Uniqueness Theorem for the Non-Local Ionization Source in Glow Discharge and Hollow Cathode

Vladimir V. Gorin

Kyiv National Taras Shevchenko University, Kiev, Ukraine,Moscow Institute of Physics and Technology, Moscow, Russia.

DOI: 10.4236/jmp.2012.330202                

Abstract

The paper is devoted to the proof of the uniqueness theorem for solution of the equation for the non-local ionization source in a glow discharge and a hollow cathode in general 3D geometry. The theorem is applied to wide class of electric field configurations, and to the walls of discharge volume, which have a property of incomplete absorption of the electrons. Cathode is regarded as interior singular source, which is placed arbitrarily close to the wall. The existence of solution is considered also. During the proof of the theorem many of useful structure formulae are obtained. Elements of the proof structure, which have arisen, are found to have physical sense. It makes clear physical construction of non-local electron avalanche, which builds a source of ionization in glow discharge at low pressures. Last has decisive significance to understand the hollow cathode discharge configuration and the hollow cathode effect.

Keywords

Integro-Differential Operator; The Fredholm 2-nd Kind Equation; Existence and Uniqueness Theorem; Nil-potency; Glow Discharge; Hollow Cathode; Non-Local Ionization; Non-Local Kinetics

Conflicts of Interest

The authors declare no conflicts of interest.

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