Solar Wind Turbulence Research Articles

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).

Magnetopause MHD surface wave theory: progress & challenges

Sharp boundaries are a key feature of space plasma environments universally, with their wave-like motion (driven by pressure variations or flow shears) playing a key role in mass, momentum, and energy transfer. This review summarises magnetohydrodynamic surface wave theory with particular reference to Earth’s magnetopause, due to its mediation of the solar-terrestrial interaction. Basic analytic theory of propagating and standing surface waves within simple models are presented, highlighting many of the typically-used assumptions. We raise several conceptual challenges to understanding the nature of surface waves within a complex environment such as a magnetosphere, including the effects of magnetic topology and curvilinear geometry, plasma inhomogeneity, finite boundary width, the presence of multiple boundaries, turbulent driving, and wave nonlinearity. Approaches to gain physical insight into these challenges are suggested. We also discuss how global simulations have proven a fruitful tool in studying surface waves in more representative environments than analytic theory allows. Finally, we highlight strong interdisciplinary links with solar physics which might help the magnetospheric community. Ultimately several upcoming missions provide motivation for advancing magnetopause surface wave theory towards understanding their global role in filtering, accumulating, and guiding turbulent solar wind driving.

Anisotropy of Density Fluctuations in the Solar Wind at 1 au

A well-known property of solar wind plasma turbulence is the observed anisotropy of the autocorrelations, or equivalently the spectra, of velocity and magnetic field fluctuations. Here we explore the related but apparently not well-studied issue of the anisotropy of plasma density fluctuations in the energy-containing and inertial ranges of solar wind turbulence. Using 10 yr (1998–2008) of in situ data from the Advanced Composition Explorer mission, we find that for all but the fastest wind category, the density correlation scale is slightly larger in directions quasi-parallel to the large-scale mean magnetic field as compared to quasi-perpendicular directions. The correlation scale in fast wind is consistent with isotropic. The anisotropy as a function of the level of correlation is also explored. We find at small correlation levels, i.e., at energy-containing scales and larger, the density fluctuations are close to isotropy for fast wind, and slightly favor more rapid decorrelation in perpendicular directions for slow and medium winds. At relatively smaller (inertial range) scales where the correlation values are larger, the sense of anisotropy is reversed in all speed ranges, implying a more “slablike” structure, especially prominent in the fast wind samples. We contrast this finding with published results on velocity and magnetic field correlations.

The unsolved problem of solar-wind turbulence

The solar wind forms the largest wind tunnel for plasma and magnetofluid turbulence that is accessible to Earth. It evolves from what is thought to be a turbulent source that continues to drive nonlinear turbulent dynamics as it expands outward via large-scale, energy-containing wind shear and shocks. In the outer heliosphere, once the gradients in the flow have coalesced and they no longer provide an adequate source for the turbulence, the excitation of wave energy by the injection of interstellar pickup ions becomes the dominant source of energy that continues to drive the turbulence. While there are established formalisms for the determination of the strength of the turbulence and the evolution of the turbulent spectra is well-established, the actual nonlinear dynamics that are responsible for its formation and evolution remain unresolved and the subject of considerable debate. We examine the evidence and attempt to illuminate the various theories while demonstrating what is needed to resolve the debates and bring the subject of plasma turbulence into a new level of understanding.

Temperature Intermittent Structures in the Fast Solar Wind

In the solar wind turbulence, proton temperature fluctuations are highly intermittent, especially at small scales in the inertial range. This phenomenon may contain information about solar wind intermittent heating. However, the physical nature of the temperature intermittency is not yet clear. Based on the measurements from Solar Orbiter between 2020 September and 2022 September, we identify 185 temperature intermittent structures at the scale of 24 s with well-defined minimum variance direction in the fast solar wind and study the nature and kinetic effects of them. According to the variations of proton temperature, the intermittent structures are classified into four types, including temperature bump, step, dip, and chain. When considering the magnetic field configuration together with other plasma properties, we find that, among the bump cases, 46 of them are linear magnetic holes (LMHs) that are mainly related to mirror-mode (MM) instability, and 43 of them are current sheets (CSs) with local temperature enhancement. The step cases are found to be associated with shock-like structures (13 cases) and tangential discontinuities (eight cases) that separate two different parcels of plasma. For the dip cases, 21 of them could be associated with the MM instability, and the rest of the 16 ones may prefer soliton scenario. The 38 chain cases are identified as compressive vortex-like structures and a mixture of LMHs and CSs. These results will help to further understand the intermittent dissipation process in the solar wind turbulence.

