Michael Terres

The early evolution of fast polar coronal hole (PCH) solar wind remains largely unconstrained by in situ measurements. In 2025 March, Parker Solar Probe (Parker) at its closest approach of 9.86 solar radii ( R _⊙ ) measured outflow from a large equatorial coronal hole (ECH), which was also measured at 1 au and at intermediate distances by Solar Orbiter (also near its perihelion). At 1 au the stream properties are consistent with PCH properties established by Ulysses. The stream was measured by Parker substantially below the Alfvén surface, with proton temperatures in excess of 2 MK and a speed at ∼10 R _⊙ which was only ∼60% of its asymptotic value. The Solar Orbiter data indicate that the acceleration is largely complete by 60 R _⊙ . Spherically polarized fluctuations in the stream are observed to develop from near-transverse and small-angle at Parker to full reversal “switchbacks” at Solar Orbiter. Comparison of the implied acceleration profile to historical Doppler-dimming measurements suggests that the stream’s low coronal acceleration is similar to that of PCH flows. Consistent with previous work, this acceleration requires significantly more energy than can be provided by the observed thermal pressure gradients, with a significant contribution likely from the abundant Alfvénic fluctuation energy observed at Parker. These observations provide unique constraints on models of the radial evolution of the fastest solar wind, and indicate that these wind streams experience gradual, steady acceleration over their first few tens of solar radii of evolution.

We report on two ³ He-rich solar energetic particle (SEP) events observed by Solar Orbiter (SO) and Parker Solar Probe (PSP) during the 2024 April 1–4 conjunction when both spacecraft are near their respective perihelion passage. The two ³ He-rich SEP events, originating from active region (AR) 13615, exhibit two key anomalies: (1) sunward streaming SEPs and (2) SEP travel path lengths exceeding 3–10 times the nominal Parker spiral expectations. Remote observations suggest these SEPs have been redirected by a slow coronal mass ejection (CME) that also originated from AR 13615 2 days prior on 2024 March 30 at 21:04 UT. Using the near-Sun CME speed and width measurements, we estimate its size and location at the onset time of the first ³ He-rich SEP event. Based on our estimates, SEPs propagating around the ICME front have traveled 0.76-0.95 au when they arrive at SO, increasing to 0.94–1.1 au at PSP. Using velocity dispersion analysis, we measure the SEP path length observed by SO during event 1 to be 0.92 ± 0.12 au, consistent with the modeled value. The measured SEP path length at PSP is 1.57 ± 0.17 au, significantly greater than our model results. These findings constitute the first multispacecraft observation of sunward streaming ³ He-rich SEPs. We discuss the implications of this phenomenon on ³ He-rich seed material and the rare widespread ³ He-rich SEP events (see Section 5.4).

The solar wind undergoes nonadiabatic heating as it travels away from the Sun. The velocity phase-space distribution of nonequilibrium ions in the solar wind indicates a source of free energy that could contribute significantly to this heating. Parker Solar Probe (PSP) has observed velocity distributions containing highly anisotropic, perpendicularly diffused proton beams with a distinctly constricted gap between the core and beam populations. These distributions resemble a “hammerhead” shape and were first reported in the fourth PSP encounter. Numerical simulations have reproduced the qualitative nature of hammerheads under certain initial conditions but have not convincingly captured the prevalence or extreme attributes of the observed beam. This necessitates a broad study of the occurrence conditions and the associated plasma processes, to better guide simulations. We statistically investigate the occurrences of these structures from 20 recent PSP encounters and find that hammerheads dominantly occur around the heliospheric current sheet (HCS). As the inclination of the HCS at PSP crossing points increases over the rising phase of the solar cycle, the occurrence of hammerheads is increasingly concentrated in narrow time periods around the HCS crossings. For comparison with previous work, we present statistical trends in the anisotropy of the proton beam and its connection to the density of proton beams as well as the drift speed of the beam to the core. Our study establishes a consistent occurrence pattern of hammerhead distributions around the HCS, indicating hammerheads are diagnostics of energization processes associated with the HCS and its escaping wind.

Velocity distribution functions (VDFs) are an essential observable for studying kinetic and wave–particle processes in solar wind plasmas. To experimentally distinguish modes of heating, acceleration, and turbulence in the solar wind, precise representations of particle phase-space VDFs are needed. In the first paper of this series, we developed the Slepian basis reconstruction (SBR) method to approximate fully agyrotropic continuous distributions from discrete measurements of electrostatic analyzers (ESAs). The method enables accurate determination of plasma moments, preserves kinetic features, and prescribes smooth gradients in phase space. In this paper, we extend the SBR method by imposing gyrotropic symmetry (g-SBR). Incorporating this symmetry enables high-fidelity reconstruction of VDFs that are partially measured, as from an ESA with a limited field of view (FOV). We introduce three frameworks for g-SBR, the gyrotropic SBR: (A) 1D angular Slepian functions on a polar cap, (B) 2D Slepian functions in a Cartesian plane, and (C) a hybrid method. We employ model distributions representing multiple anisotropic ion populations in the solar wind to benchmark these methods, and we show that the g-SBR method produces a reconstruction that preserves kinetic structures and plasma moments, even with a strongly limited FOV. For our choice of model distribution, g-SBR can recover ≥​​​​​​90% of the density when only 20% is measured. We provide the package gdf for open-source use and contribution by the heliophysics community. This work establishes direct pathways to bridge particle observations with kinetic theory and simulations, facilitating the investigation of gyrotropic plasma heating phenomena across the heliosphere.

