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The interplanetary magnetic fluctuation spectrum obeys a Kolmogorovian powerlaw at scales above the proton inertial length and gyroradius which is wellregarded 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 inertiallength. This region is characterized by a steeper spectrum that some refer toit as the dissipation range. We investigate this range of scales in theelectron magnetohydrodynamic approximation and derive an exact and universallaw for a third-order structure function. This law can predict a magneticfluctuation spectrum with an index of $-11/3$ which is in agreement with theobserved spectrum at the smallest scales. We conclude on the possible existenceof a third turbulence regime in the solar wind instead of a dissipation rangeas recently postulated.

A Universal Law for Solar-Wind Turbulence at Electron Scales