Composed of shocked solar wind, the Earth's magnetosheath serves as a natural laboratory to study the transition of turbulence from low Alfv{é}n Mach number, $M_\mathrm{A}$, to high $M_\mathrm{A}$. The simultaneous observations of magnetic field and plasma moments with unprecedented high temporal resolution provided by NASA's \textit{Magnetospheric Multiscale} Mission enable us to study the magnetosheath turbulence at both magnetohydrodynamics (MHD) and sub-ion scales. Based on 1841 burst-mode segments of MMS-1 from 2015/09 to 2019/06, comprehensive patterns of the spatial evolution of magnetosheath turbulences are obtained: (1) from the sub-solar region to the flanks, $M_\mathrm{A}$ increases from $<$ 1 to $>$ 5. At MHD scales, the spectral indices of the magnetic-field and velocity spectra present a positive and negative correlation with $M_\mathrm{A}$. However, no obvious correlations between the spectral indices and $M_\mathrm{A}$ are found at sub-ion scales. (2) from the bow shock to the magnetopause, the turbulent sonic Mach number, $M_{\mathrm{turb}}$, generally decreases from $>$ 0.4 to $<$ 0.1. All spectra steepen at MHD scales and flatten at sub-ion scales, representing a positive/negative correlations with $M_\mathrm{turb}$. The break frequency increases by 0.1 Hz when approaching the magnetopause for the magnetic-field and velocity spectra, while it remains at 0.3 Hz for the density spectra. (3) In spite of some differences, similar results are found for the quasi-parallel and quasi-perpendicular magnetosheath. In addition, the spatial evolution of magnetosheath turbulence is found to be independent of the upstream solar wind conditions, e.g., the Z-component of the interplanetary magnetic field and the solar wind speed.
Collisionless space plasma turbulence can generate reconnecting thin current sheets as suggested by recent results of numerical magnetohydrodynamic simulations. The MMS mission provides the first serious opportunity to check if small ion-electron-scale reconnection, generated by turbulence, resembles the reconnection events frequently observed in the magnetotail or at the magnetopause. Here we investigate field and particle observations obtained by the MMS fleet in the turbulent terrestrial magnetosheath behind quasi-parallel bow shock geometry. We observe multiple small-scale current sheets d…
Protons (ionized hydrogen) in the solar wind frequently exhibit distinct temperatures ($T_{\perp p}$ and $T_{\parallel p}$) perpendicular and parallel to the plasma's background magnetic-field. Numerous prior studies of the interplanetary solar-wind have shown that, as plasma beta ($β_{\parallel p}$) increases, a narrower range of temperature-anisotropy ($R_p\equiv T_{\perp p}\,/\,T_{\parallel p}$) values is observed. Conventionally, this effect has been ascribed to the actions of kinetic microinstabilities. This study is the first to use data from the Magnetospheric Multiscale Mission (MMS) t…
Magnetic reconnection (MR) and the associated concurrently occurring waves have been extensively studied at large-scale plasma boundaries, in quasi-symmetric and asymmetric configurations in the terrestrial magnetotail and at the magnetopause. Recent high-resolution observations by MMS (Magnetospheric Multiscale) spacecraft indicate that MR can occur also in the magnetosheath where the conditions are highly turbulent when the upstream shock geometry is quasi-parallel. The strong turbulent motions make the boundary conditions for evolving MR complicated. In this paper it is demonstrated that th…
The degree of deviation from the thermodynamic equilibrium in the ion velocity distribution functions (VDFs), measured by the Magnetospheric Multiscale (MMS) mission in the Earth's turbulent magnetosheath, is quantitatively investigated. Taking advantage of MMS ion data, having a resolution never reached before in space missions, and of the comparison with Vlasov-Maxwell simulations, this analysis aims at relating any deviation from Maxwellian equilibrium to typical plasma parameters. Correlations of the non-Maxwellian features with plasma quantities such as electric fields, ion temperature, c…
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 $\equiv -Π_{ij} D_{ij}$) become relevant and potentially important. Pi-D in p…
