Local Mean Magnetic Field Research Articles

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.

Influence of Alfvén Ion–Cyclotron Waves on the Anisotropy of Solar Wind Turbulence at Ion Kinetic Scales

The power spectra of the magnetic field at ion kinetic scales have been found to be significantly influenced by Alfvén ion–cyclotron (AIC) waves. Here, we study whether and how this influence of the AIC wave depends on the θVB angle (the angle between the local mean magnetic field and the solar wind velocity direction). The wavelet technique is applied to the high time-resolution (11 vectors per second) magnetic field data from WIND spacecraft measurements in a fast solar wind stream associated with an outward magnetic sector. It is found that around the ion kinetic scales (0.52 Hz–1.21 Hz), the power spectrum in the parallel angular bin 0∘<θVB<10∘ has a slope of −4.80±0.15. When we remove the left-handed polarized AIC waves (with normalized reduced magnetic helicity smaller than −0.9) from the fluctuations, the spectral index becomes −4.09±0.11. However, the power spectrum in the perpendicular angular bin 80∘<θVB<90∘ changes very little during the wave-removal process, and its slope remains −3.22±0.07. These results indicate that the influence of the AIC waves on the magnetic spectral index at the ion kinetic scales is indeed dependent on θVB, which is due to the anisotropic distribution of the waves. Apparently, when the waves are removed from the original data, the spectral anisotropy weakens. This result may help us to better understand the physical nature of the spectral anisotropy around the ion scales.

Turbulence and Waves in the Sub-Alfvénic Solar Wind Observed by the Parker Solar Probe during Encounter 10

During its 10th orbit around the Sun, the Parker Solar Probe sampled two intervals where the local Alfvén speed exceeded the solar wind speed, lasting more than 10 hours in total. In this paper, we analyze the turbulence and wave properties during these periods. The turbulence is observed to be Alfvénic and unbalanced, dominated by outward-propagating modes. The power spectrum of the outward-propagating Elsässer z + mode steepens at high frequencies while that of the inward-propagating z − mode flattens. The observed Elsässer spectra can be explained by the nearly incompressible (NI) MHD turbulence model with both 2D and Alfvénic components. The modeling results show that the z + spectra are dominated by the NI/slab component, and the 2D component mainly affects the z − spectra at low frequencies. An MHD wave decomposition based on an isothermal closure suggests that outward-propagating Alfvén and fast magnetosonic wave modes are prevalent in the two sub-Alfvénic intervals, while the slow magnetosonic modes dominate the super-Alfvénic interval in between. The slow modes occur where the wavevector is nearly perpendicular to the local mean magnetic field, corresponding to nonpropagating pressure-balanced structures. The alternating forward and backward slow modes may also be features of magnetic reconnection in the near-Sun heliospheric current sheet.

Dependence of Solar Wind Proton Temperature on the Polarization Properties of Alfvénic Fluctuations at Ion-kinetic Scales

Abstract We use fluctuating magnetic helicity to investigate the polarization properties of Alfvénic fluctuations at ion-kinetic scales in the solar wind as a function of β p , the ratio of proton thermal pressure to magnetic pressure, and θ vB , the angle between the proton flow and local mean magnetic field, B 0. Using almost 15 yr of Wind observations, we separate the contributions to helicity from fluctuations with wavevectors, k , quasi-parallel and oblique to B 0, finding that the helicity of Alfvénic fluctuations is consistent with predictions from linear Vlasov theory. This result suggests that the nonlinear turbulent fluctuations at these scales share at least some polarization properties with Alfvén waves. We also investigate the dependence of proton temperature in the β p –θ vB plane to probe for possible signatures of turbulent dissipation, finding that it correlates with θ vB . The proton temperature parallel to B 0 is higher in the parameter space where we measure the helicity of right-handed Alfvénic fluctuations, and the temperature perpendicular to B 0 is higher where we measure left-handed fluctuations. This finding is inconsistent with the general assumption that by sampling different θ vB in the solar wind we can analyze the dependence of the turbulence distribution on θ kB , the angle between k and B 0. After ruling out both instrumental and expansion effects, we conclude that our results provide new evidence for the importance of local kinetic processes that depend on θ vB in determining proton temperature in the solar wind.

