Electron swarm development in SF₆. I. Boltzmann equation analysis

Abstract

The electron swarm behaviour in SF6 gas is studied for E/N values from 141 to 707 Td by a three-term Boltzmann equation method, in which the effect of generation and loss of electrons due to ionisation and attachment is considered properly. A consistent set of electron collision cross sections, which gives the swarm parameter values in agreement with previous measurements, is determined considering the latest cross section data. The calculation is performed mainly for the steady-state Townsend condition. The validity of the results obtained has been confirmed by a Monte Carlo simulation carried out parallel to the analysis. The present results are also compared with those of the usual two-term Boltzmann analysis. It is found that the two-term approximation is fully valid for deduction of the swarm parameters for E/N values as considered despite the fact that SF6 is a strongly electronegative gas.

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“…We note that the sum of the cross sections of the two excitation processes is the same as the total cross section for excitation in Ref. 36. A plot of the SF 6 cross sections is shown in Fig.…”

“…We include one lumped excitation channel with threshold energy of 9.8 eV (see discussions regarding estimated values in Refs. 35,36). For this process, the incident electron loses the threshold energy and is isotropically scattered.…”

“…So, both the functional shape and magnitude of the cross sections must be adjusted to match the transport coefficients over some range of applied electric field values. Numerical values of the transport coefficients can be calculated by a Boltzmann code 35,36,41 in which the general electron distribution function in velocity space is approximated by a series expansion in a finite number of spherical harmonics.…”

“…For our simple SF 6 chemistry, we start with the same cross sections as used by Itoh et al 36 These include an elastic and ionization cross section, a single excitation cross section, a vibrational cross section, and three attachment cross sections for the negative ion products SF 38 This metastable product is tracked as a separate species. The remainder of the cross section is applied to a new lumped excitation process, in which the excited states are, as mentioned above, assumed to relax instantaneously.…”

“…Plasmas 18, 093501 (2011) calculation results of Itoh et al 36 and the Monte-Carlo calculation results of Satoh et al 42 Both of these references assume an 80-20 split of the excess energy between primary and secondary electrons in an ionization event. Here, we assume that the energy of the secondary electron in ionization events is given by…”