Under quasi-radial interplanetary magnetic fields (IMF), foreshock turbulence can have an impact on the magnetosheath and cusps depending on the location of the quasi-parallel shock. We perform three-dimensional simulations of Earth's dayside magnetosphere using the hybrid code HYPERS, and compare northward and southward quasi-radial IMF configurations. We study the magnetic field configuration, fluctuations in the magnetosheath and the plasma in the regions around the northern cusp. Under northward IMF with Earthward $B_x$, there is a time-varying plasma depletion layer immediately outside th…
Heliospheric plasma turbulence plays a key role in transferring the energy of large-scale magnetic field and plasma flow fluctuations to smaller scales where the energy can be dissipated, ultimately leading to plasma heating. High-quality measurements of electromagnetic fields and electron velocity distributions by the Magnetospheric Multiscale (MMS) mission in Earth's magnetosheath present a unique opportunity to characterize plasma turbulence and to determine the mechanisms responsible for its dissipation. We apply the field-particle correlation technique to a set of twenty MMS magnetosheath…
Weakly collisional space plasmas are rarely in local thermal equilibrium and often exhibit non-Maxwellian electron and ion velocity distributions that lead to the growth of microinstabilities, that is, enhanced electric and magnetic fields at relatively short wavelengths. These instabilities play an active role in the evolution of space plasmas, as does ubiquitous broadband turbulence induced by turbulent structures. This study compares certain properties of a 2.5 dimensional Particle-In-Cell (PIC) simulation for the forward cascade of Alfvenic turbulence in a collisionless plasma against the …
We present a first statistical study of subproton and electron scales turbulence in the terrestrial magnetosheath using the Cluster Search Coil Magnetometer (SCM) waveforms of the STAFF instrument measured in the frequency range [1,180] Hz. It is found that clear spectral breaks exist near the electron scale, which separate two power-law like frequency bands referred to as the dispersive and the electron dissipation ranges. The frequencies of the breaks f_b are shown to be well correlated with the electron gyroscale ρ_e rather than with the electron inertial length de. The distribution of the …
Using observational data from the \emph{Magnetospheric Multiscale} (MMS) Mission in the Earth's magnetosheath, we estimate the energy cascade rate using different techniques within the framework of incompressible magnetohydrodynamic (MHD) turbulence. At the energy containing scale, the energy budget is controlled by the von Kármán decay law. Inertial range cascade is estimated by fitting a linear scaling to the mixed third-order structure function. Finally, we use a multi-spacecraft technique to estimate the Kolmogorov-Yaglom-like cascade rate in the kinetic range, well below the ion inertial …
Low frequency turbulence in Saturn's magnetosheath is investigated using in-situ measurements of the Cassini spacecraft. Focus is put on the magnetic energy spectra computed in the frequency range $\sim[10^{-4}, 1]$Hz. A set of 42 time intervals in the magnetosheath were analyzed and three main results that contrast with known features of solar wind turbulence are reported: 1) The magnetic energy spectra showed a $\sim f^{-1}$ scaling at MHD scales followed by an $\sim f^{-2.6}$ scaling at the sub-ion scales without forming the so-called inertial range; 2) The magnetic compressibility and the …
We present a combined observational and theoretical analysis to investigate the nature of plasma turbulence at kinetic scales in the Earth's magnetosheath. In the first decade of the kinetic range, just below the ion gyroscale, the turbulence was found to be similar to that in the upstream solar wind: predominantly anisotropic, low-frequency and kinetic Alfvén in nature. A key difference, however, is that the magnetosheath ions are typically much hotter than the electrons, $T_\mathrm{i}\gg T_\mathrm{e}$, which, together with $β_\mathrm{i}\sim 1$, leads to a change in behaviour in the second de…
In the solar wind, power spectral density (PSD) of the magnetic field fluctuations generally follow the so-called Kolmogorov spectrum f^-5/3 in the inertial range, where the dynamics is thought to be dominated by nonlinear interactions between counter-propagating incompressible Alfvén wave parquets. These features are thought to be ubiquitous in space plasmas. The present study gives a new and more complex picture of magnetohydrodynamics (MHD) turbulence as observed in the terrestrial magnetosheath. The study uses three years of in-situ data from the Cluster mission to explore the nature of th…
