Cascades and Dissipative Anomalies in Nearly Collisionless Plasma Turbulence

Abstract

We develop first-principles theory of kinetic plasma turbulence governed by the Vlasov-Maxwell-Landau equations in the limit of vanishing collision rates. Following an exact renormalization-group approach pioneered by Onsager, we demonstrate the existence of a "collisionless range" of scales (lengths and velocities) in one-particle phase space where the ideal Vlasov-Maxwell equations are satisfied in a "coarse-grained sense." Entropy conservation may nevertheless be violated in that range by a "dissipative anomaly" due to nonlinear entropy cascade. We derive "4/5th-law-type" expressions for the entropy flux, which allow us to characterize the singularities (structure-function scaling exponents) required for its nonvanishing. Conservation laws of mass, momentum, and energy are not afflicted with anomalous transfers in the collisionless limit. In a subsequent limit of small gyroradii, however, anomalous contributions to inertial-range energy balance may appear due to both cascade of bulk energy and turbulent redistribution of internal energy in phase space. In that same limit, the "generalized Ohm's law" derived from the particle momentum balances reduces to an "ideal Ohm's law" but only in a coarse-grained sense that does not imply magnetic flux freezing and that permits magnetic reconnection at all inertial-range scales. We compare our results with prior theory based on the gyrokinetic (high-gyrofrequency) limit, with numerical simulations, and with spacecraft measurements of the solar wind and terrestrial magnetosphere.