Boltzmann equation analysis of the electron swarm development in nitrogen

Abstract

The electron swarm development in nitrogen is studied for E/N values from 56.6 to 1131 Td by a Boltzmann equation method in which the effect of ionisation is considered properly. Alteration of the electron collision cross-sections from the literature is limited to a minimum, although minor amendments are found necessary for the ionisation coefficient to agree well with previous measurements. The cross-sections for vibrational excitation are considered separately for its quantum number v=1-10. The electron swarm parameters are calculated for the time-of-flight, pulsed Townsend and steady-state Townsend experiments. The results show that the deduced electron drift velocity, diffusion coefficient and mean energy are generally in good agreement with previous experimental and theoretical values.

Local balance of electron energy gain and loss in SST condition

“…However, the investigation carried out by Taniguchi and colleagues showed that in the case of ionization, there is no direct balance of energy gain and loss (energy equilibrium in narrow sense). This paper [2] also confirms that the narrow-sense energy equilibrium occurrence is limited to the case when no ionization (attachment) (conservative) takes place. Furthermore, in the case of ionization (attachment) (nonconservative), the occurrence of wide-sense energy balance [Eq.…”

“…4, 5, and 6, ∆Gε(x) provides the increase of energy flow accompanying ionization growth with constant logarithmic multiplication factor. The contents of the statement by Taniguchi and colleagues [2] are explained by a numerical analysis of energy flow.…”

“…If such a balance is not achieved, the region is considered to be nonequilibrium. On the other hand, according to Taniguchi and colleagues [2], when ionization takes place, the balance between energy gain and losses cannot be achieved even in the region of equilibrium, which indicates that a correction parameter z must be introduced. In this case, z is described as the energy which should be supplied to the daughter electrons to support steady continuation of ionization growth.…”

Effective ionisation coefficients and critical breakdown electric field of CO2at elevated temperature: effect of excited states and ion kinetics

“…Four different species are involved in the determination of the effective ionization coefficient: electrons (e -), positive ions (p), unstable negative ions (nu) and stable negative ions (ns). The stable negative ions in our case are (6) ns nu N wN x (7) np ee N NN x (8) where α, η, γ, δ, ω are the Townsend coefficients of electron impact ionization, electron attachment, electron-ion recombination, electron detachment and conversion of unstable to stable negative ions, respectively. They are again expressed in m -1 , and they represent the number of "events" of the above processes, per unit length and normalized per electron.…”

Relativistic collision rate calculations for electron-air interactions

“…The difference between Eq. (2) and Eq. (1) is the relativistic Boltzmann collision integral for elastic collisions:…”