Velocity-space turbulent cascade in the near-Sun solar wind: first insights from the Parker Solar Probe mission

TL;DR

The paper investigates velocity-space turbulence in the near-Sun solar wind by applying Hermite decomposition to ion velocity distribution functions measured by Parker Solar Probe. Analyzing two distinct PSP streams (a wave-dominated flow near $R \approx 28 R_\odot$ and a more quiescent, sub-Alfvénic flow near $R \approx 11 R_\odot$), the study constructs 2D Hermite spectra and compares them with energization/dissipation proxies (LET, $M_{KP}$, enstrophy $\Omega$, PVI) to link real-space cascades with velocity-space cascades. The Hermite spectra show a near $-2$ slope in the inertial-like range ($4 \le m < 12$), with the wave stream dominated by low-$m$ power due to a beam/hammerhead structure and the turbulent stream exhibiting stronger high-$m$ power, indicating a more developed velocity-space cascade and intermittent behavior. Together, these results support a dual real- and velocity-space cascade in the inner heliosphere and highlight the role of velocity-space distortions in irreversible heating of collisionless plasmas, motivating future multi-spacecraft observations and improved VDF reconstruction methods.

Abstract

In space plasmas, the rarity of collisions leads to complex structures in the velocity space where a turbulent cascade of the velocity distribution function fluctuations is thought to occur. Previous studies have explored this phenomenon using the Hermite decomposition of the ion velocity distribution function (VDF) in both magnetosheath data and numerical simulations. In this work, we investigate the Hermite spectrum of the ion VDFs measured by Parker Solar Probe in the inner heliosphere. We analyze a superalfvénic stream at a radial distances of $R \approx 28 R_{sun}$ and a subalfvénic at $R \approx 11 R_{sun}$, the former characterized by a prevalence of VDFs with suprathermal beams (also known as hammerhead). The Hermite analysis is also compared with various proxies of energization and dissipation, in order to establish a connection between turbulent cascades in real space and those in the velocity space. A qualitative agreement between the energization proxies and the Hermite analysis is observed. The results are suggestive of the presence of a dual cascade in real and velocity space.

Figures (6)

• Figure 1: Magnetic field, velocity field, density and parallel and perpendicular temperatures and magnetic helicity in the wave stream (top) and turbulent stream (bottom).
• Figure 2: Representative VDFs for the wave stream (top) and turbulent stream (bottom). The VDFs are integrated along $\phi$ and plotted in the Energy-$\theta$ plane Verniero2020ApJS in field aligned coordinates. These are the original non-gyrotropic PSP VDFs for which the procedure described in Sec \ref{['sec:data_methods']} has not been applied yet.
• Figure 3: Top to bottom: Power spectral density and kurtosis of the magnetic field and average Hermite spectrum for the wave stream (black) and turbulent stream (red). In gray typical reference slopes (these are not fits) to aid the eye. The slopes for the Hermite spectra are the ones from the Servidio2017PhRvL.119t5101S phenomenological model.
• Figure 4: From top to bottom: Kaufman-Paterson measure and normalized enstrophy, $PVI$, $LET$, and Hermite spectrogram for the wave stream (top) and the turbulent stream (bottom). The shaded areas highlight regions of interest described in the main text. The Hermite spectrograms are represented through the scientifically derived color map batlow CrameriNatureComm2020.
• Figure 5: VDF processing for the wave stream. VDF averaged over $\phi$ and plotted in the Energy-$\theta$ plane (left), VDF averaged over $\theta$ and plotted in the Energy-$\phi$ plane (center), VDF after the procedure describer in Sec \ref{['sec:data_methods']} before the interpolation into the Hermite Grid.