Abstract
A recently developed method for the solution of thespace-dependent electron Boltzmann equation in higher-orderaccuracy has been adopted to study the behaviour of the electronsin the anode region of a dc glow discharge. This method is basedupon a multiterm approximation of the Legendre polynomialexpansion of the electron velocity distribution function.Generalizing the boundary conditions, in particular for thepartially absorbing anode, the impact of the anode fall and theinfluence of the electron absorption at the anode on the spatialbehaviour of the electron kinetic properties have beeninvestigated in various approximation orders. The analysis hasshown that the simplified treatment of the kinetic equation usingonly the first two terms of the velocity distribution expansioncan lead to considerable falsifications of the convergentbehaviour. In general, the convergent solution of the significantcomponents of the electron velocity distribution and all importantmacroscopic quantities is obtained by a multiterm approximationincluding six to eight terms of that expansion. The discrepanciesbetween the two-term and convergent results are found to dependsensitively on the parameters of the anode fall. In addition, themultiterm results are compared with corresponding ones obtained by accurate Monte Carlo simulations. Very good agreement between the convergent eight-term Boltzmann and Monte Carlo simulations isfound.
Published Version
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