Variational formulation of the Gardner's restacking algorithm

The incompressibility of the phase flow of Hamiltonian wave-plasma interactions restricts the class of realizable wave-driven transformations of the particle distribution. After the interaction, the distribution remains composed of the original phase-space elements, or local densities, which are only rearranged (“restacked”) by the wave. A variational formalism is developed to study the corresponding limitations on the energy and momentum transfer. A case of particular interest is a toroidal plasma immersed in a dc magnetic field. The restacking algorithm by Gardner [Phys. Fluids 6 (1963) 839] is formulated precisely. The minimum energy state for a plasma with a given current is determined.