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Turbulence is characterized by the formation of small-scale structures, observed to occur down to electron scales. Furthermore, spacecraft observations have found active magnetic reconnection within such electron-scale current sheets. This points to small-scale structures serving as a pathway of energy conversion in collisonless plasma turbulence. However, the extent of their contribution to turbulent energy dissipation, compared to other energy conversion mechanisms, is still under investigation. The instruments of the MMS spacecraft are able to adequately resolve electron-scale processes, and in recent years have been gathering a large volume of burst resolution data in near-Earth space, allowing us to investigate this further. Here, we present the results of a statistical study of electron-scale structures observed by MMS in Earth’s magnetosheath. We show that the abundance of these structures as well as their properties, appear to depend more on the local turbulence parameters rather than on the large-scale dynamics of the magnetosheath, and bow-shock configuration. We report their contribution to the overall dissipation and their significance in plasma heating and particle acceleration. These results provide further insight into the pathways of energy conversion in collisionless turbulence, and contribute to our understanding of turbulent dissipation and particle energization.

Calculating the pressure-strain terms has recently been performed to quantify energy conversion between the bulk flow energy and the internal energy of plasmas. It has been applied to numerical simulations and satellite data from the Magnetospheric MultiScale Mission. The method requires spatial gradients of the velocity and the use of the full pressure tensor. Here we present a derivation of the errors associated with calculating the pressure-strain terms from multi-spacecraft measurements and apply it to previously studied examples of magnetic reconnection at the magnetopause and the magnetotail. The errors are small in a dense magnetosheath event but much larger in the more tenuous magnetotail. This is likely due to larger counting statistics in the dense plasma at the magnetopause than in the magnetotail. The propagated errors analyzed in this work are important to understand uncertainties of energy conversion measurements in space plasmas and have applications to current and future multi-spacecraft missions.

Recent Parker Solar Probe (PSP) observations have shown the presence of sudden reversals in the radial magnetic field, known as switchbacks. Applying a method based on wavelet analysis, here we study the nature of power and spectral-index anisotropies in switchback and non-switchback intervals using PSP data. While a similar spectral-index anisotropy, consistent with critical balance, is found in the switchback and non-switchback intervals, power anisotropy is more enhanced in the non-switchback samples. This result may be attributed to the ‘less developed’ turbulence in the non-switchback periods.

Turbulence near an interplanetary shock is of practical interest because turbulent magnetic fluctuations are key to the diffusive shock acceleration and transport of energetic particles, which can lead to significant space weather effects. In this work, we examine burst-mode observations by the Magnetospheric Multiscale Mission (MMS) for an interplanetary shock passage at a distance of 25 Re­ on 8 January 2018. The instrumental resolution offers an opportunity to examine the energy transfer rate of solar wind turbulence in both the upstream and downstream regions. We implement a Hampel filtering-based technique to mitigate the instrumental noise in plasma moment data. We use a Kolmogorov-Yaglom Law for the third-order structure function and a von Kármán-decay law to calculate the energy dissipation rates at the inertial scale and energy-containing scale, respectively. The results show that the region downstream of the shock has stronger and better developed turbulence and a higher energy transfer rate than the upstream region. N.N. has been supported by STFC studentship and UCL Doctoral School. This research has also been supported by grant RTA6280002 from Thailand Science Research and Innovation, by the MMS Theory and Modeling team grant 80NSSC19K0565, and the NASA LWS program grant 80NSSC20K0377 under NMC subcontract 655-001.

The subject of switchbacks, defined either as large angular deflections or polarity reversals of the magnetic field, has generated substantial interest in the space physics community since the launch of the Parker Solar Probe (PSP) in 2018. Previous studies have characterized switchbacks in several different ways and have been restricted to data available from the first few orbits. Here, we analyze the frequency of occurrence of switchbacks per unit distance for the first full eight orbits of PSP. In this work, events that reverse the sign of the magnetic field relative to a regional average are considered switchbacks. A significant finding is that the rate of occurrence falls off sharply approaching the Sun near 0.2 au (40 R ⊙) and rises gently from 0.2 au outward. The analysis is varied for different magnetic field cadences and for different local averages of the ambient field, confirming the robustness of the results. We discuss implications for the mechanisms of switchback generation. A publicly available database has been created with the identified reversals.

