Many works have attempted to estimate the correlation and integral timescales associated with turbulent fluctuations in the solar wind, which are interpreted as lengthscales based on Taylor’s hypothesis. However, accurate estimates of these timescales from spacecraft observations heavily rely on the accurate estimation of autocorrelation functions (ACFs), which have been recently shown to depend strongly on the interval length used to estimate them. In this Letter, we show that this dependence on interval length may be artificial, because common ACF estimators do not correctly capture the long-lag behavior of the true ACF of the underlying turbulence. We introduce a new ergodicity-based methodology to unambiguously estimate the integral timescale, and a new ACF estimator with better ergodic convergence than current ones. Due to its ergodic properties, the new ACF estimator properly captures the long-lag behavior, and is independent of the interval length. We use this approach to estimate the integral and correlation scales of magnetic fluctuations in the solar wind near 1 au.

In this paper, we investigate the population of energetically dominant sunward-propagating Alfvén waves (SAWs) using more than 20 yr of data provided by the Wind spacecraft near 1 au. We refer to SAWs as energetically dominant sunward-propagating Alfvén waves within inertial range scales. Key parameters such as normalized cross helicity, plasma compressibility, and magnetic compressibility are used to determine the SAWs. Incorporating the polarity of the heliospheric magnetic field, Alfvén wave modes are identified, which enables the determination of the propagation direction. Occurrence rates of SAWs vary from 1% to 14% depending on the timescale and solar wind stream type considered. Particularly, the relationship between large-scale magnetic field switchbacks and SAWs (for a 1 hr long timescale) is investigated. A methodology utilizing pitch angle distributions of suprathermal electron strahl is employed to identify inverted magnetic field topology. The intervals containing SAWs are cross-referenced and examined with intervals identified as switchbacks . For a sample of 1636 1 hr SAW intervals, 17.5% are associated with magnetic field switchbacks occurring at scales larger than 1 hr. The analysis lends support to the idea of switchbacks as one of the candidate sources for a portion of the SAW population.

Shocks associated with interplanetary coronal mass ejections are known to energize charged particles and give rise to solar energetic particles. Many of these energetic particles move ahead of the shock to create a foreshock region. The foreshock region primarily consists of solar wind plasma, exhibiting turbulent velocity and magnetic fields. Such turbulent behavior results from inherent solar wind turbulence modified by energetic particles. We analyze magnetic field data from six such ICME shocks observed by the Wind spacecraft. The analysis of the shock upstream shows that the magnetic power spectral density (PSD) maintains a power-law slope of −5/3. We also identify clear intermittent peaks in the PSD. After characterizing these peaks, we investigate various possibilities for their generation. Our analysis indicates that these peaks in the PSD are due to the resonant interaction of Alfvén waves with the bulk solar wind protons and protons with energy up to 10 keV. However, evidence of Alfvén wave interaction with highly energetic protons is not evident in our analysis, and we anticipate that such evidence is obscured by the prevailing solar wind turbulence in the shock upstream.

The slow solar wind has been recently observed to have a number of intervals that are dominated by large-scale Alfvenic fluctuations, especially within 1 au, with similar turbulence characteristics to those found in fast wind streams, including a 1/f range. These results suggest that the slow solar wind exists in at least two flavors: the typical slow wind that generally does not exhibit a 1/f range and an Alfvenic wind that is more similar to fast wind streams. The Alfvenic slow wind is usually differentiated from the typical slow wind (not dominated by Alfvenic fluctuations) by the normalized cross helicity, sigma c . Values of divided by sigma c divided by near unity are associated with Alfvenic fluctuations, whereas values near zero are typically thought of as non-Alfvenic. This classification by cross helicity excludes the case of solar wind fluctuations dominated by balanced Alfvenic turbulence, i.e., the turbulence regime where there is equal energy flux of counterpropagating fluctuations propagating along the mean field. We use a large statistical analysis to isolate intervals of slow wind at 1 au in a 20 yr period of Wind data. These intervals are sorted into subsets corresponding to the type of slow wind via the mean values of their magnetic compressibility and cross helicity. Our analysis finds several intervals of low-cross-helicity slow wind dominated by balanced Alfvenic turbulence, which possess similar characteristics found in high-cross-helicity streams. Our results support the conclusion that a 1/f spectrum may be a property associated with streams dominated by Alfvenic turbulence, whether the turbulence is balanced or imbalanced.

