Dual phase-space cascades in 3D hybrid-Vlasov-Maxwell turbulence

To explain energy dissipation via turbulence in collisionless, magnetized plasmas, the existence of a dual real- and velocity-space cascade of ion-entropy fluctuations below the ion gyroradius has been proposed. Such a dual cascade, predicted by the gyrokinetic theory, has previously been observed in gyrokinetic simulations of two-dimensional, electrostatic turbulence. For the first time we show evidence for a dual phase-space cascade of ion-entropy fluctuations in a three-dimensional simulation of hybrid-kinetic, electromagnetic turbulence. Energy spectra are largely consistent with a generalized theory for the cascade that accounts for the spectral anisotropy of critically balanced, intermittent, sub-ion-Larmor-scale fluctuations. The observed velocity-space cascade is anisotropic with respect to the magnetic-field direction, with linear phase mixing along magnetic-field lines proceeding mainly at spatial scales above the ion gyroradius and nonlinear phase mixing across magnetic-field lines proceeding at perpendicular scales below the ion gyroradius. Such phase-space anisotropy could be sought in heliospheric and magnetospheric data of solar-wind turbulence.