Scale-dependent anisotropy of electric field fluctuations in solar wind turbulence

ABSTRACT We study the variation of average powers and spectral indices of electric field fluctuations with respect to the angle between average flow direction and the mean magnetic field in solar wind turbulence. Cluster spacecraft data from the years 2002 and 2007 are used for the present analysis. We perform a scale-dependent study with respect to the local mean magnetic field using wavelet analysis technique. Prominent anisotropies are found for both the spectral index and power levels of the electric power spectra. Similar to the magnetic field fluctuations, the parallel (or antiparallel) electric fluctuation spectrum is found to be steeper than the perpendicular spectrum. However, the parallel (or antiparallel) electric power is found to be greater than the perpendicular one. Below 0.1 Hz, the slope of the parallel electric power spectra deviates substantially from that of the total magnetic power spectra, supporting the existence of Alfvénic turbulence.

Observational Quantification of Three-dimensional Anisotropies and Scalings of Space Plasma Turbulence at Kinetic Scales

Abstract A statistical survey of spectral anisotropy of space plasma turbulence is performed using five years of measurements from the Magnetospheric Multiscale mission in the magnetosheath. By measuring the five-point second-order structure functions of the magnetic field, we have for the first time quantified the three-dimensional anisotropies and scalings at sub-ion scales (<100 km). In the local reference frame defined with respect to local mean magnetic field , the “statistical eddies” are found to be mostly elongated along and shortened in the direction perpendicular to both and local field fluctuations. From several d i (ion inertial length) toward ∼0.05 d i , the ratio between eddies’ parallel and perpendicular lengths features a trend of rise then fall, whereas the anisotropy in the perpendicular plane appears scale-invariant. Specifically, the anisotropy relations for the total magnetic field at 0.1–1.0 d i are obtained as , and , respectively. Our results provide new observational evidence to compare with phenomenological models and numerical simulations, which may help to better understand the nature of kinetic-scale turbulence.

Kinetic Scale Slow Solar Wind Turbulence in the Inner Heliosphere: Coexistence of Kinetic Alfvén Waves and Alfvén Ion Cyclotron Waves

Abstract The nature of the plasma wave modes around the ion kinetic scales in highly Alfvénic slow solar wind turbulence is investigated using data from the NASA’s Parker Solar Probe taken in the inner heliosphere, at 0.18 au from the Sun. The joint distribution of the normalized reduced magnetic helicity σ m (θ RB, τ) is obtained, where θ RB is the angle between the local mean magnetic field and the radial direction and τ is the temporal scale. Two populations around ion scales are identified: the first population has σ m (θ RB, τ) < 0 for frequencies (in the spacecraft frame) ranging from 2.1 to 26 Hz for 60° < θ RB < 130°, corresponding to kinetic Alfvén waves (KAWs), and the second population has σ m (θ RB, τ) > 0 in the frequency range [1.4, 4.9] Hz for θ RB > 150°, corresponding to Alfvén ion cyclotron waves (ACWs). This demonstrates for the first time the coexistence of KAWs and ACWs in the slow solar wind in the inner heliosphere, which contrasts with previous observations in the slow solar wind at 1 au. This discrepancy between 0.18 and 1 au could be explained either by (i) a dissipation of ACWs via cyclotron resonance during their outward journey, or by (ii) the high Alfvénicity of the slow solar wind at 0.18 au that may be favorable for the excitation of ACWs.

