Comparisons between different methods of solution of the Boltzmann equation adapted to the calculation of swarm parameters in a weakly ionised medium

Abstract

Two numerical solutions of the Boltzmann equation are developed and applied to the calculations of swarm time-of-flight parameters in molecular model gases. It is shown that the two methods not only give near similar results but are in good agreement with calculations carried out by some other authors for the same situations. Errors already pointed out in some other works are confirmed and the need of using high-order methods of solution of the Boltzmann equation is stressed.

First-principles particle simulation and Boltzmann equation analysis of negative differential conductivity and transient negative mobility effects in xenon

“…Particle-based methods trace a large number of individual particles in the external field(s) [10] and via proper sampling schemes they allow the construction of f (r, v, t) and the computation of swarm transport parameters. Boltzmann equation (BE) approaches [11] use different types of expansions of the VDF and solve the set of the resulting differential equations. Once the VDF is found, the transport parameters can readily be derived [11].…”

“…Boltzmann equation (BE) approaches [11] use different types of expansions of the VDF and solve the set of the resulting differential equations. Once the VDF is found, the transport parameters can readily be derived [11]. The most widespread approach, the "two-term approximation", retains only the first two terms in the Leg-endre polynomial expansion of the VDF, and is therefore limited to scenarios where the VDF has a small anisotropy.…”

Plasma excitation processes in flue gas simulated with Monte Carlo electron dynamics

“…The deviations of Elendif are likely to have been caused by the two-term approximation of the Boltzmann equation. The necessity of using more terms has been stressed by several authors [15,18,29]. The results of MCED for degrees of ionization 0, 10 −5 and 10 −4 were much the same (see also figure 3).…”

Electron Kinetics in He/CH4/CO2 Mixtures Used for Methane Conversion

“…The analysis of electron swarms developed by Kumar et al can be used if we consider that the electrons are moving in the hydrodynamic regime, meaning that although the electron density grows exponentially the distribution in velocity space and the transport parameters have reached equilibrium values, independent of their initial values . The theoretical basis of the treatment can be found in this latter reference, and a comparison of this treatment with other methods to solve can be found in Pinhão et al In the present problem we have used a modified version of the algorithm proposed by Segur et al, equivalent to a multiterm expansion.…”