Exact irreducible moments of the Landau collision operator in the random-velocity moment expansion

Abstract

Exact moments of the Landau collision operator are calculated for the irreducible Hermite polynomials written in terms of the random-velocity variable. We present closed, algebraic formulas which can be implemented in computer algebra systems. The formulas reproduce the results for the total-velocity moment expansion (J-Y Ji and E D Held, 2006 Phys. Plasmas 13 102 103) and for the random-velocity moment expansion with the small mass-ratio approximation (J-Y Ji and E D Held, 2008 Phys. Plasmas 15 102 101). For verification of the formulas, example calculations for several lowest order moments are presented. The collisional moments can be applied in the derivations of Braginskii and integral (nonlocal) closures for arbitrary relative flow velocity between electrons and ions.