Kinetic Fluctuation-Dissipation Relation in collisionless plasmas: a correlated noise source

Abstract

We here focus on small-scale dynamics of collisionless plasmas by employing a generalized kinetic Langevin framework driven by a stochastic time-correlated forcing. Our investigation captures the steady-state Fluctuation-Dissipation Relation (FDR) where the energy injection at low frequencies is due to the time-correlated forcing and the small-scale energy conversion occurs via Landau damping, the latter --though formally reversible-- acting as an effective dissipation mechanism. We analytically extract the resulting asymptotic spectral scalings across multiple physical regimes and characterize the velocity-space cascade by decomposing the plasma distribution function with Hermite polynomials. The framework is then generalized to a multi-scale forcing scenario in which correlation rates are distributed according to a power-law distribution. This extension provides closed-form analytical expressions that may serve to interpret spacecraft in-situ observations. All analytical predictions are successfully validated through direct numerical integrations of the underlying kinetic equations.