Evolution of the magnetic field rotation distributions in the inner heliosphere

The nature and evolution of the solar wind magnetic field rotations is studied in data from the Parker Solar Probe We investigated the magnetic field deflections in the inner heliosphere below 0.5 au in a distance- and scale-dependent manner to shed some light on the mechanism behind their evolution. We used the magnetic field data from the FIELDS instrument suite to study the evolution of the magnetic field vector increment and rotation distributions that contain switchbacks. We find that the rotation distributions evolve in a scale-dependent fashion. They have the same shape at small scales regardless of the radial distance, in contrast to larger scales, where the shape evolves with distance. The increments are shown to evolve towards a log-normal shape with increasing radial distance, even though the log-normal fit works quite well at all distances, especially at small scales. The rotation distributions are shown to evolve towards a previously developed rotation model moving away from the Sun. Our results suggest a scenario in which the evolution of the rotation distributions is primarily the result of the expansion-driven growth of the fluctuations, which are reshaped into a log-normal distribution by the solar wind turbulence.

Radial Spectral Evolution of the Elsässer Variable z − in the Slow Solar Wind

The nature of the Elsässer variable z − plays a significant role in the understanding of solar wind turbulence. The radial spectral evolution of z − observed by the Helios spacecraft suggests that z − has a persistent background spectrum in the low-frequency range from 0.3 to 1 au. However, the radial evolution in the near-Sun solar wind remains unknown. Here we use Parker Solar Probe measurements to analyze the averaged spectra of z − in the slow solar wind from 0.1 to 0.5 au and compare the results with the WIND observations at 1 au. We find that the averaged spectra of z − do not show the low-frequency break at the low-frequency breakpoint on the power spectra of z +, magnetic field, and velocity. The energy in the frequency range of 10−4–10−2 Hz demonstrates a radial decay from 0.1 to 0.5 au and keeps nearly constant to 1 au. The spectral index of z − gradually decreases from −1.27 at 0.1–0.2 au to −1.59 at 0.4–0.5 au and then slowly declines to −1.70 at 1 au. The radial behaviors of the ∥, ⊥1, and ⊥2 components of z − in the field-aligned coordinates are similar to that of the trace of z −. Our findings suggest a faster radial spectral evolution of z − in the near-Sun solar wind and provide strong observational constraints for the solar wind turbulence model.

A numerical study of electron-magnetohydrodynamics tearing modes in parameter ranges of experimental interest

We perform a numerical study of the linear dynamics of tearing modes in slab incompressible electron-magnetohydrodynamics (EMHD) by considering some parameter ranges, which can be of interest for laboratory plasmas (e.g., helicon devices) or for astrophysics (e.g., solar-wind turbulence). To this purpose, several non-ideal effects are simultaneously retained (finite electron inertia, resistivity, and electron viscosity), and we make distinction between the dissipation coefficients in the direction parallel and perpendicular to the guide field. We thus identify some new reconnection regimes, characterized by a departure from the customary monotonic power-law scalings of the growth rates with respect to the non-ideal parameters. The results here presented can provide a useful indication for future studies of EMHD regimes relevant to experiments and for extensions of the EMHD tearing mode modeling to more complete regimes including kinetic effects (e.g., “electron-only” reconnection in kinetic regimes).

Parametric description of intermittent probability distribution functions in solar wind and magnetohydrodynamic turbulence

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.

The Opposite Behaviors of Proton and Electron Temperatures in Relation to Solar Wind Magnetic Energy: Parker Solar Probe Observations

Solar wind heating is an outstanding issue that has been discussed for decades. Research on the connection between solar wind particle temperatures and turbulence may provide insight into this issue. Based on Parker Solar Probe observations, this paper investigates the properties of solar wind proton and electron temperatures in relation to turbulent magnetic energy, via the calculation of correlation coefficients (CCs) between particle temperatures and magnetic energy. The calculations are regulated by the spatial scale, plasma beta (β), and the angle between the solar wind velocity and background magnetic field, where the plasma beta is the ratio of plasma thermal to magnetic pressure. Results show that the correlation between proton temperature and magnetic energy is positive and can be strong with a CC exceeding 0.8. The strong correlation preferentially occurs at ion scales, with the wind velocity and background magnetic field quasi-perpendicular and over a wide beta range (β < 3.0). On the other hand, the correlation between electron temperature and magnetic energy is commonly negative, often with an intermediate or negligible CC, accordingly. The CC with an amplitude up to 0.8 can arise at larger scales with the wind velocity and background magnetic field quasi-(anti)parallel and in the low-beta case (β < 0.6). The implication of these findings on the physics of turbulent heating in the solar wind is discussed.

