Solar Wind Turbulence Research Articles

Phase coherence of solar wind turbulence from the Sun to Earth

The transport of energetic particles in response to solar wind turbulence is important for space weather. To understand charged particle transport, it is usually assumed that the phase of the turbulence is randomly distributed (the random phase approximation) in quasi-linear theory and simulations. In this paper, we calculate the coherence index, Cϕ, of solar wind turbulence observed by the Helios 2 and Parker Solar Probe spacecraft using the surrogate data technique to check if the assumption is valid. Here, values of Cϕ = 0 and 1 indicate that the phase coherence is random and correlated, respectively. We estimate that the coherence index at the resonant scale of energetic ions (10 MeV protons) is 0.1 at 0.87 and 0.65 au, 0.18 at 0.29 au, and 0.3 (0.35) at 0.09 au for super (sub)-Alfvénic intervals, respectively. Since the random phase approximation corresponds to Cϕ = 0, this may indicate that the random phase approximation is not valid for the transport of energetic particles in the inner heliosphere, especially very close to the Sun (∼0.09 au).

Scaling Anisotropy with Stationary Background Field in Near-Sun Solar Wind Turbulence

The scaling of magnetic fluctuations provides crucial information for the understanding of solar wind turbulence. However, the observed magnetic fluctuations contain not only turbulence but also magnetic structures, leading to the violation of time stationarity. This violation would conceal the true scaling and influence the determination of the sampling angle with respect to the local background magnetic field. Here, to investigate scaling anisotropy, we utilize a simple but effective criterion ϕ < 10° to ensure the time stationarity of the magnetic field, where ϕ is the angle between the two averaged magnetic fields after cutting the interval into two halves. We study the scaling anisotropy using higher-order statistics of structure functions under the condition of stationarity for near-Sun solar wind turbulence for the first time based on measurements obtained from the Parker Solar Probe at 0.17 au. We find that the scaling indices ξ of the magnetic field show a linear dependence on the order p close to ξ(p) = p/4. The multifractal scaling of the magnetic-trace structure functions becomes monoscaling close to ξ(p) = p/3 with the local magnetic field perpendicular to the sampling direction and close to ξ(p) = p/4 with the local magnetic field parallel to the sampling direction when measured with the stationary background magnetic field. The scaling of the velocity-trace structure functions has similar but less significant changes. The near-Sun solar wind turbulence displays different scaling anisotropies from the near-Earth solar wind turbulence, suggesting the evolution of the nonlinear interaction process during solar wind expansion.

Intermittency of Magnetic Discontinuities in the Near-Sun Solar Wind Turbulence

The intermittency domain is in the magnetohydrodynamic inertial range but just above the dissipation range and contains the intermittent structures that influence the spectral index. However, the nature of these structures is still under debate and how they affect the higher-order scaling behavior in the near-Sun solar wind turbulence remains to be investigated. Here we use the magnetic field data measured by Parker Solar Probe in the near-Sun solar wind. We identify the intermittency by partial variance of increments method and conduct the multiorder structure functions analyses in the intermittency domain before and after removing the intermittency. We also perform for the first time the scaling analyses on the fluctuations of magnetic field direction given by the rotational angle , in which B 1 and B 2 are the magnetic fields measured at two instants. We find that the multifractal scaling of the magnetic field could be predicted by the log-Poisson intermittency model with 2D sheetlike structures and a simple Kolmogorov −5/3 monoscaling recovers after the removal of the intermittency. We also find a similar behavior for the scalings of θ, suggesting that magnetic discontinuities are involved in the energy transfer process of solar wind turbulence.

On the Interpretation of the Scalings of Density Fluctuations from In Situ Solar Wind Observations: Insights from 3D Turbulence Simulations

Solar wind turbulence is often perceived as weakly compressible and the density fluctuations remain poorly understood both theoretically and observationally. Compressible magnetohydrodynamic simulations provide useful insights into the nature of density fluctuations. We discuss a few important effects related to 3D simulations of turbulence and in situ observations. The observed quantities such as the power spectrum and variance depend on the angle between the sampling trajectory and the mean magnetic field due to anisotropy of the turbulence. The anisotropy effect is stronger at smaller scales and lower plasma beta. Additionally, in situ measurements tend to exhibit a broad range of variations, even though they could be drawn from the same population with the defined averages, so a careful averaging may be needed to reveal the scaling relations between density variations and other turbulence quantities such as turbulent Mach number from observations.

