Abstract
The problem of anisotropy of the electron-velocity distribution in a weakly ionized gas in an electric field is discussed. In contrast to the conventional multiple-term truncated spherical-harmonics expansion method for weakly anisotropic distributions, the present treatment is based on a new two-term perturbative solution of the kinetic equation. The expansion parameter in the theory is the ratio between the electron-energy gain on a mean free path along the electric field and the electron energy itself. The method allows us evaluation of the angular velocity distribution for an arbitrary degree of anisotropy, provided is small. For instance, both the conventional two-term spherical-harmonics expansion result for a weakly anisotropic case and the beamlike distribution characteristic of gases with large inelastic cross sections are obtained as two limiting cases of the theory. The new two-term expansion allows evaluation of coefficients fn of the conventional spherical-harmonics expansion of the distribution function to arbitrary order via a recurrent relation. The asymptotic form of these coefficients for n1 is obtained from this relation, allowing estimation of the convergence rate of the conventional expansion.
Original language | English |
---|---|
Pages (from-to) | 3541-3547 |
Number of pages | 7 |
Journal | Physical Review A |
Volume | 39 |
Issue number | 7 |
DOIs | |
State | Published - 1989 |