Theory of structures in near-electrode plasma regions

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Abstract
A number of well-known features of a constricted discharge in plasma near-electrode layers (e.g., the normal current-density effect) proceeds from the fact that the layer thickness is much smaller than longitudinal dimensions. A better understanding of these features may be achieved by means of the asymptotic approach, which treats the ratio of the above-mentioned lengths as a small parameter. In the vicinity of extreme points of the current-voltage characteristic of the distributed discharge regime (regime with a uniform distribution of the current density over the electrode surface), this approach is similar to the perturbation method, reducing the reaction-diffusion equations in the vicinity of an instability point to the Ginzburg-Landau equation, and results in a Fisher-type equation for perturbations of current-density distribution. Using this equation, stationary perturbations are found and their stability is analyzed. In addition, the above-noted asymptotic approach is applied to the analysis of normal current-density regimes. In particular, it is shown that interaction of a current spot (covered area) with lateral boundaries and/or other spots is transmitted by means of the exponentially small perturbations introduced by spots into regions occupied by the cold and hot phases. Application of the results obtained to the transition between the normal and abnormal regimes of the glow-discharge near-cathode region is discussed.