Solar Wind Turbulence Research Articles

Channel Estimation for Deep Space Communications Under the Effect of Solar Scintillation

AbstractDuring probe‐to‐Earth superior conjunction, deep space communication channels will suffer from solar scintillation, leading to amplitude attenuation of received signals. This study aims to obtain the channel state information (CSI) on deep space channels affected by solar scintillation. Classical least squares (LS) and minimum mean squared error (MMSE) methods are adopted to perform channel estimation and compensate for the channel fading. Simulation results indicate that under the effect of solar scintillation, performing channel estimation technology can significantly improve bit error rate (BER) performance compared to systems without CSI, and the MMSE algorithm outperforms the LS for both BER and normalized mean squared error (NMSE). In addition, we also find that pilot density, geometric parameters, and the outer scale of solar wind turbulence has great influence on the estimation performance.

On the 1/f Spectrum in Slow Solar Wind Turbulence: The Role of Alfvénicity

The slow solar wind has been recently observed to have a number of intervals that are dominated by large-scale Alfvénic 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 Alfvénic wind that is more similar to fast wind streams. The Alfvénic slow wind is usually differentiated from the typical slow wind (not dominated by Alfvénic fluctuations) by the normalized cross helicity, σ c . Values of ∣σ c ∣ near unity are associated with Alfvénic fluctuations, whereas values near zero are typically thought of as non-Alfvénic. This classification by cross helicity excludes the case of solar wind fluctuations dominated by balanced Alfvénic 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 Alfvénic 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 Alfvénic turbulence, whether the turbulence is balanced or imbalanced.

Investigating the Role of Inward Alfvén Waves and Structures in the Slow Solar Wind

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.

Observation of chaotic fluctuations in turbulent plasma

Turbulence is a prevalent phenomenon in space and astrophysical plasmas, often characterized by stochastic fluctuations. While laboratory experiments and numerical simulations have revealed chaotic behavior, in situ observations of turbulent plasmas in natural environments have predominantly shown highly stochastic signatures. Here, we present unprecedented in situ evidence of chaotic fluctuations in the turbulent solar wind plasma downstream of the Earth's bow shock. By analyzing the relative location of magnetic-field fluctuations on the permutation entropy–complexity plane, we demonstrate that turbulence in the magnetosheath plasma exhibits characteristics of chaotic fluctuations rather than stochastic behavior, diverging from the expected traits of well-developed turbulence. This finding challenges established notions of plasma turbulence and reveals the need for caution when using the magnetosheath as a laboratory for studying plasma turbulence.

The Independence of Magnetic Turbulent Power Spectra to the Presence of Switchbacks in the Inner Heliosphere

An outstanding gap in our knowledge of the solar wind is the relationship between switchbacks and solar wind turbulence. Switchbacks are large fluctuations, even reversals, of the background magnetic field embedded in the solar wind flow. It has been proposed that switchbacks may form as a product of turbulence and decay via coupling with the turbulent cascade. In this work, we examine how properties of solar wind magnetic field turbulence vary in the presence or absence of switchbacks. Specifically, we use in situ particle and fields measurements from Parker Solar Probe to measure magnetic field turbulent wave power, separately in the inertial and kinetic ranges, as a function of switchback magnetic deflection angle. We demonstrate that the angle between the background magnetic field and the solar wind velocity in the spacecraft frame (θ vB ) strongly determines whether Parker Solar Probe samples wave power parallel or perpendicular to the background magnetic field. Further, we show that θ vB is strongly modulated by the switchback magnetic deflection angle. In this analysis, we demonstrate that switchback deflection angle does not correspond to any significant increase in wave power in either the inertial range or at kinetic scales. This result implies that switchbacks do not strongly couple to the turbulent cascade in the inertial or kinetic ranges via turbulent wave–particle interactions. Therefore, we do not expect switchbacks to contribute significantly to solar wind heating through this type of energy conversion pathway although contributions via other mechanisms, such as magnetic reconnection, may still be significant.