Plasma velocity distribution functions (VDFs) constitute a fundamental observation of numerous operational and future missions. An efficient parameterization of VDFs is crucial for (1) preserving enough information to investigate macroscopic moments along with kinetic effects, (2) producing smooth distributions whereby it is possible to perform derivatives in phase space to support numerical solvers, and (3) economic data management and its storage. Previous studies have used spherical harmonics as an efficient basis for representing electron VDFs. In this paper, we present a novel algorithm targeted toward decomposing ion VDFs measured by electrostatic analyzers on board Magnetospheric Multiscale (MMS) Mission and Solar Orbiter (SolO) spacecraft. We use Slepian functions, custom-designed bases providing compact support in phase space, initially developed in information theory and later used for terrestrial and planetary applications. In this paper, we choose well-studied, well-measured, and complex intervals from MMS and SolO containing a range of simpler gyrotropic and agyrotropic distributions to benchmark the robustness of our reconstruction method. We demonstrate the advantages of using Slepian functions over spherical harmonics for solar wind plasma distributions. We also demonstrate that our choice of basis representation efficiently preserves phase space complexities of a 3D agyrotropic distribution function. This algorithm shown in this study will be extended to Parker Solar Probe and future missions such as Helioswarm.

The solar wind dynamics are thought to be governed by counter-propagating Alfvén waves. Alfvén waves generate a turbulent cascade through nonlinear couplings between shearing wave packets. However, imbalances, structures, and intermittency complicate the solar wind’s magnetohydrodynamic (MHD) turbulence. Simulations and theories have suggested that dynamic alignment, or the tendency for velocity and magnetic fluctuations to become more correlated as a function of scale, may dictate the turbulent cascade. Observations have hinted at dynamic alignment at large scales but remain inconclusive at small scales. To investigate the nature of dynamically aligning fluctuations in the solar wind, we examine slow wind intervals from the Helios 2 spacecraft. We develop a two-component model of solar wind turbulence consisting of Alfvénic and non-Alfvénic contributions. We assume that only counter-propagating Alfvén waves experience dynamic alignment, and the non-Alfvénic structures do not participate in the alignment process. Our model allows us to constrain the relative contribution of inward Alfvén waves and non-Alfvénic structures with respect to the amplitude of outward Alfvén waves in the slow solar wind as a function of scale under the assumption of dynamic alignment. We show that the power ratio of inward to outward Alfvén fluctuations decreases as a function of scale. At the same time, the non-Alfvénic structures to outward Alfvén fluctuations increase with decreasing scale. Increasing structures provide a possible explanation for no dynamic alignment at small scales. Our study implies the need for new theoretical models to fully account for the solar wind’s compressibility, intermittency, and imbalanced nature.

At scales much larger than the ion inertial scale and the gyroradius of thermal protons, the magnetohydrodynamic (MHD) theory is well equipped to describe the nature of solar wind turbulence. The turbulent spectrum itself is defined by a power law manifesting the energy cascading process. A break in the turbulence spectrum develops near-ion scales, signaling the onset of energy dissipation. The exact mechanism for the spectral break is still a matter of debate. In this work, we use the 20 Hz Mercury Surface, Space Environment, Geochemistry, and Ranging (MESSENGER) magnetic field data during four planetary flybys at different heliocentric distances to examine the nature of the spectral break in the solar wind. We relate the spectral break frequencies of the solar wind MHD turbulence, found in the range of 0.3–0.7 Hz, with the well-known characteristic spectral bump at frequencies ∼1 Hz upstream of planetary bow shocks. Spectral breaks and spectral bumps during three planetary flybys are identified from the MESSENGER observations, with heliocentric distances in the range of 0.3–0.7 au. The MESSENGER observations are complemented by one Magnetospheric Multiscale observation made at 1 au. We find that the ratio of the spectral bump frequency to the spectral break frequency appears to be r- and B-independent. From this, we postulate that the wavenumber of the spectral break and the frequency of the spectral bump have the same dependence on the magnetic field strength ∣B∣. The implication of our work on the nature of the break scale is discussed.