The first estimation of the energy cascade rate ${|ε_C|}$ of magnetosheath turbulence is obtained using the CLUSTER and THEMIS spacecraft data and an exact law of compressible isothermal magnetohydrodynamics turbulence. ${|ε_C|}$ is found to be of the order of ${10{^{-13}} J.m^{3}.s^{-1}}$, at least two orders of magnitude larger than its value in the solar wind (order of ${10{^{-16}} J.m^{3}.s^{-1}}$ in the fast wind). Two types of turbulence are evidenced and shown to be dominated either by incompressible Alfvénic or magnetosonic-like fluctuations. Density fluctuations are shown to amplify t…
By analyzing the magnetosheath measurements from MMS, we obtain the statistical results for the contribution of magnetic reconnection (MR) events at electron scales to the energy dissipation of coherent structures. The Partial Variance of Increments (PVI) method is employed to find coherent structures in the magnetic field data. The current sheet structures with reversal of magnetic field components are further selected. We consider the following criteria to identify the MR events, such as current sheet with magnetic field reversal, significant energy dissipation, and evident electron outflow …
We compare case studies of Magnetospheric Multiscale (MMS)-observed magnetopause electron diffusion regions (EDRs) to determine how the rate of work done by the electric field, $\vec{J}\cdot(\vec{E}+\vec{v}_e\times\vec{B})\equiv\vec{J}\cdot\vec{E}'$, and electron dynamics vary with magnetic shear angle. We provide an in-depth analysis of an MMS-observed EDR event with a guide field approximately the same size as the magnetosheath reconnecting field, which occurred on 8 December 2015. We find that $\vec{J}\cdot\vec{E}'$ was large and positive near the magnetic field reversal point, though patch…
Magnetospheric Multiscale (MMS) encountered the primary low-latitude magnetopause reconnection site when the inter-spacecraft separation exceeded the upstream ion inertial length. Classical signatures of the ion diffusion region (IDR), including a sub-ion-Alfvénic de-magnetized ion exhaust, a super-ion-Alfvénic magnetized electron exhaust, and Hall electromagnetic fields, are identified. The opening angle between the magnetopause and magnetospheric separatrix is $30^\circ\pm5^\circ$. The exhaust preferentially expands sunward, displacing the magnetosheath. Intense pileup of reconnected magneti…
Electron Heat Flux and Whistler Instability in the Earth's Magnetosheath
Swedish Institute of Space Physics（瑞典空间物理研究所）；Uppsala University（乌普萨拉大学）；Chalmers University of Technology（查尔姆斯理工大学）；Laboratory of Physics and Chemistry of the Environment and Space (LPC2E), OSUC, Univ Orleans, CNRS, CNES（环境与空间物理化学实验室（LPC2E）、OSUC、奥尔良大学、CNRS、CNES）；Laboratory for Atmospheric and Space Physics, University of Colorado（科罗拉多大学大气与空间物理实验室）；Imperial College London（帝国理工学院）
Studies of solar wind turbulence traditionally employ high-resolution magnetic field data, but high-resolution measurements of ion and electron moments have been possible only recently. We report the first turbulence studies of ion and electron velocity moments accumulated in pristine solar wind by the Fast Particle Investigation instrument onboard the Magnetospheric Multiscale (MMS) Mission. Use of these data is made possible by a novel implementation of a frequency domain Hampel filter, described herein. After presenting procedures for processing of the data, we discuss statistical propertie…
In the present paper, we investigate the power-law behaviour of the magnetic field spectra in the Earths magnetosheath region using Cluster spacecraft data under solar minimum condition. The power spectral density of the magnetic field data and spectral slopes at various frequencies are analysed. Propagation angle and compressibility are used to test the nature of turbulent fluctuations. The magnetic field spectra have the spectral slopes between -1.5 to 0 down to spatial scales of 20 ion gyroradius and show clear evidence of a transition to steeper spectra for small scales with a second power…
