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1. Combined electron firehose and electromagnetic ion cyclotron instabilities: quasilinear approach

   https://doi.org/10.1093/mnras/staa2916  

   Ali, Z; Sarfraz, M; Yoon, P H (October 2020, Monthly Notices of the Royal Astronomical Society)

   null (Ed.)

   ABSTRACT Various plasma waves and instabilities are abundantly present in the solar wind plasma, as evidenced by spacecraft observations. Among these, propagating modes and instabilities driven by temperature anisotropies are known to play a significant role in the solar wind dynamics. In situ measurements reveal that the threshold conditions for these instabilities adequately explain the solar wind conditions at large heliocentric distances. This paper pays attention to the combined effects of electron firehose instability driven by excessive parallel electron temperature anisotropy (T⊥e < T∥e) at high beta conditions, and electromagnetic ion cyclotron instability driven by excessive perpendicular proton temperature anisotropy (T⊥i > T∥i). By employing quasilinear kinetic theory based upon the assumption of bi-Maxwellian velocity distribution functions for protons and electrons, the dynamical evolution of the combined instabilities and their mutual interactions mediated by the particles is explored in depth. It is found that while in some cases, the two unstable modes are excited and saturated at distinct spatial and temporal scales, in other cases, the two unstable modes are intermingled such that a straightforward interpretation is not so easy. This shows that when the dynamics of protons and electrons are mutually coupled and when multiple unstable modes are excited in the system, the dynamical consequences can be quite complex. 

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2. Evidence of Interaction between Ion-scale Waves and Ion Velocity Distributions in the Solar Wind

   https://doi.org/10.3847/1538-4357/add467  

   Yogesh; Ofman, Leon; Boardsen, Scott A; Klein, Kristopher; Martinović, Mihailo; Sadykov, Viacheslav M; Verniero, Jaye L; Shankarappa, Niranjana; Jian, Lan K; Mostafavi, Parisa; et al (June 2025, The Astrophysical Journal)

   Abstract Recent in situ observations from Parker Solar Probe (PSP) near perihelia reveal ion beams, temperature anisotropies, and kinetic wave activity. These features are likely linked to solar wind heating and acceleration. During PSP Encounter 17 (at 11.4R_s) on 2023 September 26, the PSP/FIELDS instrument detected enhanced ion-scale wave activity associated with deviations from local thermodynamic equilibrium in ion velocity distribution functions (VDFs) observed by the PSP/Solar Probe Analyzers-Ion. Dense beams (secondary populations) were present in the proton VDFs during this wave activity. Using bi-Maxwellian fits to the proton VDFs, we found that the density of the proton beam population increased during the wave activity and, unexpectedly, surpassed the core population at certain intervals. Interestingly, the wave power was reduced during the intervals when the beam population density exceeded the core density. The drift velocity of the beams decreases from 0.9 to 0.7 of the Alfvén speed, and the proton core shows a higher temperature anisotropy (T_⊥/T_∥ > 2.5) during these intervals. We conclude that the observations during these intervals are consistent with a reconnection event during a heliospheric current sheet crossing. During this event,α-particle parameters (density, velocity, and temperature anisotropy) remained nearly constant. Using linear analysis, we examined how the proton beam drives instability or wave dissipation. Furthermore, we investigated the nonlinear evolution of ion kinetic instabilities using hybrid kinetic simulations. This study provides direct clues about energy transfer between particles and waves in the young solar wind. 

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3. Electron temperature of the solar wind

   https://doi.org/10.1073/pnas.1917905117  

   Boldyrev, Stanislav; Forest, Cary; Egedal, Jan (April 2020, Proceedings of the National Academy of Sciences)

