Abstract. Spatio-temporal development of electron swarms in gases is simulated using a propagator method based on a series of one-dimensional spatial moment equations. When the moments up to a suécient order are calculated, the spatial distribution function of electrons, p(x), can be constructed by an expansion technique using Hermite polynomials and the weights of the Hermite components are represented in terms of the electron diãusion coeécients. It is found that the higher order Hermite components tend to zero with time, that is, the normalized form of p(x) tends to a Gaussian distribution. A time constant of the relaxation is obtained as the ratio of the second-and third-order diãusion coeécients, D 2 3 =D 3 L . The validity of an empirical approximation in time-of-çight experiments that treats p(x) as a Gaussian distribution is indicated theoretically. It is also found that the diãusion coeécient is deåned as the derivative of a quantity called the cumulant which quantiåes the degree of deviation of a statistical distribution from a Gaussian distribution.

Development of the electron avalanche in argon has been studied at E/N=141, 283 and 566 Td by two exact Boltzmann equation methods, a Fourier expansion (FE) of the distribution function of electrons by Tagashira et al. (1978), and a direct estimation of moments (DEM) of the electron density distribution in the real space by starting from a Boltzmann equation. Elastic momentum transfer, total electronic excitation and ionisation collisions are considered. The electron swarm parameters obtained by FE agree exactly with those by DEM, justifying the expansion used in FE, and the swarm parameters obtained by two-term expansion (TE) are in good agreement with those obtained by the exact FE and DEM except the longitudinal diffusion coefficient DL and a higher order coefficient D3 at E/N=566 Td and the transverse diffusion coefficient DT at all the E/N studied, suggesting that the disagreement with DL and D3 is due simply to breakdown of TE at high E/N but the disagreement with DT is due to more essential insufficiency in TE. The electron velocity distributions are also obtained and discussed.

The electron swarm behaviour in methane is studied for E/p0 from 0.2 to 200 V cm-1 Torr-1 by a Boltzmann equation method. The alteration of cross sections from the literature is avoided as much as possible in the analysis. The swarm parameters are calculated for the pulsed Townsend, steady-state Townsend and time-of-flight experiments. Moreover, the accuracy of the two-term approximation is checked by a Monte Carlo simulation. The values of the ionisation coefficient, electron drift velocity and characteristic energy calculated are found to agree well with the experimental ones if these values are properly interpreted. This result suggests that the set of electron collision cross sections tailored in the present analysis is an appropriate one. The electron energy distribution, and the excitation frequencies for vibration and dissociation are also calculated and discussed.

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.

An accurate and efficient method for solving the Boltzmann equation for electron swarms in gases is proposed. The method utilises the conventional two-term expansion and a Galerkin technique for solution of the Boltzmann equations in an amalgamated form; the first two terms of the Legendre polynomial expansion of the electron energy distribution are obtained by the two-term method while the third and higher-order terms are deduced by the Galerkin method. Although a relaxation procedure has to be used for connecting the solutions and making them self-consistent by the two methods, the present amalgamated method can reduce the size of the matrix for the Galerkin technique, which may serve to make the computational time shorter. The present technique is applied to deduce the electron energy distribution and swarm parameters in methane gas, and good agreement with those calculated by Monte Carlo simulation is obtained. This shows the validity of the proposed method. The computational time of the present method is estimated to be roughly of the order of the geometric mean of those by the two-term expansion and Monte Carlo methods.