Magnetic flux ropes with helical field lines and strong core field are ubiquitous structures in space plasmas. Recently, kinetic-scale flux ropes have been identified by high-resolution observations from Magnetospheric Multiscale (MMS) spacecraft in the magnetosheath, which have drawn a lot of attention because of their non-ideal behavior and internal structures. Detailed investigation of flux rope structure and dynamics requires development of realistic kinetic models. In this paper, we generalize an equilibrium model to reconstruct a kinetic-scale flux rope previously reported via MMS observ…
Magnetic holes (MHs), with a scale much greater than \r{ho}i (proton gyroradius), have been widely reported in various regions of space plasmas. On the other hand, kinetic-size magnetic holes (KSMHs), previously called small size magnetic holes (SSMHs), with a scale of the order of magnitude of or less than \r{ho}i have only been reported in the Earth's magnetospheric plasma sheet. In this study, we report such KSMHs in the magnetosheath whereby we use measurements from the Magnetospheric Multiscale (MMS) mission, which provides three-dimensional (3D) particle distribution measurements with a …
Simultaneous observation of characteristic 3-dimensional (3D) signatures in the electron velocity distribution function (VDF) and intense quasi-monochromatic waves by the Magnetospheric Multiscale (MMS) spacecraft in the terrestrial magnetosheath are investigated. The intense wave packets are characterised and modeled analytically as quasi-parallel circularly-polarized whistler waves and applied to a test-particle simulation in view of gaining insight into the signature of the wave-particle resonances in velocity space. Both the Landau and the cyclotron resonances were evidenced in the test-pa…
We identify a dayside electron diffusion region (EDR) encountered by the Magnetospheric Multiscale (MMS) mission and estimate the terms in generalized Ohm's law that controlled energy conversion near the X-point. MMS crossed the moderate-shear (130 degrees) magnetopause southward of the exact X-point. MMS likely entered the magnetopause far from the X-point, outside the EDR, as the size of the reconnection layer was less than but comparable to the magnetosheath proton gyro-radius, and also as anisotropic gyrotropic "outflow" crescent electron distributions were observed. MMS then approached th…
A planet's magnetosheath extends from downstream of its bow shock up to the magnetopause where the solar wind flow is deflected around the magnetosphere and the solar wind embedded magnetic field lines are draped. This makes the region an important site for plasma turbulence, instabilities, reconnection and plasma depletion layers. A relatively high Alfvén Mach number solar wind and a polar-flattened magnetosphere make the magnetosheath of Saturn both physically and geometrically distinct from the Earth's. The polar flattening is predicted to affect the magnetosheath magnetic field structure a…
The Magnetospheric Multiscale (MMS) mission has observed electron whistler waves at the center and at the edges of magnetic holes in the dayside magnetosheath. The magnetic holes are nonlinear mirror structures since their magnitude is anti-correlated with particle density. In this article, we examine the growth mechanisms of these whistler waves and their interaction with the host magnetic hole. In the observations, as magnetic holes develop and get deeper, an electron population gets trapped and develops a temperature anisotropy favorable for whistler waves to be generated. In addition, the …
Using the novel Magnetospheric Multiscale (MMS) mission data accumulated during the 2019 MMS Solar Wind Turbulence Campaign, we calculate the Taylor microscale $(λ_{\mathrm{T}})$ 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 ti…
Space Research Institute, Austrian Academy of Sciences（奥地利科学院空间研究所）；Institute of Earth Physics and Space Science, HUN-REN（匈牙利研究与创新网络地球物理与空间科学研究所）；Department of Physics, Aberystwyth University（阿伯里斯特威斯大学物理系）；Institut für Theoretische Physik, Technische Universität Braunschweig（布伦瑞克工业大学理论物理研究所）；Max Planck Institute for Solar System Research（马克斯·普朗克太阳系研究所）；Swedish Institute of Space Physics（瑞典空间物理研究所）；Institute of Physics, University of Graz（格拉茨大学物理研究所）；Space and Plasma Physics, School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology（皇家理工学院电气工程学院空间与等离子体物理）；CNR/ISTP-Istituto per la Scienza e la Tecnologia dei Plasmi（国家研究委员会等离子体科学与技术研究所）；University of Sopron（肖普朗大学）
