Proton Velocity Distribution Function Research Articles

Constraining the Properties of the Multicomponent Local Interstellar Medium: MHD-kinetic Modeling Validated by Voyager and New Horizons Data

We introduce the first solar-cycle simulations from our 3D, global MHD-plasma/kinetic-neutrals model, where both hydrogen and helium atoms are treated kinetically, while electrons and helium ions are described as individual fluids. Using Voyager/PWS observations of electron density up to 160 au from the Sun for validation of several different global models, we conclude that the current estimates for the proton density in the local interstellar medium (LISM) need a revision. Our findings indicate that the commonly accepted value of 0.054 cm−3 may need to be increased to values exceeding 0.07 cm−3. We also show how different assumptions regarding the proton velocity distribution function in the outer heliosheath may affect the global solution. A new feature revealed by our simulations is that the helium ion flow may be significantly compressed and heated in the heliotail at heliocentric distances exceeding ∼400 au. Additionally, we identify a Kelvin–Helmholtz instability at the boundary of the slow and fast solar wind in the inner heliosheath, which acts as a driver of turbulence in the heliotail. These results are crucial for inferring the properties of the LISM and of the global heliosphere structure.

Solar Orbiter Observations of Proton and Alpha Particle Kinetic Signatures Related to the Presence of Switchbacks in the Inner Heliosphere: A Case Study

We investigate how ions, namely protons and alpha particles, kinetically react to the presence of strong deflections in the magnetic field, the so-called switchbacks, in the first stream of slow Alfvénic wind observed by Solar Orbiter at the heliocentric distance of 0.64 au. We focus on an isolated, large-scale switchback, and we study in detail ion kinetic properties. Beyond the expected correlation between the magnetic deflection and ion velocity related to the Alfvénic nature of the switchbacks, we find that, within the switchback, proton and alpha particle densities increase, suggesting ongoing wave activity. Very interestingly, we observe a clear correlation between the magnetic deflection and alpha particle temperature, while no correlation has been found with proton temperature. This is an indication of a possible role played by switchbacks in preferentially heating heavy ions. Our results suggest that the presence of switchbacks can induce a deformation of the proton velocity distribution function, while the preferential heating of alpha particles could be due to a denser secondary beam and a smaller relative drift speed between the beam and core.

Extended Cyclotron Resonant Heating of the Turbulent Solar Wind

Circularly polarized, nearly parallel propagating waves are prevalent in the solar wind at ion-kinetic scales. At these scales, the spectrum of turbulent fluctuations in the solar wind steepens, often called the transition range, before flattening at sub-ion scales. Circularly polarized waves have been proposed as a mechanism to couple electromagnetic fluctuations to ion gyromotion, enabling ion-scale dissipation that results in observed ion-scale steepening. Here we study Parker Solar Probe observations of an extended stream of fast solar wind ranging from ∼15 to 55 R ⊙. We demonstrate that, throughout the stream, transition range steepening at ion scales is associated with the presence of significant left-handed ion-kinetic-scale waves, which are thought to be ion cyclotron waves. We implement quasilinear theory to compute the rate at which ions are heated via cyclotron resonance with the observed circularly polarized waves given the empirically measured proton velocity distribution functions. We apply the Von Kármán decay law to estimate the turbulent decay of the large-scale fluctuations, which is equal to the turbulent energy cascade rate. We find that the ion cyclotron heating rates are correlated with, and amount to a significant fraction of, the turbulent energy cascade rate, implying that cyclotron heating is an important dissipation mechanism in the solar wind.

Coexistence of Antisunward and Sunward Ion Cyclotron Waves in the Near-Sun Solar Wind: Excitation by the Proton Cyclotron Instability

Based on observations from the Parker Solar Probe in the near-Sun solar wind, this study identifies an ion-scale wave event characterized by two distinct frequency bands. The lower-band waves exhibit right-hand polarization, while the upper-band waves have left-hand polarization. Alongside these waves, there are clear indications of the existence of both proton core and beam components, with the perpendicular temperature being higher than the parallel temperature in the measured proton velocity distribution functions (VDFs). Utilizing the plasma parameters derived from typical proton VDFs, instability analyses are conducted to investigate the mode nature of the observed waves and their excitation mechanism. The lower-band waves are identified as sunward ion cyclotron waves (ICWs), generated through the proton beam cyclotron instability; the upper-band waves are recognized as antisunward ICWs, induced by the proton core cyclotron instability. This study provides the first direct observational evidence confirming the presence of counterpropagating ICWs and proton cyclotron instability in the solar wind.