Cross Helicity Reversals in Magnetic Switchbacks

We consider 2D joint distributions of normalised residual energy $\sigma_r(s,t)$ and cross helicity $\sigma_c(s,t)$ during one day of Parker Solar Probe's (PSP's) first encounter as a function of wavelet scale $s$. The broad features of the distributions are similar to previous observations made by HELIOS in slow solar wind, namely well correlated and fairly Alfv\'enic, except for a population with negative cross helicity which is seen at shorter wavelet scales. We show that this population is due to the presence of magnetic switchbacks, brief periods where the magnetic field polarity reverses. Such switchbacks have been observed before, both in HELIOS data and in Ulysses data in the polar solar wind. Their abundance and short timescales as seen by PSP in its first encounter is a new observation, and their precise origin is still unknown. By analysing these MHD invariants as a function of wavelet scale we show that MHD waves do indeed follow the local mean magnetic field through switchbacks, with net Elsasser flux propagating inward during the field reversal, and that they therefore must be local kinks in the magnetic field and not due to small regions of opposite polarity on the surface of the Sun. Such observations are important to keep in mind as computing cross helicity without taking into account the effect of switchbacks may result in spurious underestimation of $\sigma_c$ as PSP gets closer to the Sun in later orbits.

Magnetic-field-aligned Electric Fields and Nonresonant Acceleration in Alfvénic Turbulence

Backward-propagating or reverse fluctuations in Alfvénic turbulence are shown to produce magnetic-field-aligned (MFA) electric fields capable of highly intermittent acceleration of particles along the local mean magnetic field. Probability distribution functions (PDFs) for the angles between magnetic and electric local mean fields in the plane perpendicular to the background magnetic field are calculated both analytically and through Monte Carlo simulations as functions of the fraction of reverse fluctuations. The PDFs peak at but quickly broaden as increases, up to the limit of a uniform PDF for or zero cross-helicity. Energy from a mixture of forward- and backward-propagating Alfvén waves can easily be transferred to the plasma, through the intermittent MFA electric fields, on a timescale much shorter than the Kolmogorov timescale for turbulence cascade. In such a mixture, for typical 1 au solar wind turbulence parameters, nonresonant interaction through the MFA electric fields rather than gyroresonance controls the energy exchanges between turbulent fields and particles. Possible consequences of the nonresonant interaction through the MFA fields are further suggested, from the observed fast variations of solar wind speed and resulting spectral flattening above 10−2 Hz, and the turbulence level variability/intermittency near 1 au, to the powering of chromospheric jets/spicules in the upper chromosphere and heating of the chromosphere, transition region, and corona, due to the high reflection rate of Alfvén waves in the upper chromosphere. Conditions for the direct proton acceleration (jet formation) in the chromosphere include a temperature ≤104 K and a magnetic field between about 10 and 100 G.

Understanding the Multiwavelength Observation of Geminga's Tev Halo: The Role of Anisotropic Diffusion of Particles.

In this Letter, we propose that the x-ray and the TeV observations in the vicinity of Geminga can be understood in the framework of anisotropic diffusion of injected electrons or positrons. This interpretation only requires the turbulence in the vicinity of Geminga to be sub-Alfvénic with the local mean magnetic field direction approximately aligned with our line of sight towards Geminga, without invoking extreme conditions for the environment, such as an extremely small diffusion coefficient and a weak magnetic field of submicrogauss as suggested in previous literature.

Parallel-propagating Fluctuations at Proton-kinetic Scales in the Solar Wind Are Dominated By Kinetic Instabilities

Abstract We use magnetic helicity to characterize solar wind fluctuations at proton-kinetic scales from Wind observations. For the first time, we separate the contributions to helicity from fluctuations propagating at angles quasi-parallel and oblique to the local mean magnetic field, . We find that the helicity of quasi-parallel fluctuations is consistent with Alfvén-ion cyclotron and fast magnetosonic-whistler modes driven by proton temperature anisotropy instabilities and the presence of a relative drift between α-particles and protons. We also find that the helicity of oblique fluctuations has little dependence on proton temperature anisotropy and is consistent with fluctuations from the anisotropic turbulent cascade. Our results show that parallel-propagating fluctuations at proton-kinetic scales in the solar wind are dominated by proton temperature anisotropy instabilities and not the turbulent cascade. We also provide evidence that the behavior of fluctuations at these scales is independent of the origin and macroscopic properties of the solar wind.

