Inverse cascade and magnetic vortices in kinetic Alfv\'en-wave turbulence

TL;DR

This study uses a gyrofluid model to explore inverse cascades and magnetic vortex formation in kinetic Alfvén-wave turbulence, revealing how parameters influence cascade dynamics and vortex structures in magnetized plasmas.

Contribution

It introduces a Hamiltonian two-field gyrofluid model that captures ion finite-Larmor-radius effects and magnetic fluctuations, advancing understanding of inverse cascades in KAW turbulence.

Findings

Inverse cascades are influenced by the ratio of wave period to nonlinear time.

Parametric decay instability can enhance inverse transfers at small .

Magnetic vortices and cascade slowdown occur depending on plasma  values.

Abstract

A Hamiltonian two-field gyrofluid model for kinetic Alfv\'en waves (KAWs) in a magnetized electron-proton plasma, retaining ion finite-Larmor-radius corrections and parallel magnetic field fluctuations, is used to study the inverse cascades that develop when turbulence is randomly driven at sub-ion scales. In the directions perpendicular to the ambient field, the dynamics of the cascade turns out to be nonlocal and the ratio $\chi_f$ of the wave period to the characteristic nonlinear time at the driving scale affect some of its properties. For example, at small values of $\chi_f$, parametric decay instability of the modes driven by the forcing can develop, enhancing for a while inverse transfers. The balanced state, obtained at early time when the two counter-propagating waves are equally driven, also becomes unstable at small $\chi_f$, leading to an inverse cascade. For $\beta_e$ smaller than a few units, the cascade slows down when reaching the low-dispersion spectral range. For higher $\beta_e$, the ratio of the KAW to the Alfv\'en frequencies displays a local minimum. At the corresponding transverse wavenumber, a condensate is formed, and the cascade towards larger scales is then inhibited. Depending on the parameters, a parallel inverse cascade can develop, enhancing the elongation of the ion-scale magnetic vortices that generically form.