Fluid and gyrofluid modeling of low-$\beta_e$ plasmas: phenomenology of kinetic Alfv\'en wave turbulence

TL;DR

This paper develops reduced fluid and gyrofluid models for low-beta plasmas to study kinetic Alfvén wave turbulence across scales, revealing energy transfer directions and spectral behaviors relevant to space and laboratory plasmas.

Contribution

It introduces asymptotic reduced fluid and gyrofluid models, including a two-field Hamiltonian model, for analyzing kinetic Alfvén wave turbulence in low-beta plasmas.

Findings

Magnetic energy spectra follow a $k_ot^{-7/3}$ scaling in the sub-ion range.

Generalized helicity may exhibit an inverse cascade under certain conditions.

Models provide a framework for studying turbulence from MHD to electron scales.

Abstract

Reduced fluid models including electron inertia and ion finite Larmor radius corrections are derived asymptotically, both from fluid basic equations and from a gyrofluid model. They apply to collisionless plasmas with small ion-to-electron equilibrium temperature ratio and low $\beta_e$, where $\beta_e$ indicates the ratio between the equilibrium electron pressure and the magnetic pressure exerted by a strong, constant and uniform magnetic guide field. The consistency between the fluid and gyrofluid approaches is ensured when choosing ion closure relations prescribed by the underlying ordering. A two-field reduction of the gyrofluid model valid for arbitrary equilibrium temperature ratio is also introduced, and is shown to have a noncanonical Hamiltonian structure. This model provides a convenient framework for studying kinetic Alfv\'en wave turbulence, from MHD to sub-$d_e$ scales (where $d_e$ holds for the electron skin depth). Magnetic energy spectra are phenomenologically determined within energy and generalized helicity cascades in the perpendicular spectral plane. Arguments based on absolute statistical equilibria are used to predict the direction of the transfers, pointing out that, within the sub-ion range associated with a $k_\perp^{-7/3}$ transverse magnetic spectrum, the generalized helicity could display an inverse cascade if injected at small scales, for example by reconnection processes.