Angular Independence of Break Position for Magnetic Power Spectral Density in Solar Wind Turbulence

Abstract The break in power spectral density (PSD) around the ion scales indicates the onset of dissipation and/or dispersion of kinetic turbulence. For Alfvén waves in the kinetic regime, the dissipation and dispersion are individually dependent on the propagation angle, θ kB, which has θ RB (the angle between radial direction and local mean magnetic field direction) as a proxy in solar wind measurements. The relation between θ RB and the break position helps us find the role of dissipation and/or dispersion for deforming the PSD profile. In order to locate the spectral break position automatically and quantitatively, we develop a dual-power-law fitting method to fit the PSD profiles in both MHD and kinetic ranges simultaneously. The break position f b is found to change little with θ RB, suggesting an angular independence of the spectral break. Furthermore, f b in our statistical study of fast solar wind near 1 au is consistent with a wavenumber k satisfying k(ρ p + d p) ∼ 1 (ρ p is the thermal proton gyroradius and d p is the proton inertial length), independently of θ RB. To interpret this independence, we incorporate the effects of both dissipation and dispersion in a unified description, which is the breakdown of the magnetic frozen-in condition in wavenumber space (k ∥, k ⊥). The breakdown of the frozen-in condition is relatively isotropic compared to the strong anisotropy of dispersion and dissipation. Furthermore, the spatial scale for the onset of the breakdown frozen-in condition is estimated to be the sum of ρ p and d p.

Fully Kinetic Simulation of 3D Kinetic Alfvén Turbulence.

We present results from a three-dimensional particle-in-cell simulation of plasma turbulence, resembling the plasma conditions found at kinetic scales of the solar wind. The spectral properties of the turbulence in the subion range are consistent with theoretical expectations for kinetic Alfvén waves. Furthermore, we calculate the local anisotropy, defined by the relation k_{∥}(k_{⊥}), where k_{∥} is a characteristic wave number along the local mean magnetic field at perpendicular scale l_{⊥}∼1/k_{⊥}. The subion range anisotropy is scale dependent with k_{∥}<k_{⊥} and the ratio of linear to nonlinear time scales is of order unity, suggesting that the kinetic cascade is close to a state of critical balance. Our results compare favorably against a number of insitu solar wind observations and demonstrate-from first principles-the feasibility of plasma turbulence models based on a critically balanced cascade of kinetic Alfvén waves.

How to Define the Mean Square Amplitude of Solar Wind Fluctuations With Respect to the Local Mean Magnetic Field

AbstractOver the last decade it has become popular to analyze turbulent solar wind fluctuations with respect to a coordinate system aligned with the local mean magnetic field. This useful analysis technique has provided new information and new insights about the nature of solar wind fluctuations and provided some support for phenomenological theories of MHD turbulence based on the ideas of Goldreich and Sridhar. At the same time it has drawn criticism suggesting that the use of a scale‐dependent local mean field is somehow inconsistent or irreconcilable with traditional analysis techniques based on second‐order structure functions and power spectra that, for stationary time series, are defined with respect to the constant (scale‐independent) ensemble average magnetic field. Here it is shown that for fluctuations with power law spectra, such as those observed in solar wind turbulence, it is possible to define the local mean magnetic field in a special way such that the total mean square amplitude (trace amplitude) of turbulent fluctuations is approximately the same, scale by scale, as that obtained using traditional second‐order structure functions or power spectra. This fact should dispel criticism concerning the physical validity or practical usefulness of the local mean magnetic field in these applications.