Motivated by theoretical, numerical, and observational evidence, we explore the possibility that the critical transition between sub-Alfvénic flow and super-Alfvénic flow in the solar atmosphere takes place in fragmented and disconnected subvolumes within a general Alfvén critical zone. The initial observations of sub-Alfvénic periods by Parker Solar Probe near 16 R⊙ do not yet provide sufficient evidence to distinguish this possibility from that of a folded surface that separates simply connected regions. Subsequent orbits may well enable such a distinction, but here we use a global magnetohydrodynamic model of the solar wind, coupled to a turbulence transport model, to generate possible realizations of such an Alfvén critical zone. Understanding this transition will inform theories of coronal heating, solar wind origin, solar angular momentum loss, and related physical processes in stellar winds beyond the Sun.

The dissipative mechanism in weakly collisional plasma is a topic that pervades decades of studies without a consensus solution. We compare several energy dissipation estimates based on energy transfer processes in plasma turbulence and provide justification for the pressure-strain interaction as a direct estimate of the energy dissipation rate. The global and scale-by-scale energy balances are examined in 2.5D and 3D kinetic simulations. We show that the global internal energy increase and the temperature enhancement of each species are directly tracked by the pressure-strain interaction. The incompressive part of the pressure-strain interaction dominates over its compressive part in all simulations considered. The scale-by-scale energy balance is quantified by scale filtered Vlasov-Maxwell equations, a kinetic plasma approach, and the lag dependent von K\'arm\'an-Howarth equation, an approach based on fluid models. We find that the energy balance is exactly satisfied across all scales, but the lack of a well-defined inertial range influences the distribution of the energy budget among different terms in the inertial range. Therefore, the widespread use of the Yaglom relation to estimating dissipation rate is questionable in some cases, especially when the scale separation in the system is not clearly defined. In contrast, the pressure-strain interaction balances exactly the dissipation rate at kinetic scales regardless of the scale separation., Comment: 19 pages, 7 figures

The Taylor microscale is a fundamental length scale in turbulent fluids, representing the end of fluid properties and onset of dissipative processes. The Taylor microscale can also be used to evaluate the Reynolds number in classical turbulence theory. Although the solar wind is weakly collisional, it approximately behaves as a magnetohydrodynamic (MHD) fluid at scales larger than the kinetic scale. As a result, classical fluid turbulence theory and formalisms are often used to study turbulence in the MHD range. Therefore, a Taylor microscale can be used to estimate an effective Reynolds number in the solar wind. NASA’s Parker Solar Probe (PSP) has reached progressively closer to the Sun than any other spacecraft before. The collected data have revealed many new findings in the near-Sun solar wind. Here, we use the PSP data to estimate the Taylor microscale and effective Reynolds number near the Sun. We find that the Taylor microscale and Reynolds number are small compared to the corresponding near-Earth values, indicating a solar wind that has been less processed by turbulence, with very small-scale dissipative processes near the Sun.

We use data from the first six encounters of Parker Solar Probe and employ the Partial Variance of Increments ($PVI$) method to study the statistical properties of coherent structures in the inner heliosphere with the aim of exploring physical connections between magnetic field intermittency and observable consequences such as plasma heating and turbulence dissipation. Our results support proton heating localized in the vicinity of, and strongly correlated with, magnetic structures characterized by $PVI \geq 1$. We show that on average, such events constitute $\approx 19\%$ of the dataset, though variations may occur depending on the plasma parameters. We show that the waiting time distribution ($WT$) of identified events is consistent across all six encounters following a power-law scaling at lower $WTs$. This result indicates that coherent structures are not evenly distributed in the solar wind but rather tend to be tightly correlated and form clusters. We observe that the strongest magnetic discontinuities, $PVI \geq 6$, usually associated with reconnection exhausts, are sites where magnetic energy is locally dissipated in proton heating and are associated with the most abrupt changes in proton temperature. However, due to the scarcity of such events, their relative contribution to energy dissipation is minor. Taking clustering effects into consideration, we show that smaller scale, more frequent structures with PVI between, $1\lesssim PVI \lesssim 6$, play the major role in magnetic energy dissipation. The number density of such events is strongly associated with the global solar wind temperature, with denser intervals being associated with higher $T_{p}$., Comment: Accepted for publication in APJ

