Velocity distribution function and transport coefficients of electron swarms in gases: Spherical-harmonics decomposition of Boltzmann’s equation

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Abstract
The multiterm spherical-harmonic representation of the velocity distribution function of ‘‘reacting’’ charged-particle swarms in a gaseous medium is discussed from a general viewpoint, using spherical tensors throughout, in contrast to the traditional mixed spherical-Cartesian notation usually employed in analysis of the hydrodynamic regime. The resulting hierarchy of kinetic equations generated from the Boltzmann equation has a universal validity, applicable to all experimental arrangements, as do the associated transport and reaction-rate coefficients. The structure of these equations and the nature of the eigenvalue problem associated with them are discussed generally, independently of any numerical technique adopted for their solution, of which the moment method of Lin, Robson, and Mason [J. Chem. Phys. 71, 3483 (1979)] is just one possibility.