Relaxation to nonthermal equilibria in a Lynden-Bell plasma

A plasma whose Coulomb-collision rate is very small may relax on a shorter time scale to non-Maxwellian quasi-equilibria, which, nevertheless, have a universal form, with dependence on initial conditions retained only via an infinite set of Casimir invariants enforcing phase-volume conservation. These are distributions derived by Lynden-Bell (1967) via a statistical-mechanical entropy-maximisation procedure, assuming perfect mixing of phase-space elements. A collision integral that reaches these steady states dynamically is derived and it is further shown that a large class of these distribution functions display power law tails with a power law index that depends on the Casimir invariants. Far from these equilibria, it is shown that the friction between species is anomalous and gives rise to strange relaxation effects in the presence of anisotropies.