Influence of Intermittency on the Quasi-perpendicular Scaling in Three-dimensional Magnetohydrodynamic Turbulence

Abstract Solar wind fluctuations reveal the ubiquity of intermittency, which is believed to affect the spectral signatures of turbulence. In this work, based on simulation of driven compressible MHD turbulence, we apply the wavelet technique to the magnetic field and velocity to identify intermittency, and we analyze the influence of the intermittency on the quasi-perpendicular scaling in the inertial range. The numerical results show that the original magnetic and velocity fluctuations are anisotropic, and have a power anisotropy with a spectral index approaching the Iroshnikov–Kraichnan scaling in the direction quasi-perpendicular to the local mean magnetic field. As in observations of the solar wind fluctuations, as the scale decreases in the simulation, the calculated probability distribution functions (pdfs) of the wavelet coefficients become extended on both tails of the non-Gaussian distribution, with a rapid increase in flatness. After intermittency has been removed from the driven turbulence, at each scale, the pdfs approach a Gaussian distribution, with the flatness being ∼3. Meanwhile, the quasi-perpendicular scaling for both fluctuations becomes steeper and close to a Kolmogorov scaling, which may be a result of the stronger intermittency in the quasi-perpendicular direction and at the smaller scales. These results suggest that there is intermittency superposed on the “background” turbulence that seems to have the Kolmogorov scaling, whereby the overall slope is getting flatter with the involvement of intermittency.

Magnetohydrodynamic Turbulence Mediated by Reconnection

Abstract Magnetic field fluctuations in magnetohydrodynamic turbulence can be viewed as current sheets that are progressively more anisotropic at smaller scales. As suggested by Loureiro &amp; Boldyrev and Mallet et al., below a certain critical thickness, , such current sheets become tearing-unstable. We propose that the tearing instability changes the effective alignment of the magnetic field lines in such a way as to balance the eddy turnover rate at all scales smaller than . As a result, turbulent fluctuations become progressively less anisotropic at smaller scales, with the alignment angle increasing as , where is the resistive dissipation scale. Here L 0 is the outer scale of the turbulence, S 0 is the corresponding Lundquist number, and is a parameter. The resulting Fourier energy spectrum is , where is the wavenumber normal to the local mean magnetic field, and the critical scale is . The simplest model corresponds to β = 0, in which case the predicted scaling formally agrees with one of the solutions obtained in Mallet et al. from a discrete hierarchical model of abruptly collapsing current sheets, an approach different from and complementary to ours. We also show that the reconnection-mediated interval is non-universal with respect to the dissipation mechanism. Hyper-resistivity of the form leads (in the simplest case of β = 0) to the different transition scale and the energy spectrum , where is the corresponding hyper-resistive Lundquist number.

Role of Magnetic Reconnection in Magnetohydrodynamic Turbulence.

The current understanding of magnetohydrodynamic (MHD) turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheetlike structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale λ∼LS_{L}^{-4/7}, where S_{L} is the outer-scale (L) Lundquist number and λ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion of eddies, therefore implying a fundamentally different route to energy dissipation than that predicted by the Kolmogorov-like phenomenology. In particular, our analysis predicts the existence of the subinertial, reconnection interval of MHD turbulence, with the estimated scaling of the Fourier energy spectrum E(k_{⊥})∝k_{⊥}^{-5/2}, where k_{⊥} is the wave number perpendicular to the local mean magnetic field. The same calculation is also performed for high (perpendicular) magnetic Prandtl number plasmas (Pm), where the reconnection scale is found to be λ/L∼S_{L}^{-4/7}Pm^{-2/7}.

Measures of three-dimensional anisotropy and intermittency in strong Alfvénic turbulence