ABSTRACT In this work, we find empirical evidence that the scale-dependent statistical properties of solar wind and magnetohydrodynamic (MHD) turbulence can be described in terms of a family of parametric probability distribution functions (PDFs) known as Normal Inverse Gaussian (NIG). Understanding these PDFs is one of the most important goals in turbulence theory, as they are inherently connected to the intermittent properties of solar wind turbulence. We investigate the properties of PDFs of Elsasser increments based on a large statistical sample from solar wind observations and high-resolution numerical simulations of MHD turbulence. In order to measure the PDFs and their corresponding properties, three experiments are presented: fast and slow solar wind for experimental data and a simulation of reduced MHD (RMHD) turbulence. Conditional statistics on a 23-yr-long sample of WIND data near 1 au and high-resolution pseudo-spectral simulation of steadily driven RMHD turbulence on a $2048^3$ mesh are used to construct scale-dependent PDFs. The empirical PDFs are fitted to NIG distributions, which depend on four free parameters. Our analysis shows that NIG distributions accurately capture the evolution of the PDFs, with scale-dependent parameters, from large scales characterized by a Gaussian distribution, turning to exponential tails within the inertial range and stretched exponentials at dissipative scales. We also show that empirically-measured NIG parameters exhibit well-defined scaling properties that are similar across the three empirical data sets, which may be indicative of universal behaviour.

Solar wind ions exhibit distinct kinetic non-thermal features such as preferential heating and acceleration of alpha particles compared to protons. On the other hand, Coulomb collisions in the solar wind act to eliminate these non-thermal features and gradually lead to thermal equilibrium. Previous observations at 1 au have revealed that even though the local Coulomb collisions in the solar wind plasma are rare, the cumulative effect of the collisions during a transit time of a particle can be important in terms of thermalizing the solar wind plasma populations and reducing the ion non-thermal features. Here, we analyze Parker Solar Probe observations to study the effects of Coulomb collisions on the non-thermal features (alpha-to-proton temperature ratio and differential flow) of young solar wind closer to the Sun than previously possible. Our results show that even close to the Sun (∼15Rs), these non-thermal features are organized by collisionality. Moreover, observations at these unprecedented distances allow us to investigate the preferential heating of the alpha particles close to the source for both fast and slow wind streams. We show that the alpha-to-proton temperature ratio is positively correlated with the solar wind speed, which is consistent with Wind observations. Solar wind close to the Sun is less collisionally old than when it reaches 1 au. As such, observed differences in the temperature ratio between slow and fast streams near their solar source suggest causes that go beyond different Coulomb numbers. Our results suggest that slow and fast wind streams, originating from different solar regions, may have different mechanisms for the preferential heating of alpha particles compared to protons.

In this work we analyze plasma and magnetic field data provided by the Parker Solar Probe and Solar Orbiter missions to investigate the radial evolution of the heating of Alfvénic slow wind by imbalanced Alfvén-wave (AW) turbulent fluctuations from 0.06 to 1 au. in our analysis we focus on slow solar-wind intervals with highly imbalanced and incompressible turbulence (i.e., magnetic compressibility C _B = δ B / B ≤ 0.25, plasma compressibility C _n = δ n / n ≤ 0.25, and normalized cross helicity σ _c ≥ 0.65). First, we estimate the AW turbulent dissipation rate from the wave energy equation and find that the radial profile trend is similar to the proton heating rate. Second, we find that the scaling of the empirical AW turbulent dissipation rate Q _W obtained from the wave energy equation matches the scaling from the phenomenological AW turbulent dissipation rate Q _CH09 (with Q _CH09 ≃ 1.55 Q _W ) derived by Chandran & Hollweg based on the model of reflection-driven turbulence. Our results suggest that, as in the fast solar wind, AW turbulence plays a major role in the ion heating that occurs in incompressible slow-wind streams.

