General Spherical Harmonics Formulation of Plasma Boltzmann Equation

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Abstract
The Boltzmann equation for the phase space distribution of electrons in the presence of ions is reduced to an infinite set of differential equations which do not involve angle variables. The usual method of expanding the electron phase space distribution function in terms of spherical harmonics is employed and it is assumed, in analyzing the scattering process, that the ion velocities can be neglected in comparison with the electron velocities. The expansion includes both polar and azimuthal angles obviating the assumption of symmetry about a polar axis made in previous work. The differential equation for the general component of the spherical harmonics expansion is derived and explicit equations for the first few components are presented. The component equations are seen to be considerably more tractable for cases which involve electric and/or magnetic fields along a single axis.