Effect of intermittent structures on the spectral index of the magnetic field in the slow solar wind

Abstract. Intermittent structures are ubiquitous in the solar wind turbulence, and they can significantly affect the power spectral index (which reflects the cascading process of the turbulence) of magnetic field fluctuations. However, to date, an analytical relationship between the intermittency level and the magnetic spectral index has not been shown. Here, we present the continuous variation in the magnetic spectral index in the inertial range as a function of the intermittency level. Using the measurements from the Wind spacecraft, we find 42 272 intervals with different levels of intermittency and with a duration of 5–6 min from 46 slow-wind streams between 2005 and 2013. Among them, each of the intermittent intervals is composed of one dominant intermittent structure and background turbulent fluctuations. For each interval, a magnetic spectral index αB is determined for the Fourier spectrum of the magnetic field fluctuations in the inertial range between 0.01 and 0.3 Hz. A parameter Imax, which corresponds to the maximum of the trace of the partial variance increments of the intermittent structure, is introduced as an indicator of the intermittency level. Our statistical result shows that, as Imax increases from 0 to 20, the magnetic spectrum becomes gradually steeper and the magnetic spectral index αB decreases from −1.63 to −2.01. Accordingly, for the first time, an empirical relation is established between αB and Imax: αB=0.4exp⁡(-Imax/5)-2.02. The result will help us to uncover more details about the contributions of the intermittent structures to the magnetic power spectra and, furthermore, about the physical nature of the energy cascade taking place in the solar wind. It will also help to improve turbulence theories that contain intermittent structures.

Helios 2 observations of solar wind turbulence decay in the inner heliosphere

Aims. A linear scaling of the mixed third-order moment of the magnetohydrodynamic (MHD) fluctuations is used to estimate the energy transfer rate of the turbulent cascade in the expanding solar wind. Methods. In 1976, the Helios 2 spacecraft measured three samples of fast solar wind originating from the same coronal hole, at different distances from the Sun. Along with the adjacent slow solar wind streams, these intervals represent a unique database for studying the radial evolution of turbulence in samples of undisturbed solar wind. A set of direct numerical simulations of the MHD equations performed with the Lattice-Boltzmann code FLAME was also used for interpretation. Results. We show that the turbulence energy transfer rate decays approximately as a power law of the distance and that both the amplitude and decay law correspond to the observed radial temperature profile in the fast wind case. Results from MHD numerical simulations of decaying MHD turbulence show a similar trend for the total dissipation, suggesting an interpretation of the observed dynamics in terms of decaying turbulence and that multi-spacecraft studies of the solar wind radial evolution may help clarify the nature of the evolution of the turbulent fluctuations in the ecliptic solar wind.

Interaction between the turbulent solar wind and a planetary magnetosphere: A 2D comet example

Context. Using the newly developed code Menura, we present the first global picture of the interaction between a turbulent solar wind and a planetary obstacle in our solar system, namely a comet. Aims. This first publication sheds light on the macroscopic effect of the upstream solar wind turbulence on the induced magnetosphere of a comet. Methods. Using a hybrid particle-in-cell simulation code, we modelled a medium activity comet using turbulent and laminar solar wind input, for a direct comparison between the two regimes. Results. We show how the turbulent characteristics of the solar wind lead to a smaller obstacle size. We then present how the upstream turbulent structures, traced by the perpendicular magnetic field fluctuations absent in the laminar case, self-consistently drape and pile up around the denser inner coma, forming intense plasmoids downstream of the nucleus, pulling away dense cometary ion bubbles. This pseudo-periodic erosion phenomenon re-channels the global cometary ion escape; as a result, the innermost coma is found to be on average 45% less dense in the turbulent case than predicted by simulating a laminar upstream flow.

