The role of dissipation in the theory and simulations of homogeneous plasma turbulence, and resolution of the entropy paradox

Abstract

The role of dissipation in the theory and simulations of homogeneous plasma slices is analyzed with the goal of understanding the ‘‘entropy paradox,’’ which is that a certain positive-definite functional of the perturbed distribution function increases without bound in some situations even though the potentials appear to have achieved a steady state. Confusion arises from an interchange of the limits t→∞ and η→0, where η is a measure of dissipation. It is argued that it is never strictly correct to neglect η; the averaged dissipation approaches a nonzero limit (proportional to the averaged flux) even as η→0. An exactly soluble model is worked out to illustrate the point. In collisionless particle simulations, the particle and heat fluxes may nevertheless saturate with their correct values. The relations of kinetic and fluid entropy balances are discussed with the aid of (1) the Terry–Horton model for collisionless drift waves, and (2) a simple model of the ion-temperature-gradient-driven mode. The rationale for simulations of homogeneous slices of plasma is given, with particular emphasis being placed on the relationship of dissipation in such slices to dissipation in a complete physical domain.