We study the nature of pressure-strain interaction at reconnection sites, detected by NASA's Magnetospheric Multiscale (MMS) Mission. We employ data from a series of published case studies, including a large-scale reconnection event at the magnetopause, three small-scale reconnection events at the magnetosheath current sheets, and one example of the recently discovered electron-only reconnection. In all instances, we find that the pressure-strain shows signature of conversion into (or from) internal energy at the reconnection site. The electron heating rate is larger than the ion heating rate and the compressive heating is dominant over the incompressive heating rate in all cases considered. The magnitude of thermal energy conversion rate is close to the electromagnetic energy conversion rate in the reconnection region. Although in most cases the pressure-strain interaction indicates that the particle internal energy is increasing, in one case the internal energy is decreasing. These observations indicate that the pressure-strain interaction can be used as an independent measure of energy conversion and dynamics in reconnection regions, in particular independent of measures based on the electromagnetic work. Finally, we explore a selected reconnection site in a turbulent Particle-in-Cell (PIC) simulation which further supports the observational results., The following article has been accepted by Physics of Plasmas

Numerous prior studies have shown that as proton beta increases, a narrower range of proton temperature anisotropy values is observed. This effect has often been ascribed to the actions of kinetic microinstabilities because the distribution of observational data aligns with contours of constant instability growth rates in the beta-anisotropy plane. However, the linear Vlasov theory of instabilities assumes a uniform background in which perturbations grow. The established success of linear-microinstability theories suggests that the conditions in regions of extreme temperature anisotropy may remain uniform for a long enough time so that the instabilities have the chance to grow to sufficient amplitude. Turbulence, on the other hand, is intrinsically non-uniform and non-linear. Thin current sheets and other coherent structures generated in a turbulent plasma, may destroy the uniformity fast enough. It is therefore not a-priori obvious whether the presence of intermittency and coherent structures favors or disfavors instabilities. To address this question, we examined the statistical distribution of growth rates associated with proton temperature-anisotropy driven microinstabilities and local nonlinear time scales in turbulent plasmas. Linear growth rates are, on average, substantially less than the local nonlinear rates. However, at the regions of extreme values of temperature anisotropy, near the "edges" of the populated part of the proton temperature anisotropy-parallel beta plane, the instability growth rates are comparable or faster than the turbulence time scales. These results provide a possible answer to the question as to why the linear theory appears to work in limiting plasma excursions in anisotropy and plasma beta., Accepted for publication in Physics of Plasmas

Context. The observation of numerous magnetic switchbacks and associated plasma jets in Parker Solar Probe (PSP) during its first five orbits, particularly near the Sun, has attracted considerable attention. Switchbacks have been found to be systematically associated with correlated reversals in the direction of the propagation of Alfvénic fluctuations, as well as similar reversals of the electron strahl. Aims. Here we aim to see whether the energetic particles change direction at the magnetic field switchbacks. Methods. We use magnetic field data from the MAG suite’s fluxgate magnetometer instrument to identify switchback regions. We examine the radial anisotropy of the energetic particles measured by the EPI-Lo instrument of the IS⊙IS suite. Results. We find that energetic particles measured by EPI-Lo generally do not preferentially change their directionality from that of the background magnetic field to that of the switchbacks. Conclusions. A reasonable hypothesis is that particles with smaller gyroradii, such as strahl electrons, can reverse direction by following the magnetic field in switchbacks, but that larger gyroradii particles cannot. This provides the possibility of setting a constraint on the radius of the curvature of the magnetic field in switchbacks, a property not otherwise observed by PSP. We expect that particles at higher energies than those detectable by EPI-Lo will also not respond to switchbacks. The observed reversals of radial energetic particle flux are separate phenomena, likely associated with source locations or other propagation effects occurring at greater radial distances.

In an earlier paper (Wan et al. 2012), the authors showed that a similarity solution for anisotropic incompressible 3D magnetohydrodynamic (MHD) turbulence, in the presence of a uniform mean magnetic field $\vB_0$, exists if the ratio of parallel to perpendicular (with respect to $\vB_0$) similarity length scales remains constant in time. This conjecture appears to be a rather stringent constraint on the dynamics of decay of the energy-containing eddies in MHD turbulence. However, we show here, using direct numerical simulations, that this hypothesis is indeed satisfied in incompressible MHD turbulence. After an initial transient period, the ratio of parallel to perpendicular length scales fluctuates around a steady value during the decay of the eddies. We show further that a Taylor--K\'arm\'an-like similarity decay holds for MHD turbulence in the presence of a mean magnetic field. The effect of different parameters, including Reynolds number, DC field strength, and cross-helicity, on the nature of similarity decay is discussed., Comment: Accepted for publication in Journal of Fluid Mechanics

