Boundary Effects in the Townsend-Huxley Experiment

Abstract

The Townsend–Huxley transverse diffusion experiment has been modelled using kinetic theory, with the aim of explaining the successes and shortcomings of some current ratio formulae that are based on hydrodynamic theory. These are shown to be essentially identical in form, apart from the estimated magnitudes of the boundary layer corrections to the second and fourth transverse position moments of the current density. The main reason for the shortcomings is shown to be the inability of hydrodynamic theory to describe the relaxation of the input electron energy distribution towards the steady state free space form. As a byproduct of the studies, exact eigensolutions have been found for the associated ‘infinite slab’ problem, using the constant collision frequency model with the two-term approximation.

Rotational and Vibrational Excitation of Nitrogen by Electron Impact

“…The method of mixtures, as used by Haddad (1984), was adopted to make a sensitive and conclusive test of the new theoretical rotational and vibrational cross sections near threshold. This method, used first by Townsend and Bailey (1922) and subsequently by a number of workers (see, for example, Haddad and Crompton 1980;Haddad 1984;Petrović and Crompton 1987;England et al 1988;Elford 1988, 1991;Schmidt et al 1994), provides a means of either deriving more accurate elastic cross sections for the monatomic buffer gas or inelastic cross sections for the molecular additive (for a review see Schmidt 1995), or testing more definitively theoretically derived inelastic cross sections. Here we focus on the latter application as applied to the inelastic N 2 cross sections, and begin by briefly reviewing the method and its advantages.…”

Multiterm solution of the reactive space–time-dependent Boltzmann equation

“…For electron swarms in a gas, the presence and influence of boundaries is known to be a difficult and long-standing problem, even for dc fields, [3][4][5] largely due to the steep spatial gradients induced by the bounding surface and the complex interaction of spatial effects with the field. Here spatial gradients may be quite strong and careful analysis of both space and time variation is essential for accurate modeling of the discharge.…”

Boundary conditions for the electron kinetic equation using expansion techniques

“…Starting from Eq. (16), boundary conditions for the expansion coefficients with an even index can be derived by means of a procedure similar to that described in section 3.1 using the relation (32) given in the appendix.…”

“…(14) seems to be impossible when a truncated Legendre polynomial expansion for solving Eq. (2) is used [32,36].…”

“…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.…”