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The solar wind is a magnetized plasma and as such exhibits collective plasma behavior associated with its characteristic spatial and temporal scales. The characteristic length scales include the size of the heliosphere, the collisional mean free paths of all species, their inertial lengths, their gyration radii, and their Debye lengths. The characteristic timescales include the expansion time, the collision times, and the periods associated with gyration, waves, and oscillations. We review the past and present research into the multi-scale nature of the solar wind based on in-situ spacecraft measurements and plasma theory. We emphasize that couplings of processes across scales are important for the global dynamics and thermodynamics of the solar wind. We describe methods to measure in-situ properties of particles and fields. We then discuss the role of expansion effects, non-equilibrium distribution functions, collisions, waves, turbulence, and kinetic microinstabilities for the multi-scale plasma evolution.

The heating of ions and electrons due to turbulent dissipation plays a crucial role in the thermodynamics of the solar wind and other plasma environments. Using magnetic field and thermal plasma observations from the first two perihelia of the Parker Solar Probe, we model the relative heating rates as a function of the radial distance, magnetic spectra, and plasma conditions, enabling us to better characterize the thermodynamics of the inner heliosphere. We employ the Howes et al. steady-state cascade model, which considers the behavior of turbulent, low-frequency, wavevector-anisotropic, critically balanced Alfvénic fluctuations that dissipate via Landau damping to determine proton-to-electron heating rates Q p /Q e . We distinguish ion cyclotron frequency circularly polarized waves from low-frequency turbulence and constrain the cascade model using spectra constructed from the latter. We find that the model accurately describes the observed energy spectrum from over 39.4% of the intervals from Encounters 1 and 2, indicating the possibility for Landau damping to heat the young solar wind. The ability of the model to describe the observed turbulent spectra increases with the ratio of thermal-to-magnetic pressure, β p , indicating that the model contains the necessary physics at higher β p . We estimate high magnitudes for the Kolmogorov constant which is inversely proportional to the nonlinear energy cascade rate. We verify the expected strong dependency of Q p /Q e on β p and the consistency of the critical balance assumption.

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ ∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ ∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ ∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ ∥ = (5.16 ± 1.22) × 1018 r 1.17±0.08 E 0.71±0.02 (cm2 s−1) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.

Linear theory is a well-developed framework for characterizing instabilities in weakly collisional plasmas, such as the solar wind. In the previous installment of this series, we analyzed ∼1.5M proton and α particle velocity distribution functions (VDFs) observed by Helios I and II to determine the statistical properties of the standard instability parameters such as the growth rate, frequency, the direction of wave propagation, and the power emitted or absorbed by each component, as well as to characterize their behavior with respect to the distance from the Sun and collisional processing. In this work, we use this comprehensive set of instability calculations to train a machine-learning algorithm consisting of three interlaced components that: (1) predict if an interval is unstable from observed VDF parameters; (2) predict the instability properties for a given unstable VDF; and (3) classify the type of the unstable mode. We use these methods to map the properties in multidimensional phase space to find that the parallel-propagating, proton-core-induced ion cyclotron mode dominates the young solar wind, while the oblique fast magnetosonic mode regulates the proton beam drift in the collisionally old plasma.

Circularly polarized waves consistent with parallel-propagating ion cyclotron waves (ICWs) and fast magnetosonic waves (FMWs) are often observed by the Parker Solar Probe (PSP) at ion kinetic scales. Such waves damp energy via cyclotron resonance, and cyclotron damping is expected to play a significant role in the enhanced, anisotropic heating of the solar wind observed in the inner heliosphere. We employ a linear plasma dispersion solver, PLUME, to evaluate the frequencies of ICWs and FMWs in the plasma rest frame and Doppler-shift them to the spacecraft frame, calculating their damping rates at frequencies where persistently high values of circular polarization are observed. We find that such ion-scale waves are observed during 20.37% of PSP Encounters 1 and 2 observations and their plasma frame frequencies are consistent with them being transient ICWs. We estimate significant ICW dissipation onto protons, consistent with previous empirical estimates for the total turbulent damping rates, indicating that ICW dissipation could account for the observed enhancements in the proton temperature and its anisotropy with respect to the mean magnetic field.