Крупномасштабные связи геомагнитных индексов SYM-H и ASY-H с северо-южной компонентой ММП и бета-параметром солнечного ветра

Using annual average values, the relationships are examined of the geomagnetic indices SYM-H, ASY-H, and Dst with solar wind parameters in 1981–2015. The data used was divided into two samples according to the sign of the north-south component Bn of the interplanetary magnetic field (IMF). Variations in the annual average values of each of the Dst, SYM-H, and ASY-H indices for southward and northward IMF have been found to be similar and their linear correlation coefficients r to be high: 0.871, 0.863, and 0.943 respectively. The similarity between variations of the indices with different signs of Bn is probably due to their connection with the number of sunspots. It has been established that Dst, SYM-H, and ASY-H depend on the solar wind parameter β: their absolute values decrease with increasing β, regardless of Bn sign. The decrease in the indices with increasing β is likely to be caused by the transition of the magnetosphere to a quiet state due to the increasing predominance of thermal pressure over magnetic one in the solar wind and a decrease in the level of solar wind turbulence. SYM-H and ASY-H have been found to reveal the closest relationships with β, whereas SYM-H more strongly depends on β for southward IMF (r=0.744) than for northward IMF (r=0.677). On the contrary, for ASY-H r=–0.741 at northward IMF and r=–0.719 at southward IMF. Similar to SYM-H, Dst (to a lesser extent) significantly correlates with β at southward IMF (r=0.629) and weaker at northward IMF (r=0.456).

Large-scale relationships of the geomagnetic indices SYM-H and ASY-H with the north-south IMF component and the solar wind beta parameter

Using annual average values, the relationships are examined of the geomagnetic indices SYM-H, ASY-H, and Dst with solar wind parameters in 1981–2015. The data used was divided into two samples according to the sign of the north-south component Bn of the interplanetary magnetic field (IMF). Variations in the annual average values of each of the Dst, SYM-H, and ASY-H indices for southward and northward IMF have been found to be similar and their linear correlation coefficients r to be high: 0.871, 0.863, and 0.943 respectively. The similarity between variations of the indices with different signs of Bn is probably due to their connection with the number of sunspots. It has been established that Dst, SYM-H, and ASY-H depend on the solar wind parameter β: their absolute values decrease with increasing β, regardless of Bn sign. The decrease in the indices with increasing β is likely to be caused by the transition of the magnetosphere to a quiet state due to the increasing predominance of thermal pressure over magnetic one in the solar wind and a decrease in the level of solar wind turbulence. SYM-H and ASY-H have been found to reveal the closest relationships with β, whereas SYM-H more strongly depends on β for southward IMF (r=0.744) than for northward IMF (r=0.677). On the contrary, for ASY-H r=–0.741 at northward IMF and r=–0.719 at southward IMF. Similar to SYM-H, Dst (to a lesser extent) significantly correlates with β at southward IMF (r=0.629) and weaker at northward IMF (r=0.456).

A Potential Link between Space Weather and Atmospheric Parameters Variations: A Case Study of November 2021 Geomagnetic Storm

On 4 November 2021, during the rising phase of solar cycle 25, an intense geomagnetic storm (Kp = 8−) occurred. The effects of this storm on the outer magnetospheric region up to the ionospheric heights have already been examined in previous investigations. This work is focused on the analysis of the solar wind conditions before and during the geomagnetic storm, the high-latitude electrodynamics conditions, estimated through empirical models, and the response of the atmosphere in both hemispheres, based on parameters from the ECMWF ERA5 atmospheric reanalysis dataset. Our investigations are also supported by counter-test analysis and Monte Carlo tests. We find, for both hemispheres, a significant correspondence, within 1–2 days, between high-latitude electrodynamics variations and changes in the temperature, specific humidity, and meridional and zonal winds, in both the troposphere and stratosphere. The results indicate that, in the complex solar wind–atmosphere relationship, a significant role might be played by the intensification of the polar cap potential. We also study the reciprocal relation between the ionospheric Joule heating, calculated from a model, and two adiabatic invariants used in the analysis of solar wind turbulence.

The low-frequency power spectrum of slow solar wind turbulence

The low-frequency power spectrum of slow solar wind turbulence

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.

Testing for Markovian character of transfer of fluctuations in solar wind turbulence on kinetic scales.