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

An important challenge in the accurate estimation of power spectra of plasma fluctuations in the solar wind at very low frequencies is that it requires extremely long signals, which will necessarily contain a mixture of qualitatively different solar wind streams, such as fast and slow wind streams, different magnetic polarities, or a mixture of compressible and incompressible fluctuations, along with other transient structures. This mixture of streams with qualitatively different properties unavoidably affects the structure of the power spectra by conflating all these different properties into a single power spectrum. In this work, we present a conditional statistical analysis that allows us to accurately estimate the power spectrum, at arbitrarily low frequencies, for "pure" slow solar wind streams, defined as those for which the solar wind speed is below 500 km s(-1). The conditional analysis is based on the estimation of autocorrelation functions (ACF) of arbitrarily long but discontiguous signals, which result from excluding portions of the signal that do not satisfy the required properties. We use numerical simulations of magnetohydrodynamic (MHD) turbulence and magnetic field signals from the Wind spacecraft to test the estimator's convergence to its true ensemble-averaged counterpart. Finally, we use this methodology on a fourteen-year-long Wind data interval to obtain the magnetic power spectrum of slow wind at extremely low frequencies. We show, for the first time, a full 1/f range in the slow wind, with a low-frequency spectral break below which the spectrum flattens and exhibits a well-defined peak at the solar rotation frequency.

Since its launch, the Parker Solar Probe (PSP) mission revealed the presence of numerous fascinating phenomena occurring closer to the Sun, such as the presence of ubiquitous switchbacks (SBs). The SBs are large magnetic field deflections of the local magnetic field relative to a background field. We investigated the statistical properties of the SBs during the first ten encounters between 13.3 and 70 Solar Radii using data from the SWEAP and FIELDS suites onboard PSP . We find that the occurrence rate of small deflections with respect to the Parker spiral decreases with radial distance (R). In contrast, the occurrence rate of the large deflections (SBs) increases with R, as does the occurrence rate of SB patches. We also find that the occurrence of SBs correlates with the bulk velocity of the solar wind, i.e., the higher the solar wind velocity, the higher the SB occurrence. For slow wind, the SB occurrence rate shows a constantly increasing trend between 13.3 and 70 solar radii. However, for fast wind, the occurrence rate saturates beyond 35 solar radii. Sub-Alfvenic regions encountered during encounters 8-10 have not shown significant SBs. This analysis of the PSP data hints that some of the SBs are decaying and some are being created in-situ.

We present EUV solar observations showing evidence for omnipresent jetting activity driven by small-scale magnetic reconnection at the base of the solar corona. We argue that the physical mechanism that heats and drives the solar wind at its source is ubiquitous magnetic reconnection in the form of small-scale jetting activity (a.k.a. jetlets). This jetting activity, like the solar wind and the heating of the coronal plasma, is ubiquitous regardless of the solar cycle phase. Each event arises from small-scale reconnection of opposite-polarity magnetic fields producing a short-lived jet of hot plasma and Alfvén waves into the corona. The discrete nature of these jetlet events leads to intermittent outflows from the corona, which homogenize as they propagate away from the Sun and form the solar wind. This discovery establishes the importance of small-scale magnetic reconnection in solar and stellar atmospheres in understanding ubiquitous phenomena such as coronal heating and solar wind acceleration. Based on previous analyses linking the switchbacks to the magnetic network, we also argue that these new observations might provide the link between the magnetic activity at the base of the corona and the switchback solar wind phenomenon. These new observations need to be put in the bigger picture of the role of magnetic reconnection and the diverse form of jetting in the solar atmosphere.

Since its launch in 2018, the Parker Solar Probe (PSP) mission revealed the presence of numerous fascinating phenomena occurring closer to the Sun, such as the presence of ubiquitous switchbacks (SBs). The SBs are large magnetic field deflections of the local magnetic field relative to a background field. We investigated the statistical properties of the SBs during the first 10 encounters between 13.28 and 58 solar radii ( R _⊙ ) using data from the SWEAP and FIELDS suites on board PSP. We find that the occurrence percentage of small deflections with respect to the Parker spiral decreases with radial distance ( R ). In contrast, the occurrence percentage of the large deflections (SBs) increases with R , as does the SB patches. We also find that the occurrence of SBs correlates with the bulk velocity of the solar wind, i.e., the higher the solar wind velocity, the higher the SB occurrence. For V _sw ≤ 400 km s ^−1 , the SB occurrence percentage shows a constantly increasing trend between 13 and 58 R _⊙ . However, for V _sw > 400 km s ^−1 , the occurrence percentage saturates beyond 35 R _⊙ . The occurrence percentage of mini SB patches (<60 s) shows a decreasing trend with R , while the occurrence percentage of long-duration SB patches (>200 s) increases with R . Sub-Alfvénic regions that we analyzed during Encounters 8–10 have not shown any SBs. This analysis of the PSP data hints that some of the SBs are decaying and some are being created in situ.

