Implications of Superstatistics for steady-state plasmas

Abstract

Colissionless plasmas are non-extensive systems which, due to the long-range interaction between their components, are incapable of reaching thermal equilibrium, even in a steady state. These systems cannot, therefore, be described statistically by a single canonical distribution with well-defined inverse temperature β = 1/kBT and are commonly described via two alternative approaches: namely Tsallis statistics and Superstatistics. The use of Superstatistics in describing steady-state plasmas has been proposed by several authors, more recently Ourabah et al. In this work we study the consequences of this assumption of Superstatistics for steady-state plasmas. We explicitly show that only the ensembles characterized by the condition P(x|ρ) = ρ(H(x)) are consistent with a generalized definition of temperature introduced recently. We show how this formalism is employed in the case of plasma, considering interaction with external electromagnetic fields as well as between particles in the plasma. Our results clearly illustrate why low-energy particles tend to the Maxwellian distribution of velocities, while high-energy particles contribute to the long tails of the velocity distribution.