We apply statistical analysis to search for processes responsible for turbulence in physical systems. In our previous studies, we have shown that solar wind turbulence in the inertial range of large magnetohydrodynamic scales exhibits Markov properties. We have recently extended this approach on much smaller kinetic scales. Here we are testing for the Markovian character of stochastic processes in a kinetic regime based on magnetic field and velocity fluctuations in the solar wind, measured onboard the Magnetospheric Multiscale (MMS) mission: behind the bow shock, inside the magnetosheath, and near the magnetopause. We have verified that the Chapman-Kolmogorov necessary conditions for Markov processes is satisfied for local transfer of energy between the magnetic and velocity fields also on kinetic scales. We have confirmed that for magnetic fluctuations, the first Kramers-Moyal coefficient is linear, while the second term is quadratic, corresponding to drift and diffusion processes in the resulting Fokker-Planck equation. It means that magnetic self-similar turbulence is described by generalized Ornstein-Uhlenbeck processes. We show that for the magnetic case, the Fokker-Planck equationleads to the probability density functions of the kappa distributions, which exhibit global universal scale invariance with a linear scaling and lack of intermittency. On the contrary, for velocity fluctuations, higher order Kramers-Moyal coefficients should be taken into account and hence scale invariance is not observed. However, the nonextensity parameter in Tsallis entropy provides a robust measure of the departure of the system from equilibrium. The obtained results are important for a better understanding of the physical mechanism governing turbulent systems in space and laboratory.

Modification of the turbulence properties at the bow shock: statistical results

Turbulent solar wind is known to be a main driver of the processes inside the magnetosphere, including geomagnetic storms and substorms. Experimental studies of the last decade demonstrate additional ways of interplanetary plasma transport to the magnetosphere, including small-scale processes in the magnetosphere boundary layers. This fact implies that properties of the solar wind turbulence can affect the geomagnetic activity. However, in front of the magnetosphere are a bow shock and a magnetosheath region which contribute to the changes in the properties of the solar wind turbulence and may result in destructions of the association between solar wind turbulence and the magnetosphere. The present study provides the statistics of two-point simultaneous measurements of the turbulence properties in the solar wind and the magnetosheath based on Wind and THEMIS spacecraft data. Changes in the turbulence properties are analyzed for different background conditions. Solar wind bulk speed and temperature are shown to be the main factors that influence the modification of turbulence at the quasi-perpendicular bow shock at frequencies higher than the break frequency (ion transition range). Inside the magnetosheath, significant steepening of spectra occurs with an increase in temperature anisotropy without a connection to the upstream spectrum scaling that underlines the crucial role of the instabilities in turbulence properties behind the bow shock.

Embedded Coherent Structures from Magnetohydrodynamics to Sub-ion Scales in Turbulent Solar Wind at 0.17 au

We study intermittent coherent structures in solar wind turbulence from MHD to kinetic plasma scales using Parker Solar Probe data during its first perihelion (at 0.17 au) in the highly Alfvénic slow solar wind. We detect coherent structures using Morlet wavelets. For the first time, we apply a multiscale analysis in physical space. At MHD scales within the inertial range, times scales τ ∈ (1, 102) s, we find (i) current sheets including switchback boundaries and (ii) Alfvén vortices. Within these events are embedded structures at smaller scales: typically Alfvén vortices at ion scales, τ ∈ (0.08, 1) s, and compressible vortices at sub-ion scales, τ ∈ 8(10−3, 10−2) s. The number of coherent structures grows toward smaller scales: we observe ∼200 events during a 5 hr time interval at MHD scales, ∼103 at ion scales, and ∼104 at sub-ion scales. In general, there are multiple structures of ion and sub-ion scales embedded within one MHD structure. There are also examples of ion and sub-ion scale structures outside MHD structures. To quantify the relative importance of different types of structures, we do a statistical comparison of the observed structures with the expectations of models of the current sheets and vortices. The results show the dominance of Alfvén vortices at all scales in contrast to the widespread view of the dominance of current sheets. This means that Alfvén vortices are important building blocks of Alfvénic solar wind turbulence.

The Incompressible Magnetohydrodynamic Energy Cascade Rate Upstream of Mars: Effects of the Total Energy and the Cross-helicity on Solar Wind Turbulence

