Exact collisional moments for plasma fluid theories
Authors: D. Pfefferlé and E. Hirvijoki
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.
Submitted to: Physics of Plasmas
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Download PPPL-53691.6 MB (16 pp)
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