Frequency-dispersed Ion Acoustic Waves in the Near-Sun Solar Wind: Signatures of Impulsive Ion Beams

This work reports a novel plasma wave observation in the near-Sun solar wind: frequency-dispersed ion acoustic waves. Similar waves have previously been reported in association with interplanetary shocks or planetary bow shocks, but the waves reported here occur throughout the solar wind sunward of ∼60 solar radii, far from any identified shocks. The waves reported here vary their central frequency by factors of 3–10 over tens of milliseconds, with frequencies that move up or down in time. Using a semiautomated identification algorithm, thousands of wave instances are recorded during each near-Sun orbit of the Parker Solar Probe spacecraft. Wave statistical properties are determined and used to estimate their plasma frame frequency and the energies of protons most likely to be resonant with these waves. Proton velocity distribution functions are explored for one wave interval, and proton enhancements that may be consistent with proton beams are observed. A conclusion from this analysis is that properties of the observed frequency-dispersed ion acoustic waves are consistent with driving by cold, impulsively accelerated proton beams near the ambient proton thermal speed. Based on the large number of observed waves and their properties, it is likely that the impulsive proton beam acceleration mechanism generating these waves is active throughout the inner heliosphere. This may have implications for the acceleration of the solar wind.

Observations of co-existing rising and falling tone emissions of electromagnetic ion cyclotron waves

We report observations of co-existing rising and falling tone emissions of electromagnetic ion cyclotron (EMIC) waves by THEMIS E spacecraft. The investigation of these fine structures of the EMIC waves is essential from the point of view of understanding the connection between the proton holes and the proton hills in velocity phase-space. The wave packets of rising and falling tones are tracked by Poynting vector analysis, where we observe that the rising tones are propagating northward and the falling tones are propagating southward. The nonlinear wave growth theory supports our observations. We propose a model where the proton velocity distribution function evolves through the formation of proton holes on the negative side of the distribution function and mirrored resonant protons forming proton hills on the positive side of the distribution function, allowing us to observe the co-existing rising and falling tone EMIC waves.Graphical abstract

Local Proton Heating at Magnetic Discontinuities in Alfvénic and Non-Alfvénic Solar Wind

We investigate the local proton energization at magnetic discontinuities/intermittent structures and the corresponding kinetic signatures in velocity phase space in Alfvénic (high cross helicity) and non-Alfvénic (low cross helicity) wind streams observed by Parker Solar Probe. By means of the partial variance of increments method, we find that the hottest proton populations are localized around compressible, coherent magnetic structures in both types of wind. Analysis of parallel and perpendicular temperature distributions suggest that the Alfvénic wind undergoes preferential enhancements of T ∥ at such structures, whereas the non-Alfvénic wind experiences preferential T ⊥ enhancements. Although proton beams are present in both types of wind, the proton velocity distribution function displays distinct features. Hot beams, i.e., beams with beam-to-core perpendicular temperature T ⊥,b /T ⊥,c up to three times larger than the total distribution anisotropy, are found in the non-Alfvénic wind, whereas colder beams are in the Alfvénic wind. Our data analysis is complemented by 2.5D hybrid simulations in different geometrical setups, which support the idea that proton beams in Alfvénic and non-Alfvénic wind have different kinetic properties and different origins. The development of a perpendicular nonlinear cascade, favored in balanced turbulence, allows a preferential relative enhancement of the perpendicular plasma temperature and the formation of hot beams. Cold field-aligned beams are instead favored by Alfvén wave steepening. Non-Maxwellian distribution functions are found near discontinuities and intermittent structures, pointing to the fact that the nonlinear formation of small-scale structures is intrinsically related to the development of highly nonthermal features in collisionless plasmas. Our results contribute to understanding the role of different coherent structures in proton energization and their implication in collisionless energy dissipation processes in space plasmas.

