Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis

Abstract

In reference (Robson R E, Li B and White R D 2000 J. Phys. B: At. Mol. Opt. Phys. 33 507), we revisited the Franck–Hertz experiment, and gave solutions of the Boltzmann equation describing the spatially-resolved relaxation profiles of a non-hydrodynamic swarm of electrons streaming at a steady rate from a plane source into mercury vapour. In this paper, we extend this study to other cases and develop a formalism for both ions and electrons and consider situations where both conservative and non-conservative collisions may take place. As in Robson et al (2000), we employ a `two-temperature' Burnett function representation of operators in velocity space in the Boltzmann equation. Configuration space is represented by a finite mesh of points and a finite difference technique is developed accordingly. Boundary conditions are specified for the general problem and techniques for solving the resulting large system of algebraic equations are discussed. The importance of a `multi-term' analysis and the existence of negative differential conductivity (NDC) under non-hydrodynamic conditions is displayed by considering electrons in methane. The explicit effect of ionization on the spatial relaxation profiles is considered along with a study on the importance of treating ionization as a true non-conservative process as opposed to another inelastic process. The spatial relaxation profiles are compared with predictions from eigenvalue theory.

A Monte Carlo study of photoelectron extraction efficiency from CsI photocathodes into Xe–CH4 and Ne–CH4 mixtures

“…Although the cross-sections used in the present work may not guarantee the completeness established by the so called swarm method as usually required in gas discharge and plasma physics [77][78][79][80][81], figures 2 to 4 show that in the low E/N range relevant for the present work (drift fields E/N~<20Td near the photocathode), our calculations give sufficiently accurate drift parameters. In particular, they reproduce well known characteristic effects very sensitive to cross-sections, namely the anisotropy of diffusion when electrons drift under an electric field [36,[82][83][84][85], and negative differential conductivity [81,[86][87][88][89][90]. The NDC effect -a decrease of drift velocity with increasing E/N -may be observed for instance in some mixtures of noble gases with molecular additives (e.g.…”

Colloquium: Physically based fluid modeling of collisionally dominated low-temperature plasmas

“…These equations have appeared many times in the literature ͓see, e.g., Robson ͑1986, 1994͒;Petrović and Vrhovac ͑1998͒;Li et al ͑2002͔͒, in which discussions of the balance equation for the spatially homogeneous temperature tensor T 0 can also be found. It is a matter of first solving the nonlinear equations ͑59͒ and ͑60͒, then the linear equations ͑61͒ and ͑62͒, and the problem is completely solved.…”

Boundary conditions for the electron kinetic equation using expansion techniques

“…in [25]. But it is stated in that paper that these conditions do not represent conditions at any physical boundary.…”

“…in [25][26][27][28][29]. However, a physical motivation for the condition of the emission of electrons from the cathode of the discharge has been given for the first contribution to the distribution anisotropy only.…”