In this study, we probe the turbulence characteristic within the small-scale magnetic flux ropes (SSMFRs) close to the Sun using Parker Solar Probe (PSP) magnetic field data. The study includes 50 SSMFRs observed by PSP during Encounter 1, 2, and 3 between 35.74 R _☉ and 142.29 R _☉ distance from the Sun. We observed that the average spectral index for all the selected SSMFR events is –1.49 ± 0.21. In line with expectations, we also saw average ∣ σ _m ∣ values close to zero throughout the inertial range. We also observed that the size of the eddy at the highest frequency is much smaller than the size of the SSMFRs, indicating anisotropy within it. Thus, our finding supports anisotropic models that feature the Iroshnikov–Kraichnan index. Our findings agree with the turbulence properties of the solar wind near the Sun. We also observe low ∼0.1 compressibility, indicating SSMFRs are dominant by Alfvénic fluctuations. In light of this, we believe such an incompressible MHD spectrum results from nonlinear interactions between Alfvénic fluctuations. As a result, our research contributes to understanding the energy cascade process and its transport in solar plasma within the inner heliosphere.

Launched on 12 Aug. 2018, NASA’s Parker Solar Probe had completed 13 of its scheduled 24 orbits around the Sun by Nov. 2022. The mission’s primary science goal is to determine the structure and dynamics of the Sun’s coronal magnetic field, understand how the solar corona and wind are heated and accelerated, and determine what processes accelerate energetic particles. Parker Solar Probe returned a treasure trove of science data that far exceeded quality, significance, and quantity expectations, leading to a significant number of discoveries reported in nearly 700 peer-reviewed publications. The first four years of the 7-year primary mission duration have been mostly during solar minimum conditions with few major solar events. Starting with orbit 8 (i.e., 28 Apr. 2021), Parker flew through the magnetically dominated corona, i.e., sub-Alfvénic solar wind, which is one of the mission’s primary objectives. In this paper, we present an overview of the scientific advances made mainly during the first four years of the Parker Solar Probe mission, which go well beyond the three science objectives that are: (1) Trace the flow of energy that heats and accelerates the solar corona and solar wind; (2) Determine the structure and dynamics of the plasma and magnetic fields at the sources of the solar wind; and (3) Explore mechanisms that accelerate and transport energetic particles.

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In this Letter we investigate the dependency with scale of the empirical probability distribution functions (PDF) of Elsasser increments using large sets of WIND data (collected between 1995 and 2017) near 1 au. The empirical PDF are compared to the ones obtained from high-resolution numerical simulations of steadily driven, homogeneous reduced MHD turbulence on a 2048 3 rectangular mesh. A large statistical sample of Alfvénic increments is obtained by using conditional analysis based on the solar wind average properties. The PDF tails obtained from observations and numerical simulations are found to have exponential behavior in the inertial range, with an exponential decrement that satisfies power laws of the form α l ∝ l − μ , where l is the scale size, with μ between 0.17 and 0.25 for observations and 0.43 for simulations. PDF tails were extrapolated assuming their exponential behavior extends to arbitrarily large increments in order to determine structure function scaling laws at very high orders. Our results point to potentially universal scaling laws governing the PDF of Elsasser increments and to an alternative approach to investigate high-order statistics in solar wind observations.

Abstract Solar and stellar winds are ubiquitous flows of charged particles (i.e., electrons, protons, and heavier ions) permeating the astral spheres1. Through these winds, stars lose angular momentum, slow down their rotation as they age, shape planetary systems, and affect the composition and the physical and chemical evolution of planetary atmospheres and, consequently, the habitability of these planets2,3. How the solar wind is generated at the source, heated, and accelerated, and what determines its variability, are long-standing fundamental questions. Here we argue that the physical mechanism that heats and drives the solar wind at its source is ubiquitous magnetic reconnection in the form of small-scale jetting activity4. Jetlets, like the solar wind and the heating of the coronal plasma, are ubiquitous regardless of the solar cycle phase. Each event arises out of small-scale reconnection of opposite polarity magnetic fields producing a short-lived jet of hot plasma and Alfvén waves into the corona. The discrete nature of these jetlet events leads to intermittent outflows from the corona, which homogenize as they propagate away from the Sun and form the solar wind. This discovery establishes the importance of small-scale magnetic reconnection in solar and stellar atmospheres in understanding ubiquitous phenomena such as coronal heating and solar wind acceleration.