Proton- and Alpha-driven Instabilities in an Ion Cyclotron Wave Event

Ion-scale wave events or wave storms in the solar wind are characterized by enhancements in magnetic field fluctuations as well as coherent magnetic field polarization signatures at or around the local ion cyclotron frequencies. In this paper, we study in detail one such wave event from Parker Solar Probe's (PSP) fourth encounter, consisting of an initial period of left-handed (LH) polarization abruptly transitioning to a strong period of right-handed (RH) polarization, accompanied by a clear core beam structure in both the alpha and proton velocity distribution functions. A linear stability analysis shows that the LH-polarized waves are anti-sunward propagating Alfvén/ion cyclotron waves primarily driven by a proton cyclotron instability in the proton core population, and the RH polarized waves are anti-sunward propagating fast magnetosonic/whistler waves driven by a firehose-like instability in the secondary alpha beam population. The abrupt transition from LH to RH is caused by a drop in the proton core temperature anisotropy. We find very good agreement between the frequencies and polarizations of the unstable wave modes as predicted by linear theory and those observed in the magnetic field spectra. Given the ubiquity of ion-scale wave signatures observed by PSP, this work gives insight into which exact instabilities may be active and mediating energy transfer in wave–particle interactions in the inner heliosphere, as well as highlighting the role a secondary alpha population may play as a rarely considered source of free energy available for producing wave activity.

The Effects of Nonequilibrium Velocity Distributions on Alfvén Ion-cyclotron Waves in the Solar Wind

In this work, we investigate how the complex structure found in solar wind proton velocity distribution functions (VDFs), rather than the commonly assumed two-component bi-Maxwellian structure, affects the onset and evolution of parallel-propagating microinstabilities. We use the Arbitrary Linear Plasma Solver, a numerical dispersion solver, to find the real frequencies and growth/damping rates of the Alfvén modes calculated for proton VDFs extracted from Wind spacecraft observations of the solar wind. We compare this wave behavior to that obtained by applying the same procedure to core-and-beam bi-Maxwellian fits of the Wind proton VDFs. We find several significant differences in the plasma waves obtained for the extracted data and bi-Maxwellian fits, including a strong dependence of the growth/damping rate on the shape of the VDF. By applying the quasilinear diffusion operator to these VDFs, we pinpoint resonantly interacting regions in velocity space where differences in VDF structure significantly affect the wave growth and damping rates. This demonstration of the sensitive dependence of Alfvén mode behavior on VDF structure may explain why the Alfvén ion-cyclotron instability thresholds predicted by linear theory for bi-Maxwellian models of solar wind proton background VDFs do not entirely constrain spacecraft observations of solar wind proton VDFs, such as those made by the Wind spacecraft.

Ion Energization and Thermalization in Magnetic Reconnection Exhaust Region in the Solar Wind

Plasma energization and thermalization in magnetic reconnection is an important topic in astrophysical studies. We select two magnetic reconnection exhausts encountered by Solar Orbiter and analyze the associated ion heating in the kinetic regime. Both cases feature asymmetric plasma merging in the exhaust and anisotropic heating. For a quantitative investigation of the associated complex velocity-space structures, we adopt a three-dimensional Hermite representation of the proton velocity distribution function to produce the distribution of Hermite moments. We also derive the enstrophy and Hermite spectra to analyze the free energy conversion and transfer in phase space. We find a depletion of Hermite power at small m (corresponding to large-scale structures in velocity space) inside the reconnection exhaust region, concurrent with enhanced proton temperature and decreased enstrophy. Furthermore, the slopes of the 1D time-averaged parallel Hermite spectra are lower inside the exhaust and consistent with the effect of phase mixing that creates small fluctuations in velocity space. These fluctuations store free energy at higher m and are smoothed by weak collisionality, leading to irreversible thermalization. We also suggest that the perpendicular heating may happen via perpendicular phase mixing resulting from finite Larmor radius effects around the exhaust boundary.

Strong Perpendicular Velocity-space Diffusion in Proton Beams Observed by Parker Solar Probe

Abstract The SWEAP instrument suite on Parker Solar Probe (PSP) has detected numerous proton beams associated with coherent, circularly polarized, ion-scale waves observed by PSP’s FIELDS instrument suite. Measurements during PSP Encounters 4−8 revealed pronounced complex shapes in the proton velocity distribution functions (VDFs), in which the tip of the beam undergoes strong perpendicular diffusion, resulting in VDF level contours that resemble a “hammerhead.” We refer to these proton beams, with their attendant “hammerhead” features, as the ion strahl. We present an example of these observations occurring simultaneously with a 7 hr ion-scale wave storm and show results from a preliminary attempt at quantifying the occurrence of ion-strahl broadening through three-component ion VDF fitting. We also provide a possible explanation of the ion perpendicular scattering based on quasilinear theory and the resonant scattering of beam ions by parallel-propagating, right circularly polarized, fast magnetosonic/whistler waves.