We analyze a high-resolution simulation of magnetopause reconnection observed by the Magnetospheric Multiscale (MMS) mission and explain the occurrence of strongly localized dissipation with an amplitude more than an order of magnitude larger than expected. Unlike symmetric reconnection, wherein reconnection of the ambient reversed magnetic field drives the dissipation, we find the annihilation of the self-generated, out-of-plane (Hall) magnetic field plays the dominant role. Electrons flow along the magnetosheath separatrices, converge in the diffusion region, and jet past the X-point into th…
Compressive plasma turbulence is investigated at sub-ion scales in the solar wind using both the Fast Plasma Investigation (FPI) instrument on the Magnetospheric MultiScale mission (MMS), as well as using calibrated spacecraft potential data from the Spin Plane Double Probe (SDP) instrument. The data from FPI allow a measurement down to the sub-ion scale region ($f_{sc}\gtrsim 1$ Hz) to be investigated before the instrumental noise becomes significant at a spacecraft frame frequency of $f_{sc}\approx 3$Hz, whereas calibrated spacecraft potential allows a measurement up to $f_{sc}\approx 40$Hz.…
Kinetic Alfvén waves (KAWs) are the short-wavelength extension of the MHD Alfvén-wave branch in the case of highly-oblique propagation with respect to the background magnetic field. Observations of space plasma show that small-scale turbulence is mainly KAW-like. We apply two theoretical approaches, collisional two-fluid theory and collisionless kinetic theory, to obtain predictions for the KAW polarizations depending on $β_\mathrm{p}$ (the ratio of the proton thermal pressure to the magnetic pressure) at the ion gyroscale in terms of fluctuations in density, bulk velocity, and pressure. We pe…
Two- and three-dimensional particle-in-cell simulations of a recent encounter of the Magnetospheric Multiscale Mission (MMS) with an electron diffusion region at the magnetopause are presented. While the two-dimensional simulation is laminar, turbulence develops at both the x-line and along the magnetic separatrices in the three-dimensional simulation. The turbulence is strong enough to make the magnetic field around the reconnection island chaotic and produces both anomalous resistivity and anomalous viscosity. Each contribute significantly to breaking the frozen-in condition in the electron …
We analyze the development and influence of turbulence in three-dimensional particle-in-cell simulations of guide-field magnetic reconnection at the magnetopause with parameters based on observations of an electron diffusion region by the Magnetospheric Multiscale (MMS) mission. Along the separatrices the turbulence is a variant of the lower hybrid drift instability (LHDI) that produces electric field fluctuations with amplitudes much greater than the reconnection electric field. The turbulence controls the scale length of the density and current profiles while enabling significant transport a…
We report the observations of an electron vortex magnetic hole corresponding to a new type of coherent structures in the magnetosheath turbulent plasma using the Magnetospheric Multiscale (MMS) mission data. The magnetic hole is characterized by a magnetic depression, a density peak, a total electron temperature increase (with a parallel temperature decrease but a perpendicular temperature increase), and strong currents carried by the electrons. The current has a dip in the center of the magnetic hole and a peak in the outer region of the magnetic hole. The estimated size of the magnetic hole …
Magnetic reconnection plays an important role in converting energy while modifying field topology. This process takes place in varied plasma environments in which the transport of magnetic flux is intrinsic. Identifying active magnetic reconnection sites in in-situ observations is challenging. A new technique, Magnetic Flux Transport (MFT) analysis, has been developed recently and proven in numerical simulation for identifying active reconnection efficiently and accurately. In this study, we examine the MFT process in 37 previously reported electron diffusion region (EDR)/reconnection-line cro…
