Boundary Effects in Solution of Boltzmann's Equation for Electron Swarms

Abstract

The combined effect of interaction of electrons with walls, neutral molecules and an electrostatic field is considered through analytic solution of Boltzmann's equation. In the first instance, we discuss a half-range decomposition in velocity space, corresponding to electrons moving to and from the walls, which is valid for all types of electron-molecule interactions. The half-range equations are solved in the steady state for zero field and the constant mean free path model, and it is shown that the familiar full-range 'two-term' approximation equations are adequate in this case, as far as estimating bulk properties of the electrons is concerned. For the nonzero field, again in the steady state, the full-range equations are solved for the constant collision frequency model.

Boundary Effects in the Townsend-Huxley Experiment

“…by Robson and Ness (1986). It would be calculationally very convenient if this method could be used also for the present type of problems.…”

“…Lowke et al 1977;Braglia and Lowke 1979;Robson 1981;Braglia 1982), and also for the pure Lorentz gas problem (e.g. Davison and Sykes 1957;Williams 1971;Cole et al 1984), the steady state Townsend experiment (e.g.…”

“…Davison and Sykes 1957;Williams 1971;Cole et al 1984), the steady state Townsend experiment (e.g. Sugawara et al 1992;Robson 1995), and the, in many ways rather similar, quasi-Rayleigh gas problem (e.g. Burscha and Titulaer 1982;Beals and Protopopescu 1983;Naqvi et al 1984).…”

Boundary conditions for the electron kinetic equation using expansion techniques

“…of the order 2̺ + 1 with ̺ ∈ N 0 , where the integration of the angular variable x of the momentum space occurs over the half-range [31] as shown in Fig 1. The substitution of f (0, U, x) in Eq. (7) by its l-term approximation according to Eq.…”

“…For the numerical determination of the corresponding expansion coefficients of the EMDF, the choice of suitable boundary conditions plays an important role. Based on an ansatz similar to that proposed by Marshak [30][31][32][33] and a fundamental integral relation for Legendre polynomials, explicit expressions for the expansion coefficients have been derived that can be used as boundary conditions and relate macroscopic properties of the electrons with the expansion coefficients at the spatial margins of the discharge volume. In particular, the boundary conditions presented make it possible to accu- In order to demonstrate the superiority of the new boundary conditions, a comparison with commonly used boundary conditions is presented using the example of an abnormal oxygen glow discharge.…”