Solar wind turbulence is a dynamical phenomenon that evolves with heliocentric distance. Orbiting Mars since 2014 September, Mars Atmosphere and Volatile EvolutioN offers a unique opportunity to explore some of its main properties beyond ∼1.38 au. Here, we analyze solar wind turbulence upstream of Mars' bow shock, utilizing more than 5 years of magnetic field and plasma measurements. This analysis is based on two complementary methodologies: (1) the computation of magnetohydrodynamic (MHD) invariants characterizing incompressible fluctuations; (2) the estimation of the incompressible energy cascade rate at MHD scales (i.e., 〈ε T 〉MHD). Our results show the solar wind incompressible fluctuations are primarily in a magnetically dominated regime, with the component traveling away from the Sun having a higher median pseudoenergy. Moreover, turbulent fluctuations have a total energy per mass of up to ∼ 300 km2 s−2, a range smaller than reported at 1 au. For these conditions, we determine the probability distribution function of 〈ε T 〉MHD ranges mainly between ∼ −1 × 10−16 and ∼1 × 10−16 J m−3 s −1, with a median equal to −1.8 × 10−18 J m−3 s −1, suggesting back transfer of energy. Our results also suggest that ∣〈ε T 〉MHD∣ is correlated with the total energy per mass of fluctuations and that the median of 〈ε T 〉MHD does not vary significantly with the cross-helicity. We find, however, that the medians of the inward and outward pseudoenergy cascade rates vary with the solar wind cross-helicity. Finally, we discuss these results and their implications for future studies that can provide further insight into the factors affecting the solar wind energy transfer rate.

The Relative Prevalence of Wave Packets and Coherent Structures in the Inertial and Kinetic Ranges of Turbulence as Seen by Solar Orbiter

The Solar Orbiter (SO) mission provides the opportunity to study the evolution of solar wind turbulence. We use SO observations of nine extended intervals of homogeneous turbulence to determine when turbulent magnetic field fluctuations may be characterized as: (i) wave packets and (ii) coherent structures (CSs). We perform the first systematic scale-by-scale decomposition of the magnetic field using two wavelets known to resolve wave packets and discontinuities, the Daubechies 10 (Db10) and Haar, respectively. The probability distribution functions (PDFs) of turbulent fluctuations on small scales exhibit stretched tails, becoming Gaussian at the outer scale of the cascade. Using quantile–quantile plots, we directly compare the wavelet fluctuations PDFs, revealing three distinct regimes of behavior. Deep within the inertial range (IR) both decompositions give essentially the same fluctuation PDFs. Deep within the kinetic range (KR) the PDFs are distinct as the Haar decompositions have larger variance and more extended tails. On intermediate scales, spanning the IR–KR break, the PDF is composed of two populations: a core of common functional form containing ∼97% of fluctuations, and tails that are more extended for the Haar decompositions than the Db10 decompositions. This establishes a crossover between wave-packet (core) and CS (tail) phenomenology in the IR and KR, respectively. The range of scales where the PDFs are two-component is narrow at 0.9 au (4–16 s) and broader (0.5–8 s) at 0.4 au. As CS and wave–wave interactions are both candidates to mediate the turbulent cascade, these results offer new insights into the distinct physics of the IR and KR.

Evaluation of Scale-dependent Kurtosis with HelioSwarm

Plasma turbulence involves complex, nonlinear interactions of electromagnetic fields and charged particles across multiple scales. Studying these phenomena in space plasmas, like the solar wind, is facilitated by the intrinsic scale separations and the availability of in situ spacecraft observations. However, the single-point or single-scale configurations of current spacecraft limit our understanding of many properties of the turbulent solar wind. To overcome these limitations, multipoint measurements spanning a range of characteristic scales are essential. This Letter prepares for the enhanced measurement capabilities of upcoming multispacecraft missions by demonstrating that higher-order statistics, specifically kurtosis, as a baseline for intermittency can be accurately measured. Using synthetic turbulent fields with adjustable intermittency levels, we achieve scale separations analogous to those in the solar wind and apply these techniques to the planned trajectories of the HelioSwarm mission. This approach promises significant advancements in our understanding of plasma turbulence.

Large-scale Linear Magnetic Holes with Magnetic Mirror Properties in Hybrid Simulations of Solar Wind Turbulence

Magnetic holes (MHs) are coherent magnetic field dips whose size ranges from fluid to kinetic scale, ubiquitously observed in the heliosphere and in planetary environments. Despite the long-standing effort in interpreting the abundance of observations, the origin and properties of MHs are still debated. In this Letter, we investigate the interplay between plasma turbulence and MHs, using a 2D hybrid simulation initialized with solar wind parameters. We show that fully developed turbulence exhibits localized elongated magnetic depressions, whose properties are consistent with linear MHs frequently encountered in space. The observed MHs develop self-consistently from the initial magnetic field perturbations by trapping hot ions with large pitch angles. Ion trapping produces an enhanced perpendicular temperature anisotropy that makes MHs stable for hundreds of ion gyroperiods, despite the surrounding turbulence. We introduce a new quantity, based on local magnetic field and ion temperature values, to measure the efficiency of ion trapping, with potential applications to the detection of MHs in satellite measurements. We complement this method by analyzing the ion velocity distribution functions inside MHs. Our diagnostics reveal the presence of trapped gyrotropic ion populations, whose velocity distribution is consistent with a loss cone, as expected for the motion of particles inside a magnetic mirror. Our results have potential implications for the theoretical and numerical modeling of MHs.

