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

Turbulence plays an important role in the processes responsible for solar wind heating and acceleration by transferring energy to small scales where it is ultimately dissipated. Understanding turbulence dynamics at kinetic scales is therefore essential for determining how heating occurs in a weakly-collisional plasma. While much progress has been made at magnetohydrodynamic and ion scales, sub-electron scale turbulence remains poorly understood due to limited measurements beyond magnetic field fluctuations. However, Parker Solar Probe (PSP), equipped with its high-resolution instruments and unique near-Sun orbit, provides an excellent opportunity to study turbulence at such scales. In addition to the magnetic field (B), we obtain for the first time, the density (n) spectra (using spacecraft potential measurements) extending to scales smaller than the electron gyro-radius (ρ_e). At scales larger than ρ_e, n and B spectra exhibit similar slopes (-2.62, -2.56), indicative of Kinetic Alfvén turbulence. Below ρ_e, both spectra steepen, with B steepening more than n (-3.84 vs -3.28). This difference between the slopes of the two fields is consistent with turbulence becoming electrostatic in nature and the presence of an electron entropy cascade. While the n spectra has a slope close to the -10/3 prediction, the B spectra is much shallower than the expected -16/3 slope of entropy cascade. We speculate that this apparent shallowing may be due to the finite frequency resolution of the instrument and the presence of weakly damped electromagnetic fluctuations near ρ_e.