Relaxation process of the electron velocity distribution in neon

Abstract

The relaxation process from an initial velocity distribution to the equilibrium distribution for electrons in neon is calculated by a finite difference method for the ratios of electric field to gas number density E/N between 56.6 and 566 Td (E/p0=20 and 200 V cm-1 Torr-1 at 0 degrees C) without using the usual two-term spherical harmonics expansion of the velocity distribution. The pulsed Townsend condition, in which the evolution of all the electrons involved in an avalanche is observed as a function of time only, is assumed. The results suggest that the electron velocity distribution reaches through randomisation the equilibrium distribution which has a structure with a minimum near the origin in the velocity space.

Is the classical two-term approximation of electron kinetic theory satisfactory for swarms and plasmas?

“…(Note that a full multi-term analysis for electrons had already commenced in a limited fashion some years previously [11], and the scaling of twoterm errors with m/m 0 reported recently in [12,13] had already been observed by then.) Subsequent multiterm techniques were developed in the early 1980s, with the group of Phelps, Pitchford and co-workers [8,31] notable, while other groups including Tagashira and co-workers [32][33][34][35] tried to avoid the spherical harmonic representation. For further details of the development in the early 1980s, readers are referred to review [36] and references therein.…”

A technology demonstration of propagator matrix power method for calculation of electron velocity distribution functions in gas in long-term transient and succeeding equilibrium states under dc electric fields

“…2 21 2 are, respectively, the velocity components parallel and perpendicular to E. The region of (i − 1)Δε ⩽ ε < iΔε surrounded by the thick curves represents an equienergy band, which corresponds to the ith submatrix n i of the EVDF column vector f.…”

“…17,18) The present PMPM belongs to the time-evolution type. It is applied to transient EVDF under dc electric field, [19][20][21][22][23][24][25][26] and that in equilibrium 6) is also obtained as a result of sufficiently long relaxation. This calculation is, in a physical point of view, equivalent to that by the time-dependent multi-term BE analyses, 27,28) but the PM and PMPM do not need mathematically complicated series expansion of the EVDF required in the BE analyses.…”

The effective ionization coefficients and electron drift velocities in gas mixtures of CF3I with N2and CO2obtained from Boltzmann equation analysis

“…[11] Therefore, the two-term expansion has an insufficiency that it can not give D v and D v⊥ separately, where D v and D v⊥ are the diffusion coefficients parallel and perpendicular to the field direction, respectively. [21] However, in the case of low pressure at 1 Torr, the velocity distribution of the electron is nearly isotropic, and the difference between D v and D v⊥ is sufficiently small. [22] The two-term approximation of the Boltzmann equation is still valid for calculating the corresponding rate and transport coefficients with the advantages of short computing time and considerable accuracy in discharge modelling.…”