeling of the ignition of a self-sustaining discharge, (ii) modeling of the quasi-stationary evolution of the discharge with increasing current, and (iii) the determination of the current range where a quasistationary discharge ceases to exist and the above-mentioned nonstationary transition begins.…”