Li, B., White, R.D., and Robson, R.E. (2002) Spatially periodic structures in electron swarms: ionization, NDC effects and multi-term analysis. Journal of Physics D: applied physics, 35 (22). pp. 2914-2924.

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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.

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