Inverse cascade and magnetic vortices in kinetic Alfven-wave turbulence

A Hamiltonian two-field gyrofluid model for kinetic Alfven 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 non-local and the ratio.f of the wave period to the characteristic nonlinear time at the driving scale affects 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 KAWto the Alfven 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.