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 with 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 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.