Nonlinear Frequency Shifts due to Phase Coherent Interactions in Incompressible Hall MHD Turbulence

TL;DR

This paper develops a reduced model for wave interactions in incompressible Hall MHD turbulence, revealing how phase coherent interactions cause amplitude-dependent nonlinear frequency shifts that influence energy redistribution.

Contribution

It introduces a new model focusing on phase coherent wave interactions in Hall MHD, highlighting their role in nonlinear frequency shifts and turbulence dynamics.

Findings

Resonance-driven frequency shifts dominate nonlinear effects.

Frequency shifts can lead to damping or growth of waves.

Model helps estimate energy spectral content in turbulence.

Abstract

Turbulence in the magnetized plasma is well understood to be the consequence of wave interactions. When the Hall effect is added to the minimum magnetohydrodynamics (MHD), the MHD waves become dispersive and different nonlinear interactions are expected. The emergent turbulent state will thus be expected to be different. For incompressible Hall MHD we develop a reduced model for wave-wave interactions concentrating on those processes that will lead to phase coherent modifications to the linear dispersion of a given wave. We show that these special interactions provide an amplitude-dependent contribution to the linear dispersion relation, which yields nonlinear frequency shifts. The resonance-driven frequency shifts are dominant and add damping or growth to the linear dispersion. The damping/growth rates represent the nonlinear time scales for energy redistribution and can be used in conjunction with a conjecture like the "critical balance" to estimate the energy spectral content.