Switchback-like structures observed by Solar Orbiter

Context.Rapid polarity reversals of the radial heliospheric magnetic field were discovered by Ulysses and they are now frequently observed as a common near-Sun phenomenon by NASA’s Parker Solar Probe (PSP). Other solar wind missions, including ESA-NASA Solar Orbiter (SolO), also observe similar phenomena. The nature of these fluctuations is unclear, and the relation between the “switchbacks” observed near the Sun and similar events observed at 1 AU is unknown.Aims.We make a detailed case study of the SolO plasma and magnetic field data obtained in a region that is magnetically connected to a coronal hole. We aim to check whether such fluctuations might have the same origin as the “switchbacks” observed by PSP.Methods.We used PSP magnetic field and plasma data to support our analysis of SolO data. We used the magnetic field data, electron pitch angle distributions, proton velocity distribution functions, andα-particle parameters measured by SolO to perform a detailed analysis of the observed solar wind perturbations.Results.On 27 September 2020, PSP and SolO were located around the same Carrington longitude and their latitudinal separation was very small. Solar wind plasma and magnetic field data during this time interval confirms that (at least at certain times) the solar wind observed by both spacecraft does originate from the same coronal hole region and that during these time intervals, SolO experiences several short variations similar to the “switchbacks” regularly observed by PSP.Conclusions.The suprathermal electron pitch angle distributions andα-particle speed variations indicate that the magnetic field line was bent by 180° by solar wind velocity shear. Variations in electron and proton velocity distribution functions suggest that bent field lines reconnect with each other, producing flux ropes. The observed flux ropes might be the surviving and modified remains of the switchbacks created near Sun and observed by PSP.

Multiscale views of an Alfvénic slow solar wind: 3D velocity distribution functions observed by the Proton-Alpha Sensor of Solar Orbiter

Context.The Alfvénic slow solar wind is of particular interest, as it is often characterized by intense magnetic turbulence, complex proton 3D velocity distribution functions (VDF), and an ensuing richness of kinetic and dynamic processes.Aims.We take advantage of the fast time cadence of measurements taken by the Proton-Alpha Sensor (PAS) on board Solar Orbiter to analyze the kinetic properties of the proton population, the variability of their VDFs, and the possible link with propagating magnetic structures. We also study the magnetic (B) and velocity (V) correlation that characterizes this type of wind down to the ion gyroperiod.Methods.We analyzed the VDFs measured by PAS, a novelty that take advantages of the capability of 3D measurements at a 4 Hz cadence. In addition, we considered MAG observations.Results.We first show that there is a remarkable correlation between theBandVcomponents observed down to timescales approaching the ion gyrofrequency. This concerns a wide variety of fluctuations, such as waves, isolated peaks, and discontinuities. The great variability of the proton VDFs is also documented. The juxtaposition of a core and a field-aligned beam is the norm but the relative density of the beam, drift speed, and temperatures can considerably change on scales as short as as a few seconds. The characteristics of the core are comparatively more stable. These variations in the beam characteristics mostly explain the variations in the total parallel temperature and, therefore, in the total anisotropy of the proton VDFs. Two magnetic structures that are associated with significant changes in the shape of VDFs, one corresponding to relaxation of total anisotropy and the other to its strong increase, are analyzed here. Our statistical analysis shows a clear link between total anisotropy (and, thus, beam characteristics) and the direction ofBwith respect to the Parker spiral. In the present case, flux tubes aligned with Parker spiral contain an average proton VDF with a much more developed beam (thus, with larger total anisotropy) than those that are inclined, perpendicular, or even reverse with regard to the outward direction.Conclusions.These observations document the variability of the proton VDF shape in relation to the propagation of magnetic structures. This is a key area of interest for understanding of the effect of turbulence on solar wind dynamics.

