Speaker
Description
Given a collisionless plasma, how much of its energy can turbulence actually extract? A natural answer is to rearrange the distribution function into its lowest-energy configuration, subject to the constraints of the underlying dynamics; an idea that has been used across time and disciplines, from Lorenz's available potential energy in meteorology to Gardner's restacking argument [1] and the ergotropy of quantum systems. In a Vlasov plasma the constraints are the Casimir invariants, and the energy difference between the initial and resulting ground state is the available energy. We point out that this construction, in its usual form, is inconsistent with the field equations: the Gardner ground state is homogeneous and therefore supports no electric field, even though energy conservation requires the liberated energy to reside in precisely that field. We show how to repair this by additionally constraining the ground-state density, and we illustrate the consequences with deliberately simple examples: a two-stream waterbag model, in which energy conservation, Debye screening and positivity of the density conspire to produce phase-transition-like behaviour; and drift-kinetic ions with adiabatic electrons, for which the available energy falls by 83% relative to the naïve bound. Several issues remain unresolved, notably the excessive freedom given by a kinetic electron species.
References:
[1] CS Gardner, Phys. Fluids 6, 839 (1963)