In this Letter, we report observations of magnetic switchback (SB) features near 1 au using data from the Wind spacecraft. These features appear to be strikingly similar to the ones observed by the Parker Solar Probe mission closer to the Sun: namely, one-sided spikes (or enhancements) in the solar-wind bulk speed V that correlate/anticorrelate with the spikes seen in the radial-field component B R . In the solar-wind streams that we analyzed, these specific SB features near 1 au are associated with large-amplitude Alfvénic oscillations that propagate outward from the Sun along a local background (prevalent) magnetic field B 0 that is nearly radial. We also show that, when B 0 is nearly perpendicular to the radial direction, the large-amplitude Alfvénic oscillations display variations in V that are two sided (i.e., V alternately increases and decreases depending on the vector Δ B = B − B 0). As a consequence, SBs may not always appear as one-sided spikes in V, especially at larger heliocentric distances where the local background field statistically departs from the radial direction. We suggest that SBs can be well described by large-amplitude Alfvénic fluctuations if the field rotation is computed with respect to a well-determined local background field that, in some cases, may deviate from the large-scale Parker field.

We investigate the validity of Taylor's hypothesis (TH) in the analysis of velocity and magnetic field fluctuations in Alfvenic solar wind streams measured by Parker Solar Probe (PSP) during the first four encounters. The analysis is based on a recent model of the spacetime correlation of magnetohydrodynamic (MHD) turbulence, which has been validated in high-resolution numerical simulations of strong reduced MHD turbulence. We use PSP velocity and magnetic field measurements from 24 h intervals selected from each of the first four encounters. The applicability of TH is investigated by measuring the parameter epsilon = delta u(0)/ root 2V(perpendicular to), which quantifies the ratio between the typical speed of large-scale fluctuations, delta u(0), and the local perpendicular PSP speed in the solar wind frame, V-perpendicular to. TH is expected to be applicable for epsilon <= 0.5 when PSP is moving nearly perpendicular to the local magnetic field in the plasma frame, irrespective of the Alfven Mach number M-A = V-SW/V-A, where V-SW and V-A are the local solar wind and Alfven speed, respectively. For the four selected solar wind intervals, we find that between 10 and 60% of the time, the parameter epsilon is below 0.2 and the sampling angle (between the spacecraft velocity in the plasma frame and the local magnetic field) is greater than 30 degrees For angles above 30 degrees, the sampling direction is sufficiently oblique to allow one to reconstruct the reduced energy spectrum E(k(perpendicular to)) of magnetic fluctuations from its measured frequency spectra. The spectral indices determined from power-law fits of the measured frequency spectrum accurately represent the spectral indices associated with the underlying spatial spectrum of turbulent fluctuations in the plasma frame. Aside from a frequency broadening due to large-scale sweeping that requires careful consideration, the spatial spectrum can be recovered to obtain the distribution of fluctuation's energy across scales in the plasma frame.

The fourth orbit of Parker Solar Probe (PSP) reached heliocentric distances down to 27.9 Rs, allowing solar wind turbulence and acceleration mechanisms to be studied in situ closer to the Sun than previously possible. The turbulence properties were found to be significantly different in the inbound and outbound portions of PSP's fourth solar encounter, likely due to the proximity to the heliospheric current sheet (HCS) in the outbound period. Near the HCS, in the streamer belt wind, the turbulence was found to have lower amplitudes, higher magnetic compressibility, a steeper magnetic field spectrum (with spectral index close to -5/3 rather than -3/2), a lower Alfvenicity, and a "1/f" break at much lower frequencies. These are also features of slow wind at 1 au, suggesting the near-Sun streamer belt wind to be the prototypical slow solar wind. The transition in properties occurs at a predicted angular distance of ~4 degrees from the HCS, suggesting ~8 degrees as the full-width of the streamer belt wind at these distances. While the majority of the Alfvenic turbulence energy fluxes measured by PSP are consistent with those required for reflection-driven turbulence models of solar wind acceleration, the fluxes in the streamer belt are significantly lower than the model predictions, suggesting that additional mechanisms are necessary to explain the acceleration of the streamer belt solar wind.