Magnetic reconnection as a mechanism to produce multiple thermal proton populations and beams locally in the solar wind

Context.Spacecraft data revealed early on the frequent observation of multiple near-thermal proton populations in the solar wind. Decades of research on their origin have focused on processes such as magnetic reconnection in the low corona and wave-particle interactions in the corona and locally in the solar wind.Aims.This study aims to highlight the fact that such multiple thermal proton populations and beams are also produced by magnetic reconnection occurring locally in the solar wind.Methods.We used high-resolution Solar Orbiter proton velocity distribution function measurements, complemented by electron and magnetic field data, to analyze the association of multiple thermal proton populations and beams with magnetic reconnection during a period of slow Alfvénic solar wind on 16 July 2020.Results.At least six reconnecting current sheets with associated multiple thermal proton populations and beams, including a case of magnetic reconnection at a switchback boundary, were found on this day. This represents 2% of the measured distribution functions. We discuss how this proportion may be underestimated, and how it may depend on solar wind type and distance from the Sun.Conclusions.Although suggesting a likely small contribution, but which remains to be quantitatively assessed, Solar Orbiter observations show that magnetic reconnection must be considered as one of the mechanisms that produce multiple thermal proton populations and beams locally in the solar wind.

Resolution dependence of magnetosheath waves in global hybrid-Vlasov simulations

Abstract. Kinetically driven plasma waves are fundamental for a description of the thermodynamical properties of the Earth's magnetosheath. The most commonly observed ion-scale instabilities are generated by temperature anisotropy of the ions, such as the mirror and proton cyclotron instabilities. We investigate here the spatial resolution dependence of the mirror and proton cyclotron instabilities in a global hybrid-Vlasov simulation using the Vlasiator model; we do this in order to find optimal resolutions and help future global hybrid-Vlasov simulations to save resources when investigating those instabilities in the magnetosheath. We compare the proton velocity distribution functions, power spectra and growth rates of the instabilities in a set of simulations with three different spatial resolutions but otherwise identical set-up. We find that the proton cyclotron instability is absent at the lowest resolution and that only the mirror instability remains, which leads to an increased temperature anisotropy in the simulation. We conclude that the proton cyclotron instability, its saturation and the reduction of the anisotropy to marginal levels are resolved at the highest spatial resolution. A further increase in resolution does not lead to a better description of the instability to an extent that would justify this increase at the cost of numerical resources in future simulations. We also find that spatial resolutions between 1.32 and 2.64 times the inertial length in the solar wind present acceptable limits for the resolution within which the velocity distribution functions resulting from the proton cyclotron instability are still bi-Maxwellian and reach marginal stability levels. Our results allow us to determine a range of spatial resolutions suitable for the modelling of the proton cyclotron and mirror instabilities and should be taken into consideration regarding the optimal grid spacing for the modelling of these two instabilities, within available computational resources.

Particle-in-cell Simulations of the Parallel Proton Firehose Instability Influenced by the Electron Temperature Anisotropy in Solar Wind Conditions

Abstract In situ observations of the solar wind show a limited level of particle temperature anisotropy with respect to the interplanetary magnetic field direction. Kinetic electromagnetic instabilities are efficient to prevent the excessive growth of the anisotropy of particle velocity distribution functions. Among them, the firehose instabilities are often considered to prevent the increase of the parallel temperature and hence to shape the velocity distribution functions of electrons and protons in the solar wind. We present a nonlinear modeling of the parallel firehose instability, retaining a kinetic description for both the electrons and protons. One-dimensional (1D) fully kinetic particle-in-cell simulations using the energy conserving semi-implicit method (ECsim) are performed to clarify the role of the electron temperature anisotropy in the development of the parallel proton firehose instability. We found that in the presence of an electron temperature anisotropy, such that the temperature parallel to the background magnetic field is higher than the temperature in the perpendicular direction, the onset of the parallel proton firehose instability occurs earlier and its growth rate is faster. The enhanced wave fluctuations contribute to the particle scattering reducing the temperature anisotropy to a stable, nearly isotropic state. The simulation results compare well with linear theory. A test case of 1D simulations at oblique angles with respect to the magnetic field is also considered, as a first step to study the cumulative effect of protons and electrons on the full spectrum of instabilities.

