Cascades and Dissipative Anomalies in Ne

In this study, we develop a first-principles theory of kinetic plasma turbulence governed by the Vlasov-Maxwell-Landau equations in the regime of vanishing collision rates. By employing an exact renormalization-group method inspired by Onsager, we reveal the presence of a “collisionless range” in the phase space characterized by lengths and velocities where the ideal Vlasov-Maxwell equations are satisfied in a coarse-grained sense. We also explore how entropy can be conserved in this range while being violated by a dissipative anomaly resulting from nonlinear entropy cascades. Our analysis derives “4/5th-law” type expressions for the entropy flux, which help us characterize the necessary singularities for non-vanishing scaling exponents. Although conservation laws for mass, momentum, and energy remain intact in the collisionless limit, we identify potential anomalous contributions to the inertial-range energy balance in scenarios with small gyroradii. Additionally, we derive a generalized Ohm’s law applicable in the particle momentum balances, which simplified reduces to an ideal formulation, highlighting its limitations concerning magnetic flux conservation. Lastly, we compare our findings with previous theories, numerical simulations, and empirical data from spacecraft measurements of solar wind and terrestrial magnetosphere.