Imbalanced Turbulence Modified by Large-scale Velocity Shears in the Solar Wind

We have investigated how the degree of imbalance in solar wind turbulence is modified by large-scale velocity shears in the solar wind plasma. The balance between counterpropagating Alfvénic fluctuations, which interact nonlinearly to generate the turbulence, has been quantified by the cross helicity and Elsasser ratio. Velocity shears at a 30 minute timescale were identified, with the shear amplitude defined in terms of the linear Kelvin–Helmholtz (KH) instability threshold. The shears were associated with 74 interplanetary coronal mass ejection (ICME) sheaths observed by the Wind spacecraft at 1 au between 1997 and 2018. Typically weaker shears upstream of the sheaths and downstream in the ICME ejecta were also analyzed. In shears below the KH threshold, imbalance was approximately invariant or weakly rising with shear amplitude. Above the KH threshold, fluctuations tended toward a balanced state with increasing shear amplitude. Magnetic compressibility was also found to increase above the KH threshold. These findings are consistent with velocity shears being local sources of sunward fluctuations that act to reduce net imbalances in the antisunward direction, and suggest that the KH instability plays a role in this process.

A statistical study of the compressible energy cascade rate in solar wind turbulence: Parker solar probe observations

We investigated incompressible and compressible magnetohydrodynamic (MHD) energy cascade rates in the solar wind at different heliocentric distances. We used in situ magnetic field and plasma observations provided by the Parker Solar Probe mission and exact relations in fully developed turbulence. To estimate the compressible cascade rate, we applied two recent exact relations for compressible isothermal and polytropic MHD turbulence, respectively. Our observational results show a clear increase in the absolute value of the compressible and incompressible cascade rates as we get closer to the Sun. Moreover, we obtained an increase in both isothermal and polytropic cascade rates with respect to the incompressible case as compressibility increases in the plasma. Further discussion about the relation between the compressibility and the heliocentric distance is carried out. Furthermore, we compared both exact relations as compressibility increases in the solar wind, and although we note a slight trend to observe larger cascades using a polytropic closure, we obtained essentially the same cascade rate in the range of compressibility observed. Finally, we investigated the signed incompressible and compressible energy cascade rates and its connection with the real cascade rate.

Density Derivation Using Controlled Spacecraft Potential in Earth's Magnetosheath and Multi‐Scale Fluctuation Analysis

AbstractIn situ measurements from the Magnetospheric Multiscale (MMS) mission are used to estimate electron density from spacecraft potential and investigate compressive turbulence in the Earth's magnetosheath. During the MMS Solar Wind Turbulence Campaign in February 2019, the four MMS spacecraft were arranged in a logarithmic line constellation enabling the study of measurements from multiple spacecraft at varying distances. We estimate the electron density from spacecraft potential for a time interval in which the ion emitters actively control the potential. The derived electron density data product has a higher temporal resolution than the plasma instruments, enabling the examination of fluctuation for scales down to the sub‐ion range. The inter‐spacecraft separations range from 132 to 916 km; this corresponds to scales of 3.5–24.1 ion inertial lengths. As an example, the derived density and magnetic field data are used to study fluctuations in the magnetosheath through time lags on a single spacecraft and spatial lags between pairs of spacecraft over almost one decade in scale. The results show an increase in anisotropy as the scale decreases, similar for the density and the magnetic field. This suggests different drivers in the strongly compressive magnetosheath and the weakly compressive solar wind. Compressive structures such as magnetic holes, compressive vortices and jets might play key roles.

