Coexistence of weak and strong wave turbulence in incompressible Hall magnetohydrodynamics

TL;DR

This paper investigates the coexistence of weak and strong wave turbulence in incompressible Hall MHD, revealing how different wave populations transition between turbulence regimes and influence anisotropy and energy transfer.

Contribution

It provides a detailed numerical analysis of wave turbulence regimes in Hall MHD, highlighting the coexistence and interaction of ion cyclotron and whistler waves across scales.

Findings

Ion cyclotron waves transition from weak to strong turbulence at smaller scales.

Whistler waves exhibit weak turbulence across all scales.

Resonant triadic interactions persist at large scales despite non-linearity.

Abstract

We report a numerical investigation of three dimensional, incompressible, Hall magnetohydrodynamic turbulence with a relatively strong mean magnetic field. Using helicity decomposition and cross-bicoherence analysis, we observe that the resonant three--wave coupling is substantial among ion cyclotron and whistler waves. A detailed study of the degree of non-linearity of these two populations shows that the ion cyclotron component experiences a transition from weak to strong wave turbulence going from large to small scales, while the whistler fluctuations display a weak wave turbulence character for all scales. This non-trivial coexistence of the two regimes with the two populations of waves gives rise to anomalous anisotropy and scaling properties. The weak and strong wave turbulence components can be distinguished rather efficiently using spatio-temporal Fourier transforms. The analysis shows that while resonant triadic interactions survive the highly non-linear bath of ion cyclotron fluctuations at large scales for which the degree of non-linearity is low for both populations of waves, whistler waves tend to be killed by the non-linear cross-coupling at smaller scales where the ion cyclotron component is in the strong wave turbulent regime. Such situation may have far-reaching implications for the physics of magnetized turbulence in many astrophysical and space plasmas where different waves coexist and compete to transfer non-linearly energy across scales.