Entanglement of helicity and energy in kinetic Alfven wave/whistler turbulence

TL;DR

This paper investigates magnetic helicity in kinetic Alfvén wave and whistler turbulence, revealing exact spectral relations and proposing a new understanding of solar wind turbulence at sub-ion scales.

Contribution

It derives exact solutions for magnetic helicity spectra in anisotropic turbulence, linking helicity and energy spectra and challenging previous assumptions based solely on energy spectra.

Findings

Exact entanglement relation between helicity and energy spectra.

Spectral indices n=-2.5 and = -3.5 for energy and helicity.

Helicity spectra follow a limit = -3, consistent with constant helicity flux.

Abstract

The role of magnetic helicity is investigated in kinetic Alfv\'en wave and oblique whistler turbulence in presence of a relatively intense external magnetic field $b_0 {\bf e_\parallel}$. In this situation, turbulence is strongly anisotropic and the fluid equations describing both regimes are the reduced electron magnetohydrodynamics (REMHD) whose derivation, originally made from the gyrokinetic theory, is also obtained here from compressible Hall MHD. We use the asymptotic equations derived by Galtier \& Bhattacharjee (2003) to study the REMHD dynamics in the weak turbulence regime. The analysis is focused on the magnetic helicity equation for which we obtain the exact solutions: they correspond to the entanglement relation, $n+\tilde n = -6$, where $n$ and $\tilde n$ are the power law indices of the perpendicular (to ${\bf b_0}$) wave number magnetic energy and helicity spectra respectively. Therefore, the spectra derived in the past from the energy equation only, namely $n=-2.5$ and $\tilde n = - 3.5$, are not the unique solutions to this problem but rather characterize the direct energy cascade. The solution $\tilde n = -3$ is a limit imposed by the locality condition; it is also the constant helicity flux solution obtained heuristically. The results obtained offer a new paradigm to understand solar wind turbulence at sub-ion scales where it is often observed that $-3 < n < -2.5$.