Cross-helicity dominated distributed chaos (CHDC) for magnetohydrodynamic (large-scale) and kinetic (small-scale) ranges of space plasmas has been studied using results of direct numerical simulations and of measurements made in the Earth's magnetosheath and in free solar wind by the instruments onboard of the Magnetospheric Multiscale Mission and CLUSTER spacecrafts. Existence of two generic types of transition from the magnetohydrodynamic (MHD) to kinetic range has been shown: 1) from the Kolmogorov-like (scaling) MHD turbulence to the kinetic CHDC and 2) from the magnetohydrodynamic CHDC to…
Based on global hybrid simulation results, we predict that foreshock turbulence can reach the magnetopause and lead to reconnection as well as Earth-sized indents. Both the interplanetary magnetic field (IMF) and solar wind are constant in our simulation, and hence all dynamics are generated by foreshock instabilities. The IMF in the simulation is mostly Sun-Earth aligned with a weak northward and zero dawn-dusk component, such that subsolar magnetopause reconnection is not expected without foreshock turbulence modifying the magnetosheath fields. We show a reconnection example to illustrate th…
Anomalous Electric Fields in Earth's Turbulent Magnetosheath: Insights From 3D Hybrid Simulations
Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange（法国蔚蓝海岸大学、蔚蓝海岸天文台、法国国家科学研究中心、拉格朗日实验室）；Northumbria University（诺森比亚大学）；University of Tokyo（东京大学）；Stanford University（斯坦福大学）；Kavli Institute for Particle Astrophysics and Cosmology（卡弗里粒子天体物理学与宇宙学研究所）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）
Turbulence properties and kinetic signatures of electron in Kelvin-Helmholtz waves during a geomagnetic storm
University of Maryland College Park（马里兰大学帕克分校）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；University of New Hampshire（新罕布什尔大学）；Dartmouth College（达特茅斯学院）；University of Maryland Baltimore（马里兰大学巴尔的摩分校）
In space and astrophysical plasmas turbulence leads to the development of coherent structures characterized by a strong current density and important magnetic shears. Using hybrid-kinetic simulations of turbulence (3D with different energy injection scales) we investigate the development of these coherent structures and characterize their shape. First, we present different methods to estimate the overall shape of the 3D structure using local measurements, foreseeing application on satellite data. Then we study the local magnetic configuration inside and outside current peak regions, comparing …
The statistical properties of ions in two-dimensional fully developed turbulence have been compared between two different numerical algorithms. In particular, we compare Hybrid Particle In Cell (hybrid PIC with fluid electrons) and full PIC simulations, focusing on particle diffusion and acceleration phenomena. To investigate several heliospheric plasma conditions, a series of numerical simulations has been performed by varying the plasma $β$ - the ratio between kinetic and magnetic pressure. These numerical studies allow the exploration of different scenarios, going from the solar corona (low…
Magnetic reconnection has been suggested to play an important role in the dynamics and energetics of plasma turbulence by spacecraft observations, simulations and theory over the past two decades, and recently, by magnetosheath observations of MMS. A new method based on magnetic flux transport (MFT) has been developed to identify reconnection activity in turbulent plasmas. This method is applied to a gyrokinetic simulation of two-dimensional (2D) plasma turbulence. Results on the identification of three active reconnection X-points are reported. The first two X-points have developed bi-directi…
How turbulent energy is dissipated in weakly collisional space and astrophysical plasmas is a major open question. Here, we present the application of a field-particle correlation technique to directly measure the transfer of energy between the turbulent electromagnetic field and electrons in the Earth's magnetosheath, the region of solar wind downstream of the Earth's bow shock. The measurement of the secular energy transfer from the parallel electric field as a function of electron velocity shows a signature consistent with Landau damping. This signature is coherent over time, close to the p…
MMS Insights into CME Driven Sub-Alfvénic Solar Wind at 1 AU
University of Maryland（马里兰大学）；NASA Goddard Space Flight Center（NASA戈达德太空飞行中心）；University of New Hampshire（新罕布什尔大学）；University of Delaware（特拉华大学）；University of Colorado Boulder（科罗拉多大学博尔德分校）
