Speaker
Description
We review the Lynden-Bell formalism of deriving maximum entropy states subject to the short-time conservation of certain (fragile) collisionless invariants. The conservation of these collisionless invariants endows the system with a partial “memory” of its prior conditions but is fragile precisely 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 simple (and possibly universal form). 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.