SPECTRAL REPRESENTATION OF THE ISOTROPIC COULOMB COLLISIONAL OPERATOR

A spectral representation for the isotropic part of the Coulomb collis ional operator is given. The particle distribution function is expande d in a series of generalized Laguerre polynomials, and the Coulomb col lisional operator is expressed in terms of the spectral amplitudes. Wh en the spectral representation is applied to the Fokker-Planck equatio n, a system of coupled ordinary differential equations for the spectra l amplitudes is obtained. The spectral coefficients I elated to the Co ulomb operator are defined through recurrence relations, which we redu ce to simplified form. This makes possible accurate and efficient anal ytical and numerical evaluations of the interaction matrices. The resu lts presented can be used in analytical investigations of the properti es of the Coulomb collisional operator as well as in numerical calcula tions for plasmas far from thermal equilibrium The method can also be generalized to include angular dependencies for non-isotropic particle distributions.