MHD Inertial and Energy-containing Range Turbulence Anisotropy in the Young Solar Wind

We study solar wind turbulence anisotropy in the inertial and energy-containing ranges in the inbound and outbound directions during encounters 1–9 by the Parker Solar Probe (PSP) for distances between ∼21 and 65 R ⊙. Using the Adhikari et al. approach, we derive theoretical equations to calculate the ratio between the 2D and slab fluctuating magnetic energy, fluctuating kinetic energy, and the outward/inward Elsässer energy in the inertial range. For this, in the energy-containing range, we assume a wavenumber k −1 power law. In the inertial range, for the magnetic field fluctuations and the outward/inward Elsässer energy, we consider that (i) both 2D and slab fluctuations follow a power law of k −5/3, and (ii) the 2D and slab fluctuations follow the power laws with k −5/3 and k −3/2, respectively. For the velocity fluctuations, we assume that both the 2D and slab components follow a k −3/2 power law. We compare the theoretical results of the variance anisotropy in the inertial range with the derived observational values measured by PSP, and find that the energy density of 2D fluctuations is larger than that of the slab fluctuations. The theoretical variance anisotropy in the inertial range relating to the k −5/3 and k −3/2 power laws between 2D and slab turbulence exhibits a smaller value in comparison to assuming the same power law k −5/3 between 2D and slab turbulence. Finally, the observed turbulence energy measured by PSP in the energy-containing range is found to be similar to the theoretical result of a nearly incompressible/slab turbulence description.

Validity of using Elsässer variables to study the interaction of compressible solar wind fluctuations with a coronal mass ejection

Context. Alfvénic fluctuations, as modelled by the non-linear interactions of Alfvén waves of various scales, are seen to dominate solar wind turbulence. However, there is also a non-negligible component of non-Alfvénic fluctuations. The Elsässer formalism, which is central to the study of Alfvénic turbulence due to its ability to differentiate between parallel and anti-parallel Alfvén waves, cannot strictly separate wavemodes in the presence of compressive magnetoacoustic waves. In this study, we analyse the deviations generated in the Elsässer formalism as density fluctuations are naturally generated through the propagation of a linearly polarised Alfvén wave. The study was performed in the context of a coronal mass ejection (CME) propagating through the solar wind, which enables the creation of two solar wind regimes, pristine wind and a shocked CME sheath, where the Elsässer formalism can be evaluated. Aims. We studied the deviations of the Elsässer formalism in separating parallel and anti-parallel components of Alfvénic solar wind perturbations generated by small-amplitude density fluctuations. Subsequently, we evaluated how the deviations cause a misinterpretation of the composition of waves through the parameters of cross helicity and reflection coefficient. Methods. We used an ideal 2.5D magnetohydrodynamic model with an adiabatic equation of state. An Alfvén pump wave was injected into the quiet solar wind by perturbing the transverse magnetic field and velocity components. This wave subsequently generates density fluctuations through the ponderomotive force. A CME was injected by inserting a flux-rope modelled as a magnetic island into the quasi-steady solar wind. Results. The presence of density perturbations creates a ≈10% deviation in the Elsässer variables and reflection coefficient for the Alfvén waves as well as a deviation of ≈0.1 in the cross helicity in regions containing both parallel and anti-parallel fluctuations.

Exploring Observational Heliophysics Across All Scales: Reflections and Insights From the 2023 NASA Heliophysics Summer School

