Open AccessMolecular gas electron distribution function with space and time variation
Author(s) -
M. Garcia
Publication year - 1995
Language(s) - English
Resource type - Reports
DOI - 10.2172/251391
Subject(s) - electric field , electron , logarithm , exponential function , field (mathematics) , electric discharge in gases , distribution function , function (biology) , physics , distribution (mathematics) , spacetime , time derivative , computational physics , statistical physics , mechanics , mathematics , classical mechanics , mathematical analysis , quantum mechanics , evolutionary biology , pure mathematics , biology
The desire for improved control over electric discharge phenomena in a wide variety of scientific, technological, manufacturing, and waste processing activities spurs the development of non-equilibrium, non-uniform, and time dependent models. This paper addresses the situation of a slightly ionized, uniform gas with a space and time varying electric field, and in which inelastic collisions occur. The purpose here is to present a reasonably consistent, and reasonably accessible analytical result for the electron kinetics in a gas discharge regime of technological interest. This paper will be structured as follows. First, the analytical result for the logarithmic derivative in energy of the electron distribution function is state. Then, a discussion of the derivation is given. Examples of the solution are shown for an idealized nitrogen-like gas where a uniform electric field ramps in time between static conditions, and then for sinusoidal behavior. Further examples show the effect of a static electric field that decays exponentially with distance. Finally, the combined effect of field gradients in space and time is demonstrated by mapping out the average electron energy in the model gas for a field with sinusoidal temporal variation and exponential spatial decay