Simulation results from a global magnetohydrodynamic model of the solar corona and the solar wind are compared with Parker Solar Probe's (PSP) observations during its first several orbits. The fully three-dimensional model (Usmanov et al., 2018, ApJ, 865, 25) is based on Reynolds-averaged mean-flow equations coupled with turbulence transport equations. The model accounts for effects of electron heat conduction, Coulomb collisions, Reynolds stresses, and heating of protons and electrons via nonlinear turbulent cascade. Turbulence transport equations for turbulence energy, cross helicity, and correlation length are solved concurrently with the mean-flow equations. We specify boundary conditions at the coronal base using solar synoptic magnetograms and calculate plasma, magnetic field, and turbulence parameters along the PSP trajectory. We also accumulate data from all orbits considered, to obtain the trends observed as a function of heliocentric distance. Comparison of simulation results with PSP data show general agreement. Finally, we generate synthetic fluctuations constrained by the local rms turbulence amplitude given by the model, and compare properties of this synthetic turbulence with PSP observations.

Earth's magnetotail region provides a unique environment to study plasma turbulence. We investigate the turbulence developed in an exhaust produced by magnetic reconnection at the terrestrial magnetotail region. Magnetic and velocity spectra show broad-band fluctuations corresponding to the inertial range, with Kolmorogov $-5/3$ scaling, indicative of a well developed turbulent cascade. We examine the mixed, third-order structure functions, and obtain a linear scaling in the inertial range. This linear scaling of the third-order structure functions implies a scale-invariant cascade of energy through the inertial range. A Politano-Pouquet third-order analysis gives an estimate of the incompressive energy transfer rate of $\sim 10^{7}~\mathrm{J\,kg^{-1}\,s^{-1}}$. This is four orders of magnitude higher than the values typically measured in 1 AU solar wind, suggesting that the turbulence cascade plays an important role as a pathway of energy dissipation during reconnection events in the tail region., Accepted for publication in MNRAS

Using the novel Magnetospheric Multiscale (MMS) mission data accumulated during the 2019 MMS Solar Wind Turbulence Campaign, we calculate the Taylor microscale $(\lambda_{\mathrm{T}})$ of the turbulent magnetic field in the solar wind. The Taylor microscale represents the onset of dissipative processes in classical turbulence theory. An accurate estimation of Taylor scale from spacecraft data is, however, usually difficult due to low time cadence, the effect of time decorrelation, and other factors. Previous reports were based either entirely on the Taylor frozen-in approximation, which conflates time dependence, or that were obtained using multiple datasets, which introduces sample-to-sample variation of plasma parameters, or where inter-spacecraft distance were larger than the present study. The unique configuration of linear formation with logarithmic spacing of the 4 MMS spacecraft, during the campaign, enables a direct evaluation of the $\lambda_{\mathrm{T}}$ from a single dataset, independent of the Taylor frozen-in approximation. A value of $\lambda_{\mathrm{T}} \approx 7000 \, \mathrm{km}$ is obtained, which is about 3 times larger than the previous estimates., Comment: Accepted for publication in the Astrophysical Journal

We present estimates of the turbulent energy cascade rate, derived from a Hall-MHD third-order law. We compute the contribution from the Hall term and the MHD term to the energy flux. We use MMS data accumulated in the magnetosheath and the solar wind, and compare the results with previously established simulation results. We find that in observation, the MHD contribution is dominant at inertial scales, as in the simulations, but the Hall term becomes significant in observations at larger scales than in the simulations. Possible reasons are offered for this unanticipated result., Accepted for Publication in Physical Review Letters

The solar wind proton temperature at 1-au has been found to be correlated with small-scale intermittent magnetic structures, i.e., regions with enhanced temperature are associated with coherent structures such as current sheets. Using Parker Solar Probe data from the first encounter, we study this association using measurements of radial proton temperature, employing the Partial Variance of Increments (PVI) technique to identify intermittent magnetic structures. We observe that the probability density functions of high-PVI events have higher median temperatures than those with lower PVI, The regions in space where PVI peaks were also locations that had enhanced temperatures when compared with similar regions suggesting a heating mechanism in the young solar wind that is associated with intermittency developed by a nonlinear turbulent cascade.n the immediate vicinity., Comment: 6 pages, 3 figures, part of ApJ special issue for PSP