Complexity parameters of solar-wind magnetic fluctuations at 1 AU during SC23 and SC24

Context. The solar wind develops a highly turbulent character during its expansion, where plasma and electromagnetic fluctuations coexist. Considering the presence of turbulence in the plasma as a complex system, the turbulence in the solar wind in general has been measured and studied using different techniques from a systems science point of view. These techniques provide the opportunity to obtain preliminary information even before much of the physics can be assimilated and integrated. Aims. We describe this plasma as a complex system in order to understand solar wind dynamics from a new perspective. Several missions provide a wide range of data concerning critical astrophysical phenomena. This poses a challenge to implement new effective methods to complement the characterization of the constantly new, and sometimes highly reduced information, especially when dealing with observational data with intermittent gaps. Methods. We work with magnetic fluctuation time series data obtained from the Wind mission at 1 AU in order to characterize the fast and slow solar wind behavior during solar cycles 23 (SC23) and 24 (SC24). We applied the horizontal visibility graph (HVG) method to obtain the evolution of measurements of Kullback-Leibler divergence (KLD), D, and the characteristic exponent, γ, over time. Both are complexity parameters extracted from the degree distributions of the networks. Results. By contrasting our complexity parameters, γ and D, with solar activity characterized by the number of sunspots and solar wind speed, we obtain significant intercorrelations among them during both cycles and ascending, descending, minimum, and maximum phases. According to γ values, the magnetic fluctuations of the solar wind are a correlated stochastic time series at 1 AU. Also, the divergence D recognizes SC23 as the most dissipative and identifies the slow wind as more variable than the fast wind, with a better anti-correlation in the minima phases. This study reveals that in terms of solar phases γmin &gt; γdes &gt; γasc &gt; γmax, and Dmin &lt; Ddes &lt; Dasc &lt; Dmax. We show that the HVG technique leads to results that are consistent with the complex nature of solar wind turbulence.

Stochastic interpolation of sparsely sampled time series by a superstatistical random process and its synthesis in Fourier and wavelet space

We present a novel method for stochastic interpolation of sparsely sampled time signals based on a superstatistical random process generated from a multivariate Gaussian scale mixture. In comparison to other stochastic interpolation methods such as Gaussian process regression, our method possesses strong multifractal properties and is thus applicable to a broad range of real-world time series, e.g. from solar wind or atmospheric turbulence. Furthermore, we provide a sampling algorithm in terms of a mixing procedure that consists of generating a -dimensional field , where each Gaussian component is synthesized with identical underlying noise but different covariance function parameterized by a log-normally distributed parameter ξ. Due to the Gaussianity of each component , we can exploit standard sampling algorithms such as Fourier or wavelet methods and, most importantly, methods to constrain the process on the sparse measurement points. The scale mixture u(t) is then initialized by assigning each point in time t a and therefore a specific value from , where the time-dependent parameter follows a log-normal process with a large correlation time scale compared to the correlation time of . We juxtapose Fourier and wavelet methods and show that a multiwavelet-based hierarchical approximation of the interpolating paths, which produce a sparse covariance structure, provide an adequate method to locally interpolate large and sparse datasets.

Observations of Waves and Structures by Frequency–Wavenumber Spectrum in Solar Wind Turbulence

A well-known shortcoming of single-spacecraft spectral analysis is that only the 1D wavenumber spectrum can be observed, assuming the characteristic wave propagation speed is much smaller than the solar wind flow speed. This limitation has motivated an extended debate about whether fluctuations observed in the solar wind are waves or structures. Multispacecraft analysis techniques can be used to calculate the wavevector independent of the observed frequency, thus allowing one to study the frequency–wavenumber spectrum of turbulence directly. The dispersion relation for waves can be identified, which distinguishes them from nonpropagating structures. We use magnetic field data from the four Magnetospheric Multiscale (MMS) spacecraft to measure the frequency–wavenumber spectrum of solar wind turbulence based on the k-filtering and phase differencing techniques. Both techniques have been used successfully in the past for the Earth’s magnetosphere, although applications to solar wind turbulence have been limited. We conclude that the solar wind turbulence intervals observed by MMS show features of nonpropagating structures that are associated with frequencies close to zero in the plasma rest frame. However, there is no clear evidence of propagating Alfvén waves that have a nonzero rest-frame frequency. The lack of waves may be due to instrument noise and spacecraft separation. Our results support the idea of turbulence dominated by quasi-2D structures.

