# Imbalanced kinetic Alfv\'en wave turbulence: from weak turbulence theory to nonlinear diffusion models for the strong regime

## TL;DR

This paper develops a comprehensive theoretical framework for imbalanced kinetic Alfvén wave turbulence, bridging weak turbulence theory and nonlinear diffusion models, and explores how turbulence properties change with imbalance and dispersive effects.

## Contribution

It introduces a Hamiltonian gyrofluid model incorporating ion Larmor radius effects and derives kinetic equations and nonlinear diffusion models for imbalanced turbulence regimes.

## Key findings

- Spectral energy spectrum steepens with increased cross-helicity flux.
- Derived kinetic equations match large-scale MHD and small-scale electron MHD regimes.
- Dispersive effects influence turbulence maintenance and spectral dynamics.

## Abstract

A two-field Hamiltonian gyrofluid model for kinetic Alfv\'en waves retaining ion finite Larmor radius corrections, parallel magnetic field fluctuations and electron inertia, is used to study turbulent cascades from the MHD to the sub-ion scales. Special attention is paid to the case of imbalance between waves propagating along or opposite to the ambient magnetic field. For weak turbulence in the absence of electron inertia, kinetic equations for the spectral density of the conserved quantities (total energy and generalized cross-helicity) are obtained. They provide a global description, matching between the regimes of reduced MHD at large scales and electron reduced MHD at small scales, previously considered in the literature. In the limit of ultra-local interactions, Leith-type nonlinear diffusion equations in the Fourier space are derived and heuristically extended to the strong turbulence regime by modifying the transfer time appropriately. Relations with existing phenomenological models for imbalanced MHD and balanced sub-ion turbulence are discussed. It turns out that in the presence of dispersive effects, the dynamics is sensitive on the way turbulence is maintained in a steady state. Furthermore, the total energy spectrum at sub-ion scales becomes steeper as the generalized cross-helicity flux is increased.