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The velocity-space moments of the often troublesome nonlinear Landaucollision operator are expressed exactly in terms of multi-indexHermite-polynomial moments of the distribution functions. The collisionalmoments are shown to be generated by derivatives of two well-known functions,namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussiandistribution. The resulting formula has a nonlinear dependency on the relativemean flow of the colliding species normalised to the root-mean-square of thecorresponding thermal velocities, and a bilinear dependency on densities andhigher-order velocity moments of the distribution functions, with norestriction on temperature, flow or mass ratio of the species. The result canbe applied to both the classic transport theory of plasmas, that relies on theChapman-Enskog method, as well as to deriving collisional fluid equations thatfollow Grad's moment approach. As an illustrative example, we provide thecollisional ten-moment equations with exact conservation laws for momentum- andenergy-transfer rate.

Exact collisional moments for plasma fluid theories