The Nature of Turbulence at Sub-Electron Scales in the Solar Wind

Abstract: The nature of turbulence at sub-electron scales has remained an open question, central to understanding how electrons are heated in the solar wind. This is primarily because spacecraft measurements have been limited to magnetic field fluctuations alone. We resolve this by deriving new high-resolution density fluctuations from spacecraft potential measurements of Parker Solar Probe resolving scales smaller than the electron gyro-radius ($\rho_e$). A systematic comparison of the density and magnetic spectra shows that both steepen near the electron scales. Notably, the density spectrum exhibits slopes close to $-10/3$, while the magnetic spectrum becomes consistently steeper than the density spectrum at scales smaller than $\rho_e$, indicating that the turbulence becomes electrostatic. These results are consistent with theoretical predictions of an electron entropy cascade, which may explain the irreversible dissipation of turbulent energy at sub-$\rho_e$ scales.