Turbulence Driving by Interstellar Pickup Ions in the Outer Solar Wind

We revisit the question of how the unstable scattering of interstellar pickup ions (PUIs) may drive turbulence in the outer solar wind and why the energy released into fluctuations by this scattering appears to be significantly less than the standard bispherical prediction. We suggest that energization of the newly picked-up ions by the ambient turbulence during the scattering process can result in a more spherical distribution of PUIs and reduce the generated fluctuation energy to a level consistent with the observations of turbulent intensities and core solar wind heating. This scenario implies the operation of a self-regulation mechanism that maintains the observed conditions of turbulence and heating in the PUI-dominated solar wind.

Energy transfer of the solar wind turbulence based on Parker solar probe and other spacecraft observations

The supersonic solar wind, first predicted by Parker and then observed by Mariners, extends to form a heliosphere around the Sun. The energy supply from the energy containing range, the energy cascade though the inertial range, and the eventual energy dissipation are three basic processes of the energy transfer in the solar wind and have been studied for a long time. However, some basic issues remain to be discovered. Here, we review the recent progress in the mechanisms of energy transfer of the solar wind turbulence from the observational perspective. Based on the Parker solar probe observations, the energy supply mechanism by the low-frequency break sweeping is proposed to provide enough energy for the proton heating in the slow solar wind. This mechanism also works in the fast solar wind. The energy flux by the low-frequency break sweeping is consistent with that by the classical von Kármán decay mechanism. For the energy cascade in the inertial range, the scaling behavior of the third-order structure functions demonstrates the effect of the complex dynamics of the solar wind. The process of energy transfer is fundamental to understand the solar wind turbulence and help to construct the model of the space environment.

Magnetospheric Multiscale Observations of Markov Turbulence on Kinetic Scales

In our previous studies we have examined solar wind and magnetospheric plasma turbulence, including Markovian character on large inertial magnetohydrodynamic scales. Here we present the results of the statistical analysis of magnetic field fluctuations in the Earth’s magnetosheath, based on the Magnetospheric Multiscale mission at much smaller kinetic scales. Following our results on spectral analysis with very large slopes of about −16/3, we apply a Markov-process approach to turbulence in this kinetic regime. It is shown that the Chapman–Kolmogorov equation is satisfied and that the lowest-order Kramers–Moyal coefficients describing drift and diffusion with a power-law dependence are consistent with a generalized Ornstein–Uhlenbeck process. The solutions of the Fokker–Planck equation agree with experimental probability density functions, which exhibit a universal global scale invariance through the kinetic domain. In particular, for moderate scales we have the kappa distribution described by various peaked shapes with heavy tails, which, with large values of the kappa parameter, are reduced to the Gaussian distribution for large inertial scales. This shows that the turbulence cascade can be described by the Markov processes also on very small scales. The obtained results on kinetic scales may be useful for a better understanding of the physical mechanisms governing turbulence.

Simulation of Solar Wind Turbulence near Corotating Interaction Regions: Superposed Epoch Analysis of Simulations and Observations

The effect of the turbulence that is associated with solar wind corotating interaction regions (CIRs) on transport of galactic cosmic rays remains an outstanding problem in space science. Observations show that the intensities of the plasma and magnetic fluctuations are enhanced within a CIR. The velocity shear layer between the slow and fast wind embedded in a CIR is thought to be responsible for this enhancement in turbulent energy. We perform physics-based magnetohydrodynamic simulations of the plasma background and turbulent fluctuations in the solar wind dominated by CIRs for radial distances between 0.3 and 5 au. A simple but effective approach is used to incorporate the inner boundary conditions for the solar wind and magnetic field for the periods 2007–2008 and 2017–2018. Legendre coefficients at the source surface obtained from the Wilcox Solar Observatory library are utilized for dynamic reconstructions of the current sheet and the fast and slow streams at the inner boundary. The dynamic inner boundary enables our simulations to generate CIRs that are reasonably comparable with observations near Earth. While the magnetic field structure is reasonably well reproduced, the enhancements in the turbulent energy at the stream interfaces are smaller than observed. A superposed epoch analysis is performed over several CIRs from the simulation and compared to the superposed epoch analysis of the observed CIRs. The results for the turbulent energy and correlation length are used to estimate the diffusion tensor of galactic cosmic rays. The derived diffusion coefficients could be used for more realistic modeling of cosmic rays in a dynamically evolving inner heliosphere.