A familiar problem in space and astrophysical plasmas is to understand how dissipation and heating occurs. These effects are often attributed to the cascade of broadband turbulence which transports energy from large scale reservoirs to small scale kinetic degrees of freedom. When collisions are infrequent, local thermodynamic equilibrium is not established. In this case the final stage of energy conversion becomes more complex than in the fluid case, and both pressure-dilatation and pressure strain interactions (Pi-D $\equiv -\Pi_{ij} D_{ij}$) become relevant and potentially important. Pi-D in plasma turbulence has been studied so far primarily using simulations. The present study provides a statistical analysis of Pi-D in the Earth's magnetosheath using the unique measurement capabilities of the Magnetospheric Multiscale (MMS) mission. We find that the statistics of Pi-D in this naturally occurring plasma environment exhibit strong resemblance to previously established fully kinetic simulations results. The conversion of energy is concentrated in space and occurs near intense current sheets, but not within them. This supports recent suggestions that the chain of energy transfer channels involves regional, rather than pointwise, correlations., Comment: Accepted for publication in Physical Review Letters

International audience; During the Parker Solar Probe's (PSP) first perihelion pass, the spacecraft reached within a heliocentric distance of similar to 37 R-circle dot and observed numerous magnetic and flow structures characterized by sharp gradients. To better understand these intermittent structures in the young solar wind, an important property to examine is their degree of correlation in time and space. To this end, we use the well-tested partial variance of increments (PVI) technique to identify intermittent events in FIELDS and SWEAP observations of magnetic and proton-velocity fields (respectively) during PSP's first solar encounter, when the spacecraft was within 0.25 au from the Sun. We then examine distributions of waiting times (WT) between events with varying separation and PVI thresholds. We find power-law distributions for WT shorter than a characteristic scale comparable to the correlation time of the fluctuations, suggesting a high degree of correlation that may originate in a clustering process. WT longer than this characteristic time are better described by an exponential, suggesting a random memory-less Poisson process at play. These findings are consistent with near-Earth observations of solar wind turbulence. The present study complements the one by Dudok de Wit et al., which focuses on WT between observed "switchbacks" in the radial magnetic field.

Direct evidence of an inertial-range turbulent energy cascade has been provided by spacecraft observations in heliospheric plasmas. In the solar wind, the average value of the derived heating rate near 1 au is $\sim 10^{3}\, \mathrm{J\,kg^{-1}\,s^{-1}}$, an amount sufficient to account for observed departures from adiabatic expansion. Parker Solar Probe (PSP), even during its first solar encounter, offers the first opportunity to compute, in a similar fashion, a fluid-scale energy decay rate, much closer to the solar corona than any prior in-situ observations. Using the Politano-Pouquet third-order law and the von K\'arm\'an decay law, we estimate the fluid-range energy transfer rate in the inner heliosphere, at heliocentric distance $R$ ranging from $54\,R_{\odot}$ (0.25 au) to $36\,R_{\odot}$ (0.17 au). The energy transfer rate obtained near the first perihelion is about 100 times higher than the average value at 1 au. This dramatic increase in the heating rate is unprecedented in previous solar wind observations, including those from Helios, and the values are close to those obtained in the shocked plasma inside the terrestrial magnetosheath., Comment: Accepted for publication in The Astrophysical Journal Supplement, PSP special issue

Solar wind magnetic fluctuations exhibit anisotropy due to the presence of a mean magnetic field in the form of the Parker spiral. Close to the Sun, direct measurements were not available until the recently launched Parker Solar Probe (PSP) mission. The nature of the anisotropy and geometry of the magnetic fluctuations play a fundamental role in dissipation processes and in the transport of energetic particles in space. Using PSP data, we present measurements of the geometry and anisotropy of the inner heliosphere magnetic fluctuations, from fluid to kinetic scales. The results are surprising and different from 1 au observations. We find that fluctuations evolve characteristically with size scale. However, unlike 1 au solar wind, at the outer scale, the fluctuations are dominated by wavevectors quasi-parallel to the local magnetic field. In the inertial range, average wavevectors become less field aligned, but still remain more field aligned than near-Earth solar wind. In the dissipation range, the wavevectors become almost perpendicular to the local magnetic field in the dissipation range, to a much higher degree than those indicated by 1 au observations. We propose that this reduced degree of anisotropy in the outer scale and inertial range is due to the nature of large-scale forcing outside the solar corona.

