Abstract:

Generic equilibria are derived for turbulent relaxing plasmas via an entropy-maximization procedure that accounts for the short-time conservation of certain collisionless invariants. The conservation of these collisionless invariants endows the system with a partial "memory" of its prior conditions but is imperfect on long time scales due to the development of a turbulent cascade to small scales, which breaks the precise conservation of phase volume, making this memory imprecise. The equilibria are still determined by the short-time collisionless invariants, but the invariants themselves are driven to a universal form by the nature of the turbulence. This is numerically confirmed for the case of beam instabilities in one-dimensional electrostatic plasmas, where sufficiently strong turbulence appears to cause the distribution function of particle energies to develop a universal power-law tail, with exponent -2.

Abstract:

Collisionless and weakly collisional plasmas often exhibit non-thermal quasi-equilibria. Among these quasi-equilibria, distributions with power-law tails are ubiquitous. It is shown that the statistical-mechanical approach originally suggested by Lynden-Bell (Mon. Not. R. Astron. Soc., vol. 136, 1967, p. 101) can easily recover such power-law tails. Moreover, we show that, despite the apparent diversity of Lynden-Bell equilibria, a generic form of the equilibrium distribution at high energies is a ‘hard’ power-law tail ∝ε−2, where ε is the particle energy. The shape of the ‘core’ of the distribution, located at low energies, retains some dependence on the initial condition but it is the tail (or ‘halo’) that contains most of the energy. Thus, a degree of universality exists in collisionless plasmas.