   Solar wind provides an example of a weakly collisional plasma expanding from a thermal source in the presence of spatially diverging magnetic-field lines. Observations show that in the inner heliosphere, the electron temperature declines with the distance approximately as $T_e\left(r\right)\sim r^{-0.3}\dots r^{-0.7}$, which is significantly slower than the adiabatic expansion law $\sim r^{-4/3}$. Motivated by such observations, we propose a kinetic theory that addresses the nonadiabatic evolution of a nearly collisionless plasma expanding from a central thermal source. We concentrate on the dynamics of energetic electrons propagating along a radially diverging magnetic-flux tube. Due to conservation of their magnetic moments, the electrons form a beam collimated along the magnetic-field lines. Due to weak energy exchange with the background plasma, the beam population slowly loses its energy and heats the background plasma. We propose that no matter how weak the collisions are, at large enough distances from the source a universal regime of expansion is established where the electron temperature declines as $T_e\left(r\right)\propto r^{-2/5}$. This is close to the observed scaling of the electron temperature in the inner heliosphere. Our first-principle kinetic derivation may thus provide an explanation for the slower-than-adiabatic temperature decline in the solar wind. More broadly, it may be useful for describing magnetized collisionless winds from G-type stars. 

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4. Non-Thermal Solar Wind Electron Velocity Distribution Function

   https://doi.org/10.3390/e26040310  

   Yoon, Peter H; López, Rodrigo A; Salem, Chadi S; Bonnell, John W; Kim, Sunjung (April 2024, Entropy)

   The quiet-time solar wind electrons feature non-thermal characteristics when viewed from the perspective of their velocity distribution functions. They typically have an appearance of being composed of a denser thermal “core” population plus a tenuous energetic “halo” population. At first, such a feature was empirically fitted with the kappa velocity space distribution function, but ever since the ground-breaking work by Tsallis, the space physics community has embraced the potential implication of the kappa distribution as reflecting the non-extensive nature of the space plasma. From the viewpoint of microscopic plasma theory, the formation of the non-thermal electron velocity distribution function can be interpreted in terms of the plasma being in a state of turbulent quasi-equilibrium. Such a finding brings forth the possible existence of a profound inter-relationship between the non-extensive statistical state and the turbulent quasi-equilibrium state. The present paper further develops the idea of solar wind electrons being in the turbulent equilibrium, but, unlike the previous model, which involves the electrostatic turbulence near the plasma oscillation frequency (i.e., Langmuir turbulence), the present paper considers the impact of transverse electromagnetic turbulence, particularly, the turbulence in the whistler-mode frequency range. It is found that the coupling of spontaneously emitted thermal fluctuations and the background turbulence leads to the formation of a non-thermal electron velocity distribution function of the type observed in the solar wind during quiet times. This demonstrates that the whistler-range turbulence represents an alternative mechanism for producing the kappa-like non-thermal distribution, especially close to the Sun and in the near-Earth space environment. 

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5. The need for accurate measurements of thermal velocity distribution functions in the solar wind

   https://doi.org/10.3389/fspas.2022.1063841  

   Wilson, Lynn B.; Goodrich, Katherine A.; Turner, Drew L.; Cohen, Ian J.; Whittlesey, Phyllis L.; Schwartz, Steven J. (November 2022, Frontiers in Astronomy and Space Sciences)

   The current state of the art thermal particle measurements in the solar wind are insufficient to address many long standing, fundamental physical processes. The solar wind is a weakly collisional ionized gas experiencing collective effects due to long-range electromagnetic forces. Unlike a collisionally mediated fluid like Earth’s atmosphere, the solar wind is not in thermodynamic or thermal equilibrium. For that reason, the solar wind exhibits multiple particle populations for each particle species. We can mostly resolve the three major electron populations (e.g., core, halo, strahl, and superhalo) in the solar wind. For the ions, we can sometimes separate the proton core from a secondary proton beam and heavier ion species like alpha-particles. However, as the solar wind becomes cold or hot, our ability to separate these becomes more difficult. Instrumental limitations have prevented us from properly resolving features within each ion population. This destroys our ability to properly examine energy budgets across transient, discontinuous phenomena (e.g., shock waves) and the evolution of the velocity distribution functions. Herein we illustrate both the limitations of current instrumentation and why higher resolutions are necessary to properly address the fundamental kinetic physics of the solar wind. This is accomplished by directly comparing to some current solar wind observations with calculations of velocity moments to illustrate the inaccuracy and incompleteness of poor resolution data. 

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