An analysis of transverse evolution of electron swarms in gases using moment equations and a propagator method

Abstract

Abstract.A simulation technique for analysis of transverse evolution of electron swarms in gases was developed based on moment equations derived from the Boltzmann equation. A numerical calculation of the moment equations for an electron swarm was performed using a propagator method and it was demonstrated that the propagator method can be used to calculate the higher-order transverse diãusion coeécients stably. Applying a Hermite expansion technique, the electron distribution in real space and other electron swarm parameters were derived as functions of the transverse position. The calculation result was veriåed by comparisons with those by a Monte Carlo simulation and other methods. Features of the transverse electron swarm evolution were presented.

Equality of Higher-Order Diffusion Coefficients between Component and Composite Electron Swarms in Gas

“…To verify the theoretical result on the equality of the HDCs, we have performed D n calculations up to n ¼ 6 by a propagator method (PM) and Monte Carlo (MC) simulation. The PM 6,16) is a numerical technique for solving simultaneous moment equations derived from the Boltzmann equation. The D n calculation by the PM was stable.…”

Electron transport properties in the Lucas–Saelee model

“…For W r , generation of spatial moments by ionized electrons ahead of the swarm seems a convincing explanation, but the spatial dependence in the transverse direction is difficult to explain. On the other hand, Sugawara and Sakai [14] report that in SF 6 gas at 1414 Td, the ionization frequency at the periphery of a Gaussian-distributed electron swarm is about 20% higher than in the center, and that the generation rate of second spatial moments in the axial direction increases as well. As a result, D T increases by about 15% due to ionization.…”

A Computational Scheme of Propagator Method for Moment Equations to Derive Real-Space Electron Transport Coefficients in Gas Under Crossed Electric and Magnetic Fields

“…The equilibrium values of the electron transport coefficients are calculated from m C n,r (v, t) after their relaxation. One way to obtain m C n,r (v, t) in equilibrium is to follow their temporal relaxation processes as performed for electron swarms in dc E fields [14], [15], [16], [17]. On the other hand, the equilibrium solutions of m C n,r (v, t) can be obtained faster by a numerically accelerated relaxation scheme [3] under the following assumptions.…”

“…After that, analyses by the PM in various simulation modes followed; e.g., those in the steady-state Townsend mode [6], [7], [8], [9], a radiofrequency (13.56 MHz) alternating electric field mode [10], [11], [12], and an impulse electric field mode [13]. The PM has also been applied to derivation of electron transport coefficients; e.g., drift velocities [14] and longitudinal and transverse diffusion coefficients [15], [16], [17]. The simulations in these investigations were all performed in the absence of magnetic field.…”