We measure the local anisotropy of numerically simulated strong Alfv\'enic turbulence with respect to two local, physically relevant directions: along the local mean magnetic field and along the local direction of one of the fluctuating Elsasser fields. We find significant scaling anisotropy with respect to both these directions: the fluctuations are "ribbon-like" --- statistically, they are elongated along both the mean magnetic field and the fluctuating field. The latter form of anisotropy is due to scale-dependent alignment of the fluctuating fields. The intermittent scalings of the $n$th-order conditional structure functions in the direction perpendicular to both the local mean field and the fluctuations agree well with the theory of Chandran et al. 2015, while the parallel scalings are consistent with those implied by the critical-balance conjecture. We quantify the relationship between the perpendicular scalings and those in the fluctuation and parallel directions, and find that the scaling exponent of the perpendicular anisotropy (i.e., of the aspect ratio of the Alfv\'enic structures in the plane perpendicular to the mean magnetic field) depends on the amplitude of the fluctuations. This is shown to be equivalent to the anticorrelation of fluctuation amplitude and alignment at each scale. The dependence of the anisotropy on amplitude is shown to be more significant for the anisotropy between the perpendicular and fluctuation-direction scales than it is between the perpendicular and parallel scales.

Influence of intermittency on the anisotropy of magnetic structure functions of solar wind turbulence

AbstractIntermittency appears to be connected with the spectral anisotropy of solar wind turbulence. We use the Local Intermittency Measure to identify and remove intermittency from the magnetic field data measured by the Ulysses spacecraft in fast solar wind. Structure functions are calculated based on the time sequences as obtained before and after removing intermittency and arranged by time scale (τ) and ΘRB (the angle between local mean magnetic field B0 and radial direction R). Thus, the scaling exponent (ξ(p, ΘRB)) of every structure function of order (p) is obtained for different angles. Before removing intermittency, ξ(p, ΘRB) shows a distinctive dependence on ΘRB: from monofractal scaling law at ΘRB ~0° to multifractal scaling law at ΘRB ~90°. In contrast after eliminating the intermittency, ξ(p, ΘRB) is found to be more monofractal for all ΘRB. The extended structure‐function model is applied to ξ(p, ΘRB), revealing differences of its fitting parameters α (a proxy of the power spectral index) and P1 (fragmentation fraction) for the cases with and without intermittency. Parameter α shows an evident angular trend falling from 1.9 to 1.6 for the case with intermittency but has a relatively flat profile around 1.8 for the case without intermittency. Parameter P1 rises from around 0.5 to above 0.8 with increasing ΘRB for the intermittency case and is located between 0.5 and 0.8 for the case lacking intermittency. Therefore, we may infer that it is the anisotropy of intermittency that causes the scaling anisotropy of energy spectra and the unequal fragmentation of energy cascading.

SMALL-SCALE PRESSURE-BALANCED STRUCTURES DRIVEN BY MIRROR-MODE WAVES IN THE SOLAR WIND

Recently, small-scale pressure-balanced structures (PBSs) have been studied with regard to their dependence on the direction of the local mean magnetic field B0. The present work continues these studies by investigating the compressive wave mode forming small PBSs, here for B0 quasi-perpendicular to the x-axis of Geocentric Solar Ecliptic coordinates (GSE-x). All the data used were measured by WIND in the quiet solar wind. From the distribution of PBSs on the plane determined by the temporal scale and angle θxB between the GSE-x and B0 ,w e notice that at θxB = 115 ◦ the PBSs appear at temporal scales ranging from 700 s to 60 s. In the corresponding temporal segment, the correlations between the plasma thermal pressure Pth and the magnetic pressure PB ,a s well as that between the proton density Np and the magnetic field strength B, are investigated. In addition, we use the proton velocity distribution functions to calculate the proton temperatures T⊥ and T� . Minimum Variance Analysis is applied to find the magnetic field minimum variance vector BN. We also study the time variation of the cross-helicity σc and the compressibility Cp and compare these with values from numerical predictions for the mirror mode. In this way, we finally identify a short segment that has T⊥ >T � ,p rotonβ � 1, both pairs of Pth‐PB and Np‐B showing anti-correlation, and σc ≈ 0 with Cp > 0. Although the examination of σc and Cp is not conclusive, it provides helpful additional information for the wave mode identification. Additionally, BN is found to be highly oblique to B0. Thus, this work suggests that a candidate mechanism for forming small-scale PBSs in the quiet solar wind is due to mirror-mode waves.