A Universal Law for Solar-Wind Turbulence at Electron Scales

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.

💡 Research Summary

The paper addresses the long‑standing puzzle of the magnetic fluctuation spectrum observed in the solar wind at scales smaller than the electron inertial length ($d_e$). While the inertial range above the proton scales follows a Kolmogorov‑type $k^{-5/3}$ (or $k^{-3/2}$) law and the sub‑proton range exhibits a $k^{-2.5}$ slope that has been linked to dispersive whistler‑type dynamics, recent high‑resolution measurements have revealed a third, even steeper segment at electron scales. This segment has often been labeled a “dissipation range,” yet the physical processes responsible for its formation remain ambiguous.

To clarify the nature of this electron‑scale regime, the authors adopt the electron magnetohydrodynamics (EMHD) framework, which treats ions as a stationary neutralizing background and describes the dynamics of the magnetic field driven solely by the electron fluid. Within EMHD, the governing equation for the magnetic field $\mathbf{b}$ contains a nonlinear term that conserves magnetic energy and magnetic helicity, and a linear dispersive term reflecting the whistler dispersion relation $\omega\propto k^{2}$.

The central theoretical development is the derivation of an exact, universal law for the third‑order mixed structure function
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