AbstractThe field of heliophysics encompasses a diverse range of research areas and rich plasma environments, from the solar dynamo and solar wind turbulence, to the complex terrestrial thermosphere‐ionosphere‐magnetosphere (TIM) system, to investigations of both induced and intrinsic magnetospheres across the solar system. This perspective paper delves into the experiences and outcomes of a summer school held in person in Boulder, Colorado, USA, from 7–11 August, which offered a platform for interdisciplinary learning and collaboration. The event, supported by NASA's Living with a Star program and hosted by the University Corporation for Atmospheric Research and Cooperative Programs for the Advancement of Earth System Science, assembled a cohort of 26 graduate students and postdoctoral researchers from around the world, all engaged in heliophysics research. The summer school included a series of lectures, interactive activities, and a culminating capstone project. The participants' diverse backgrounds enriched discussions and encouraged novel approaches to traditional problems. The capstone projects spanned an array of topics, including investigating the origins of solar wind switchbacks, dissecting the sequence of events from solar eruptions and their corresponding terrestrial consequences, investigating the energy transfer from solar coronal mass ejections to Earth's magnetosphere, and advocating for the exploration of Coulomb collisions in understanding large‐scale global systems. Through this perspective, we shed light on the value of international and interdisciplinary collaboration in advancing heliophysics research. This perspective paper encapsulates the ethos of the summer school, serving as a testament to the continuing and collective pursuit of unraveling the mysteries of the heliosphere.

Monofractality in the Solar Wind at Electron Scales: Insights from Kinetic Alfvén Waves Turbulence.

The breakdown of scale invariance in turbulent flows, known as multifractal scaling, is considered a cornerstone of turbulence. In solar wind turbulence, a monofractal behavior can be observed at electron scales, in contrast to larger scales where multifractality always prevails. Why scale invariance appears at electron scales is a challenging theoretical puzzle with important implications for understanding solar wind heating and acceleration. We investigate this long-standing problem using direct numerical simulations of three-dimensional electron reduced magnetohydrodynamics. Both weak and strong kinetic Alfvén waves turbulence regimes are studied in the balanced case. After recovering the expected theoretical predictions for the magnetic spectra, a higher-order multiscale statistical analysis is performed. This study reveals a striking difference between the two regimes, with the emergence of monofractality only in weak turbulence, whereas strong turbulence is multifractal. This result, combined with recent studies, shows the relevance of collisionless weak KAW turbulence to describe the solar wind at electron scales.

Heliospheric Diffusion of Stochastic Parker Spirals in Radially Evolving Solar Wind Turbulence

We present a stochastic field line mapping model where the interplanetary magnetic field lines are described by a density distribution function satisfying a Fokker–Planck equation that is solved numerically. Due to the spiral geometry of the nominal Parker field and to the evolving nature of solar wind turbulence, the heliospheric diffusion of the magnetic field lines is both heterogeneous and anisotropic, including a radial component. The longitudinal distributions of the magnetic field lines are shown to be close to circular Gaussian distributions, although they develop a noticeable skewness. The magnetic field lines emanating from the Sun are found to differ, on average, from the spirals predicted by Parker. Although the spirals remain close to Archimedean, they are here underwound, on average. Our model predicts a spiral angle that is smaller by ∼5° than the Parker spiral angle at Earth’s orbit for the same solar wind speed of V sw = 400 km s−1. It also predicts an angular position on the solar disk of the best magnetically connected footpoint to an observer at 1 au that is shifted westward by ∼10° with respect to the Parker’s field model. This significantly changes the angle of the most probable magnetic connection between possible sources on the Sun and observers in the inner heliosphere. The results have direct implications for the heliospheric transport of “scatter-free” electrons accelerated in the aftermath of solar eruptions.

Coherence of Elsässer Variables in the slow solar wind from 0.1 au to 0.3 au

The highly Alfvénic fluctuations (AF) and magnetic-velocity alignment structures (MVAS) are two distinguished components in the near-Sun slow solar wind observed by Parker Solar Probe. The amplitudes of the Elsässer Variables z± of AF and MVAS show distinct features. However, how these fluctuations contribute to the slow solar wind turbulence remains unknown. Here we investigate the coherence between z+ and z− for the first time using the Parker Solar Probe measurements with a high resolution 0.8738 s in the slow solar wind from 0.1–0.3 au. We find that the coherence spectra of z+ and z− in the perpendicular directions for MVAS are remarkable higher than that for AF, in particular at large scale. There exists a break around 10 di (di is the ion inertial length) where the coherence decreases to a lower level for MVAS. A bump around 10 di appears on the coherence spectra of all three components for AF. The coherence of z+ and z− may relate to the possible nonlinear interactions reflected by the time series, the power spectra, and the self-correlation functions. These results help to understand the roles of AF and MVAS in the slow solar wind turbulence.

Identifying kinetic scale magnetic discontinuity structures in turbulent solar wind

Identifying kinetic scale magnetic discontinuity structures in turbulent solar wind