GMSK Demodulation Combining 1D‐CNN and Bi‐LSTM Network Over Strong Solar Wind Turbulence Channel

AbstractTo solve the problem of bit error rate (BER) performance degradation over strong solar wind turbulence channel, this paper addresses to Gaussian minimum frequency shift keying (GMSK) demodulation using machine learning. First, by analyzing the scintillation characteristics of the telemetry signal caused by solar wind turbulence during the solar superior conjunction, the K distribution channel model is innovatively established over strong solar wind turbulence channel. Then, the approximate probability density function of the K distribution of the established channel is studied by using Laguerre orthogonal polynomial for convenience. Additionally, the BER performance of GMSK over strong solar wind turbulence channel is analyzed. Second, using a one‐dimensional convolutional neural network (1D‐CNN) and bidirectional long short‐term memory network (Bi‐LSTM), two demodulators for GMSK are proposed. By integrating the 1D‐CNN and LSTM to extract local features and process the dynamic information of GMSK signals, we propose a novel GMSK demodulator over strong solar wind turbulence channel with combining 1D‐CNN and Bi‐LSTM. The simulation results show that, even if the solar wind turbulence has serious effects on the signal at a low signal‐to‐noise ratio, the proposed combining neural network demodulation can obtain better BER performance than the classical Viterbi algorithm, demodulation using only a single 1D‐CNN or Bi‐LSTM. The proposed GMSK demodulator is more suitable for the deep space exploration of the solar system.

The Radial Variation of the Solar Wind Turbulence Spectra near the Kinetic Break Scale from Parker Solar Probe Measurements

In this study we examine the radial dependence of the inertial and dissipation range indices, as well as the spectral break separating the inertial and dissipation range in power density spectra of interplanetary magnetic field fluctuations using Parker Solar Probe data from the fifth solar encounter between ∼0.1 and ∼0.7 au. The derived break wavenumber compares reasonably well with previous estimates at larger radial distances and is consistent with gyro-resonant damping of Alfvénic fluctuations by thermal protons. We find that the inertial scale power-law index varies between approximately −1.65 and −1.45. This is consistent with either the Kolmogorov (−5/3) or Iroshnikov–Kraichnan (−3/2) values, and has a very weak radial dependence with a possible hint that the spectrum becomes steeper closer to the Sun. The dissipation range power-law index, however, has a clear dependence on radial distance (and turbulence age), decreasing from −3 near 0.7 au (4 days) to −4 [±0.3] at 0.1 au (0.75 days) closer to the Sun.

Spacecraft radial alignments for investigations of the evolution of solar wind turbulence: A review

With the launch of the Parker Solar Probe, BepiColombo, and Solar Orbiter missions in the three-year period 2018−2020, the investigation of the evolution of solar wind turbulence, dynamics, and structures in the inner heliosphere has become more readily feasible, thanks to the increasing availability of orbital configurations suitable for multi-point observations of the Sun and the processes it drives in interplanetary space. Specifically, data analysis, models, and numerical simulations based on multi-spacecraft coordinated studies have been allowing scientists to address still unsolved questions, such as how turbulence and plasma heating evolve with the heliocentric distance. A few instances of spacecraft radial alignments have been used, even before the advent of the three most recent heliospheric missions, to track the evolution of the solar wind plasma throughout interplanetary space, leading to major advances in understanding the mechanisms underlying magnetohydrodynamic turbulence and the physical processes involved in dissipating the energy transferred along the turbulent cascade to heat the plasma. This paper aims to review the different works carried out so far on these issues, describing the diagnostics adopted and discussing the most important achievements in the field of solar wind turbulence evolution.