Modeling imbalanced collisionless Alfv\'en wave turbulence with nonlinear diffusion equations

TL;DR

This paper models strong Alfvén-wave turbulence across scales using nonlinear diffusion equations, highlighting the effects of imbalance and ion Landau damping on energy spectra in the solar wind.

Contribution

It introduces a nonlinear diffusion model capturing the dynamics of imbalanced collisionless Alfvén turbulence from MHD to electron scales, aligning with solar wind observations.

Findings

Imbalance in turbulence is amplified in collisionless regimes.

Steep magnetic spectra at sub-ion scales match observations.

Imbalance increases with small-scale energy injection, e.g., magnetic reconnection.

Abstract

A pair of nonlinear diffusion equations in Fourier space} is used to study the dynamics of strong Alfv\'en-wave turbulence, from MHD to electron scales. Special attention is paid to the regime of imbalance between the energies of counter-propagating waves commonly observed in the solar wind (SW), especially in regions relatively close to the Sun. In the collisionless regime where dispersive effects arise at scales comparable to or larger than those where dissipation becomes effective, the imbalance produced by a given injection rate of generalized cross-helicity (GCH), which is an invariant, is much larger than in the corresponding collisional regime described by the usual (or reduced) magnetohydrodynamics. The combined effect of high imbalance and ion Landau damping induces a steep energy spectrum for the transverse magnetic field at sub-ion scales. This spectrum is consistent with observations in highly Alfvenic regions of the SW, such as trailing edges, but does not take the form of a transition range continued at smaller scales by a shallower spectrum. This suggests that the observed spectra displaying such a transition result from the superposition of contributions originating from various streams with different degrees of imbalance. Furthermore, when imbalanced energy injection is supplemented at small scales in an already fully developed turbulence, for example under the effect of magnetic reconnection, a significant enhancement of the imbalance at all scales is observed.