Title: Exact collisional moments for plasma fluid theories,
Abstract: The velocity-space moments of the often troublesome nonlinear Landau
collision operator are expressed exactly in terms of multi-index
Hermite-polynomial moments of the distribution functions. The collisional
moments are shown to be generated by derivatives of two well-known functions,
namely the Rosenbluth-MacDonald-Judd-Trubnikov potentials for a Gaussian
distribution. The resulting formula has a nonlinear dependency on the relative
mean flow of the colliding species normalised to the root-mean-square of the
corresponding thermal velocities, and a bilinear dependency on densities and
higher-order velocity moments of the distribution functions, with no
restriction on temperature, flow or mass ratio of the species. The result can
be applied to both the classic transport theory of plasmas, that relies on the
Chapman-Enskog method, as well as to deriving collisional fluid equations that
follow Grad's moment approach. As an illustrative example, we provide the
collisional ten-moment equations with exact conservation laws for momentum- and
energy-transfer rate.