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 ($ρ_e$). 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 $ρ_e$, 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-$ρ_e$ scales. The magnetic spectrum, however, is not as steep as expected for the electron entropy cascade, which may be due to limited signal-to-noise ratio and the presence of weakly damped electromagnetic fluctuations near $ρ_e$.

Figures (5)

• Figure 1: Power spectral density of (a) $V_\mathrm{sc}$ and (b) $B$ (MAG - dashed, SCM - solid). The least square fits (vertically shifted for clarity) and the break frequency ($f_b$) using Eq. \ref{['eqn1']} are shown. Thin-dashed lines indicate the flat analog-to-digital converter and the frequency dependent SCM noise floors. (c) $V_\mathrm{sc}$ and $B$ spectra compensated by the sub-ion range scaling $(f^{-\alpha_1}P(f))$. The compensated spectra are shown as dotted lines for SNR $\lesssim 2$.
• Figure 2: (a) $V_\mathrm{sc}$ and (b) $B$ spectra for all intervals smoothed using a variable width running mean window. Average slopes at sub-ion and sub-electron scales are shown. Blue diamonds mark the breaks obtained from fits. Mean $f_{d_e}$ and its variation across the intervals are shown by the red marker.
• Figure 3: Distributions of the (a) $n$ and (b) $B$ spectral slopes obtained from the fits at sub-ion ($f<f_b$, in blue) and sub-electron ($f>f_b$, in red) scales. Vertical lines indicate the mean and standard error of the mean for each distribution.
• Figure 4: Break frequencies $f_{b,n}$ and $f_{b,B}$ obtained from fits relative to (a) $f_{d_e}$ and (b) $f_{\rho_e}$. (c) Mean trend of the normalized $n$–$B$ spectral ratio as a function of $f/f_{d_e}$. Violet shaded regions indicate the standard deviation ($\sigma$) across the intervals. The mean $f_{\rho_e}$ and its variation are shown by the red marker.
• Figure 5: Empirical spectra of (a) $n$ and (b) $B$ from Eq. \ref{['eqn2']}, with noise-free (dashed) and noise-added (solid) cases (units are arbitrary). Fits to the latter in the range $f_b < f < f_{\mathrm{SNR=2.5}}$ are marked in red. (c,d) Variation of slopes obtained from the fits to the empirical spectra of $n$ and $B$ with SNR and smoothness $(s)$.