Study of the electron kinetics in the anode region of a glow discharge by a multiterm approach and Monte Carlo simulations

A recently developed method for the solution of the space-dependent electron Boltzmann equation in higher-order accuracy has been adopted to study the behaviour of the electrons in the anode region of a dc glow discharge. This method is based upon a multiterm approximation of the Legendre polynomial expansion of the electron velocity distribution function. Generalizing the boundary conditions, in particular for the partially absorbing anode, the impact of the anode fall and the influence of the electron absorption at the anode on the spatial behaviour of the electron kinetic properties have been investigated in various approximation orders. The analysis has shown that the simplified treatment of the kinetic equation using only the first two terms of the velocity distribution expansion can lead to considerable falsifications of the convergent behaviour. In general, the convergent solution of the significant components of the electron velocity distribution and all important macroscopic quantities is obtained by a multiterm approximation including six to eight terms of that expansion. The discrepancies between the two-term and convergent results are found to depend sensitively on the parameters of the anode fall. In addition, the multiterm 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 is found. (author)