Linearized Coulomb Collision Operator for Simulation of Interpenetrating Plasma Streams

Weare developing an improved kinetic model for streaming instabilities in interpenetrating plasmas via appropriate extensions to the Eulerian kinetic code LOKI,
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which evolves the Vlasov-Poisson system in a Cartesian “2+2-dimensional” phase space. The effects of Coulomb collisions need to be included, both on the perturbations and on the pre-instability or mean “background.” The existing Coulomb collision operator implemented in LOKI is a single/intra plasma species linearized operator that conserves momentum and energy and satisfies a “H -theorem” for the perturbed entropy. 1,2,3 A generalization of this operator to allow for multiple plasma species, with the background in collisional equilibrium, has previously been given.4 For our purposes, we need to consider practical extensions of this operator to situations with multiple plasma streams in which, by their very nature, the “background” is not in collisional equilibrium. In this case, the strict perturbed-entropy H -theorem is no longer satisfied. This issue has been recognized, and one approach for dealing with it has been proposed for the case of plasma species with different temperatures but no relative flow.
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For the case of interpenetrating plasma streams, of interest to us, we have developed an alternate generalized linear operator, and have implemented it in a test code. This operator will be discussed, and results of both quantitative verification and qualitative “realizability” tests will be presented.