Minor ions in the solar corona are heated to extreme temperatures, far in excess of those of the electrons and protons that comprise the bulk of the plasma. These highly nonthermal distributions make minor ions sensitive probes of the collisionless processes that heat the corona and power the solar wind. The recent discovery of the “helicity barrier” offers a mechanism in which imbalanced Alfvénic turbulence in low-β plasmas preferentially heats protons over electrons, generating high-frequency, proton-cyclotron-resonant fluctuations. We use the hybrid-kinetic particle-in-cell code Pegasus++ to drive imbalanced Alfvénic turbulence in a 3D low-β plasma with additional passive ion species, He2+ and O5+. A helicity barrier naturally develops, followed by clear phase-space signatures of oblique proton-cyclotron-wave heating and Landau-resonant heating from the imbalanced Alfvénic fluctuations. The former results in characteristically arced ion velocity distribution functions, whose non-bi-Maxwellian features are shown by linear ALPS calculations to be critical to the heating process. Additional features include a steep transition-range electromagnetic spectrum, proton-cyclotron waves propagating in the direction of the imbalance, significantly enhanced proton-to-electron heating ratios, ion temperatures that are considerably more perpendicular with respect to magnetic field, and extreme heating of heavier species in a manner consistent with mass scalings inferred from spacecraft measurements. None of these features are realized in an otherwise equivalent simulation of balanced turbulence. If seen simultaneously in the fast solar wind, these signatures of the helicity barrier would testify to the necessity of incorporating turbulence imbalance in a complete theory for the evolution of 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-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.

Determining the physical mechanisms that extract energy from turbulent fluctuations in weakly collisional magnetized plasmas is necessary for a more complete characterization of the behaviour of a variety of space and astrophysical plasmas. Such a determination is complicated by the complex nature of the turbulence as well as observational constraints, chiefly that in situ measurements of such plasmas are typically only available at a single point in space. Recent work has shown that correlations between electric fields and particle velocity distributions constructed from single-point measurements produce a velocity-dependent signature of the collisionless damping mechanism. We extend this work by constructing field–particle correlations using data sets drawn from single points in strongly driven, turbulent, electromagnetic gyrokinetic simulations to demonstrate that this technique can identify the collisionless mechanisms operating in such systems. The velocity-space structure of the correlation between proton distributions and parallel electric fields agrees with expectations of resonant mechanisms transferring energy collisionlessly in turbulent systems. This work motivates the eventual application of field–particle correlations to spacecraft measurements in the solar wind, with the ultimate goal to determine the physical mechanisms that dissipate magnetized plasma turbulence.

Turbulence plays a key role in the conversion of the energy of large-scale fields and flows to plasma heat, impacting the macroscopic evolution of the heliosphere and other astrophysical plasma systems. Although we have long been able to make direct spacecraft measurements of all aspects of the electromagnetic field and plasma fluctuations in near-Earth space, our understanding of the physical mechanisms responsible for the damping of the turbulent fluctuations in heliospheric plasmas remains incomplete. Here we propose an innovative field–particle correlation technique that can be used to measure directly the secular energy transfer from fields to particles associated with collisionless damping of the turbulent fluctuations. Furthermore, this novel procedure yields information about the collisionless energy transfer as a function of particle velocity, providing vital new information that can help to identify the dominant collisionless mechanism governing the damping of the turbulent fluctuations. Kinetic plasma theory is used to devise the appropriate correlation to diagnose Landau damping, and the field–particle correlation technique is thoroughly illustrated using the simplified case of the Landau damping of Langmuir waves in a 1D-1V (one dimension in physical space and one dimension in velocity space) Vlasov–Poisson plasma. Generalizations necessary to apply the field–particle correlation technique to diagnose the collisionless damping of turbulent fluctuations in the solar wind are discussed, highlighting several caveats. This novel field–particle correlation technique is intended to be used as a primary analysis tool for measurements from current, upcoming and proposed spacecraft missions that are focused on the kinetic microphysics of weakly collisional heliospheric plasmas, including the Magnetospheric Multiscale (MMS), Solar Probe Plus, Solar Orbiter and Turbulence Heating ObserveR (THOR) missions.