The heliospheric energetic neutral atom spectrum observed by the Interstellar Boundary Explorer (IBEX) reveals that the heliosheath proton distribution is consistent with a power law. The origin of the spectrum is likely from interstellar pickup ions (PUIs) accelerated at the heliospheric termination shock (HTS). We present an explanation of the proton spectrum origin using a test particle simulation of PUIs accelerated at the HTS. PUIs experience preferential heating by the motional electric field in the shock foot, but do not develop a power-law tail without the presence of turbulence at wavenumbers (k) close to the PUI gyroradius scale (R g). Voyager 2 observations of the magnetic field downstream of the HTS indicate a moderate amount of turbulence at kR g ≅ 1, δ B / B 0 2 ≅ 0.01 , which we find to be sufficient for producing a downstream suprathermal PUI tail but not at intensities observed by IBEX. Within the shock ramp, however, Voyager observed the turbulence power at much smaller scales to be nearly 100 times stronger, suggesting the possibility of strong turbulence at the PUI gyroradius scale. We show that a proton distribution can develop a power law downstream of the HTS consistent with IBEX observations if δ B / B 0 2 ≳ 0.1 at kR g ≅ 1 in the shock foot. Shock drift acceleration of PUIs by the motional electric field is aided by interactions with turbulence upstream of the shock overshoot. Steepening of the IBEX proton spectrum in directions farther from the heliospheric nose suggests the HTS compression ratio and/or turbulence power weakens near the heliotail.

Using in situ data, accumulated in the turbulent magnetosheath by the Magnetospheric Multiscale (MMS) Mission, we report a statistical study of magnetic field curvature and discuss its role in the turbulent space plasmas. Consistent with previous simulation results, the Probability Distribution Function (PDF) of the curvature is shown to have distinct power-law tails for both high and low value limits. We find that the magnetic-field-line curvature is intermittently distributed in space. High curvature values reside near weak magnetic-field regions, while low curvature values are correlated with small magnitude of the force acting normal to the field lines. A simple statistical treatment provides an explanation for the observed curvature distribution. This novel statistical characterization of magnetic curvature in space plasma provides a starting point for assessing, in a turbulence context, the applicability and impact of particle energization processes, such as curvature drift, that rely on this fundamental quantity., Comment: Accepted for Publication in the Astrophysical Journal Letters

In presence of an externally supported, mean magnetic field a turbulent, conducting medium, such as plasma, becomes anisotropic. This mean magnetic field, which is separate from the fluctuating, turbulent part of the magnetic field, has considerable effects on the dynamics of the system. In this paper, we examine the dissipation rates for decaying incompressible magnetohydrodynamic (MHD) turbulence with increasing Reynolds number, and in the presence of a mean magnetic field of varying strength. Proceeding numerically, we find that as the Reynolds number increases, the dissipation rate asymptotes to a finite value for each magnetic field strength, confirming the K\'arm\'an-Howarth hypothesis as applied to MHD. The asymptotic value of the dimensionless dissipation rate is initially suppressed from the zero-mean-field value by the mean magnetic field but then approaches a constant value for higher values of the mean field strength. Additionally, for comparison, we perform a set of two-dimensional (2DMHD) and a set of reduced MHD (RMHD) simulations. We find that the RMHD results lie very close to the values corresponding to the high mean-field limit of the three-dimensional runs while the 2DMHD results admit distinct values far from both the zero mean field cases and the high mean field limit of the three-dimensional cases. These findings provide firm underpinnings for numerous applications in space and astrophysics wherein von K\'arm\'an decay of turbulence is assumed., Comment: Accepted for publication in Physical Review X

We employ data from the 2019 Magnetospheric Multiscale (MMS) Solar Wind Turbulence Campaign to evaluate scaling and anisotropy of second-order magnetic field structure functions and scale-dependent kurtosis from a single data interval. Prior results have been based either on the Taylor approximation, which conflates time and space dependence, or on averaging many data sets, which introduces sample-to-sample variation of plasma parameters. The present results overcome these systematic effects. We find that for length scales between 57 and 201 km the fluctuations are anisotropic with a preferred orientation of 60°–70° to the magnetic field direction. The peak kurtosis also lies in this angular range. This confirms anisotropy of the spectrum and suggests that coherent structures such as current sheets are oriented nearly perpendicular to the magnetic field direction. Both the anisotropy and the kurtosis decrease approaching the ion inertial length, here ≈91 km.