Anisotropy of Magnetohydrodynamic and Kinetic Scale Fluctuations through Correlation Tensor in Solar Wind at 0.8 au

Space plasma turbulence is inherently characterized by anisotropic fluctuations. The generalized k-th order correlation tensor of magnetic field increments allow us to separate the mixed isotropic and anisotropic structure functions from the purely anisotropic ones. In this work, we quantified the relative importance of anisotropic fluctuations in solar wind turbulence using two Alfvénic data samples gathered by the Solar Orbiter at 0.8 astronomical units. The results based on the joined statistics suggest that the anisotropic fluctuations are ubiquitous in solar wind turbulence and persist at kinetic scales. Using the RTN coordinate system, we show that their presence depends on the anisotropic sector under consideration, e.g., the RN and RT sectors exhibit enhanced anisotropy toward kinetic scales, in contrast with the TN. We then study magnetic field fluctuations parallel and perpendicular to the local mean magnetic field separately. We find that perpendicular fluctuations are representative of the global statistics, resembling the typical picture of magnetohydrodynamic turbulence, whereas parallel fluctuations exhibit a scaling law with slope ∼1 for all the joined isotropic and anisotropic components. These results are in agreement with predictions based on the critical balance phenomenology. This topic is potentially of interest for future space missions measuring kinetic and MHD scales simultaneously in a multi-spacecraft configuration.

LAPS: An MPI-parallelized 3D pseudo-spectral Hall-MHD simulation code incorporating the expanding box model

Numerical simulations have been an increasingly important tool in space physics. Here, we introduce an open-source three-dimensional compressible Hall-Magnetohydrodynamic (MHD) simulation code LAPS (UCLA-Pseudo-Spectral, https://github.com/chenshihelio/LAPS). The code adopts a pseudo-spectral method based on Fourier Transform to evaluate spatial derivatives, and third-order explicit Runge-Kutta method for time advancement. It is parallelized using Message-Passing-Interface (MPI) with a “pencil” parallelization strategy and has very high scalability. The Expanding-Box-Model is implemented to incorporate spherical expansion effects of the solar wind. We carry out test simulations based on four classic (Hall)-MHD processes, namely, 1) incompressible Hall-MHD waves, 2) incompressible tearing mode instability, 3) Orszag-Tang vortex, and 4) parametric decay instability. The test results agree perfectly with theory predictions and results of previous studies. Given all its features, LAPS is a powerful tool for large-scale simulations of solar wind turbulence as well as other MHD and Hall-MHD processes happening in space.

A Tempered Fractional Kinetic Transport Theory for Energetic Particle Interaction with Quasi-two-dimensional Turbulence in the Large-scale Solar Wind

Observational evidence is accumulating that turbulence in the solar wind is intermittent (non-Gaussian) because of the strong presence of a quasi-two-dimensional (quasi-2D), low-frequency turbulence component containing nonpropagating, closed, small-scale magnetic flux ropes with open meandering field lines in between. le Roux & Zank showed how one can derive fractional focused and Parker-type transport equations that model large-scale anomalous transport in the solar wind as the outcome of energetic particle interaction with quasi-2D turbulence. In this follow-up paper this theory is developed further to address certain limitations. (i) The second moment of the Lévy probability distribution function (PDF) specified in the theory for the particle step size is infinite, indicating unphysical transport. (ii) The expected transition of energetic particle transport from anomalous to normal diffusion beyond a certain critical transport distance was not included. (iii) The competition between anomalous diffusion and advection is not properly sustained at late times. Shortcomings (i) and (ii) are addressed by introducing an exponentially truncated Lévy PDF for the energetic particle step size in the theory, resulting in revised tempered fractional focused and Parker-type transport equations featuring tempered fractional derivatives that enable modeling of tempered Lévy flights. Furthermore, these equations are cast in a tempered fractional telegrapher form to investigate whether the fractional wave equation part of the equation can restore causality in unscattered particle transport during early times and in Lévy flights during intermediate times (Lévy walks). They are also transformed into a tempered fractional Fokker–Planck form to overcome limitation (iii).