Lagrangian description of phase space flow: turbulent heating

Anomalous electrostatic dissipation in a collisionless plasma is caused by an induced charge separation which, in the homogeneous case, is particularly large when high local concentrations of the two species occur close together. If a turbulent plasma state has evolved from an unstable initial state which is only slightly perturbed, particle bunching (with maximum number density proportional to T0−1/4 at low initial temperature T0) takes place at points of overtaking - reversal of the ordering of particles with the same initial velocity. Overtaking is governed by a differential equation which involves the applied field only implicitly. Use of this equation in a simple case shows that a bunch of particles of one species causes bunching in the other species, and that the sense of the resulting turbulent electric field is such as to oppose the laminar motion. The characteristic time of formation of an ion bunch by an electron bunch of incremental number density Δn is (4πe2Δn/mi)−1/2. When the charge separation is expressed in terms of Lagrangian coordinates, a possible example of this phenomenon is revealed by the appearance of islands in the relevant curve. The islands represent adjacent bunches of electrons and ions, and preliminary investigation indicates that they might provide a major portion of the dissipation. A computer study to amplify these findings is proposed.