Kinetic-scale Spectral Features of Cross Helicity and Residual Energy in the Inner Heliosphere

Abstract In this work, we present the first results from the flux angle (FA) operation mode of the Faraday Cup instrument on board the Parker Solar Probe (PSP). The FA mode allows rapid measurements of phase space density fluctuations close to the peak of the proton velocity distribution function with a cadence of 293 Hz. This approach provides an invaluable tool for understanding kinetic-scale turbulence in the solar wind and solar corona. We describe a technique to convert the phase space density fluctuations into vector velocity components and compute several turbulence parameters, such as spectral index, residual energy, and cross helicity during two intervals when the FA mode was used in PSP’s first encounter at 0.174 au distance from the Sun.

Investigating the nature of the link between magnetic field orientation and proton temperature in the solar wind

Solar wind fluctuations are a mixture of propagating disturbances and advected structures that transfer into the interplanetary space the complicated magnetic topology present at the basis of the corona. The large-scale interplanetary magnetic field introduces a preferential direction in the solar wind, which is particularly relevant for both the propagation of the fluctuations and their anisotropy and for the topology of the structures advected by the wind. This paper focusses on a particular link observed between angular displacements of the local magnetic field orientation from the radial direction and values of the proton temperature. In particular, we find that observations byHeliosandWindshow a positive correlation between proton temperature and magnetic field orientation. This is especially true within Alfvénic wind characterized by large-amplitude fluctuations of the background field orientation. Moreover, in the case ofWind, we found a robust dependence of the perpendicular component of the proton temperature on the magnetic field angular displacement. We interpret this signature as possibly due to a physical mechanism related to the proton cyclotron resonance. Finally, by simulating the sampling procedure of the proton velocity distribution function (VDF) of an electrostatic analyzer, we show that the observed temperature anisotropy is not due to instrumental effects.

Locally Generated ULF Waves in the Martian Magnetosphere: MAVEN Observations

AbstractWe investigate Martian ultralow frequency (ULF) electromagnetic waves generated by local plasma instabilities below the Martian bow shock. Recent Mars Atmosphere and Volatile EvolutioN (MAVEN) observations have shown that ULF waves generated upstream of the Martian bow shock can propagate down to the upper ionosphere, possibly facilitating heavy ion escape from Mars by heating the ionospheric plasma. In contrast to the upstream waves oscillating near the upstream proton cyclotron frequency, we identify narrow band ULF magnetic field fluctuations with frequencies near the local proton cyclotron frequency (fcp(local)) from MAVEN data. In addition to expected proton cyclotron waves locally generated in the magnetosheath, we newly identify compressional narrow band emissions near fcp(local) (and its harmonics for some cases) in the dayside upper ionosphere and in the nightside magnetotail. The dayside waves are preferentially observed for high solar extreme ultraviolet (EUV) conditions and are often associated with ring/shell‐like, hot protons of magnetosheath origin in the presence of cold, dense ionospheric protons. The nightside waves exhibit distinct preference for high‐solar‐EUV, strong‐solar‐wind conditions, under which both warm and cold protons are enhanced. The observed properties of these compressional waves are generally consistent with a proton Bernstein mode instability driven by a positive perpendicular slope in proton velocity distribution functions. The excited waves can cause perpendicular heating of thermal protons, thereby transferring energy from precipitating hot protons to cold ionospheric protons.

Energy conversion in turbulent weakly collisional plasmas: Eulerian hybrid Vlasov-Maxwell simulations

Kinetic simulations based on the Eulerian Hybrid Vlasov-Maxwell (HVM) formalism permit the examination of plasma turbulence with a useful resolution of the proton velocity distribution function. The HVM model is employed here to study the balance of energy, focusing on channels of conversion that lead to proton kinetic effects, including growth of internal energy and temperature anisotropies. We show that this Eulerian simulation approach, which is almost noise-free, is able to provide an accurate energy balance for protons. The results demonstrate explicitly that the recovered temperature growth is directly related to the role of the pressure-strain interaction. Furthermore, analysis of local spatial correlations indicates that the pressure-strain interaction is qualitatively associated with strong-current, high-vorticity structures although other local terms—such as the heat flux—weaken the correlation. These numerical capabilities based on the Eulerian approach will enable a deeper study of transfer and conversion channels in weakly collisional Vlasov plasmas.