A Universal Law for Solar-Wind Turbulence at Electron Scales

TL;DR

This paper derives a universal law for electron-scale turbulence in the solar wind, predicting a spectral index of -11/3, which aligns with observations and suggests a distinct turbulence regime rather than a dissipation range.

Contribution

It introduces an exact, universal third-order structure function law for electron-scale turbulence in the solar wind, challenging the dissipation range concept.

Findings

Predicts a magnetic fluctuation spectrum with index -11/3

Matches observed spectra at electron scales

Proposes a new turbulence regime in the solar wind

Abstract

The interplanetary magnetic fluctuation spectrum obeys a Kolmogorovian power law at scales above the proton inertial length and gyroradius which is well regarded as an inertial range. Below these scales a power law index around $-2.5$ is often measured and associated to nonlinear dispersive processes. Recent observations reveal a third region at scales below the electron inertial length. This region is characterized by a steeper spectrum that some refer to it as the dissipation range. We investigate this range of scales in the electron magnetohydrodynamic approximation and derive an exact and universal law for a third-order structure function. This law can predict a magnetic fluctuation spectrum with an index of $-11/3$ which is in agreement with the observed spectrum at the smallest scales. We conclude on the possible existence of a third turbulence regime in the solar wind instead of a dissipation range as recently postulated.