Dynamic Phase Alignment in Inertial Alfven Turbulence

TL;DR

This paper investigates inertial Alfvén turbulence in low-beta plasmas, revealing dual cascades of energy and helicity, a scale-dependent phase alignment, and specific spectral scalings, with implications for space and astrophysical plasmas.

Contribution

It introduces a detailed analysis of phase alignment and dual cascades in inertial Alfvén turbulence, providing new spectral scalings and anisotropy relations.

Findings

Energy and helicity cascade directly in inertial Alfvén turbulence.

Kinetic and magnetic energy spectra follow specific power laws.

Phase alignment angle scales as $k_ot^{-1}$, enabling compatible cascades.

Abstract

In weakly-collisional plasma environments with sufficiently low electron beta, Alfv\'enic turbulence transforms into inertial Alfv\'enic turbulence at scales below the electron skin-depth, $k_\perp d_e\gtrsim 1$. We argue that, in inertial Alfv\'enic turbulence, both energy and generalized kinetic helicity exhibit direct cascades. We demonstrate that the two cascades are compatible due to the existence of a strong scale-dependence of the phase alignment angle between velocity and magnetic field fluctuations, with the phase alignment angle scaling as $\cos\alpha_k\propto k_{\perp}^{-1}$. The kinetic and magnetic energy spectra scale as $\propto k_{\perp}^{-5/3}$ and $\propto k_{\perp}^{-11/3}$, respectively. As a result of the dual direct cascade, the generalized-helicity spectrum scales as $\propto k^{-5/3}_{\perp}$, implying progressive balancing of the turbulence as the cascade proceeds to smaller scales in the $k_{\perp} d_e \gg 1$ range. Turbulent eddies exhibit a phase-space anisotropy $k_{\parallel} \propto k_{\perp}^{5/3}$, consistent with critically-balanced inertial Alfv\'en fluctuations. Our results may be applicable to a variety of geophysical, space, and astrophysical environments, including the Earth's magnetosheath and ionosphere, solar corona, non-relativistic pair plasmas, as well as to strongly rotating non-ionized fluids.