Long-time properties of MHD turbulence and the role of symmetries

We investigate long-time properties of three-dimensional MHD turbulence in the absence of forcing and examine in particular the role played by the quadratic invariants of the system and by the symmetries of the initial configurations. We observe that, when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time whereas by perturbing these solutions either explicitly or implicitly using for example single precision for long times, the flows depart from their original behavior and can become either strongly helical, or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as predicted by statistical arguments for non-dissipative systems with the addition of an energy minimization principle, as already analyzed in \cite{stribling_90} for random initial conditions using a moderate number of Fourier modes. Furthermore, the alignment properties of these flows, between velocity, vorticity, magnetic potential, induction and current, correspond to the dominance of two main regimes, one helically dominated and one in quasi-equipartition of kinetic and magnetic energy. We also contrast the scaling of the ratio of magnetic energy to kinetic energy as a function of wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function of wavenumber. We find that the former ratio is constant with an approximate equipartition for scales smaller than the largest scale of the flow whereas the ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure

Collisionless Plasma Turbulence: Insights from Magnetohydrodynamic and Hall Magnetohydrodynamic Simulations and Observations of the Earth's Magnetosphere

Turbulence is a ubiquitous phenomenon that occurs throughout the universe, in both neutral fluids and plasmas. For collisionless plasmas, kinetic effects, which alter the nonlinear dynamics and result in small-scale dissipation, are still not well understood in the context of turbulence. This work uses direct numerical simulations (DNS) and observations of Earth's magnetosphere to study plasma turbulence. Long-time relaxation in magnetohydrodynamic (MHD) turbulence is examined using DNS with particular focus on the role of magnetic and cross helicity and symmetries of the initial con-figurations. When strong symmetries are absent or broken through perturbations, flows evolve towards states predicted by statistical mechanics with an energy minimization principle, which features two main regimes; one magnetic helicity dominated and one with quasi-equipartition of kinetic and magnetic energy. The role of the Hall effect, which contributes to the dynamics of collisionless plasmas, is also explored numerically. At scales below the ion inertial length, a transition to a magnetically dominated state, associated with advection becoming subdominant to dissipation, occurs. Real-space current, vorticity, and electric fields are examined. Strong current structures are associated with alignment between the current and magnetic field, which may be important in collisionless plasmas where field-aligned currents can be unstable. Turbulence within bursty bulk ow braking events, thought to be associated with near-Earth magnetotail reconnection, are then studied using the THEMIS spacecraft. It is proposed that strong field-aligned currents associated with turbulent intermittency destabilize into double layers, providing a collisionless dissipation mechanism for the turbulence. Plasma waves may also radiate from the region, removing energy from the turbulence and potentially depositing it in the aurora. Finally, evidence for turbulence in the Kelvin-Helmholtz instability (KHI) on the Earth's magnetopause is found using data from the Magnetospheric Multiscale (MMS) mission. With MMS, spatial properties, including spatial intermittency and anisotropy, can be examined along with temporal properties and ion and electron velocity spectra can be examined observationally into the kinetic scales. Quasi-two-dimensional anisotropy perpendicular to the magnetic field is found. Field-aligned current instabilities and wave radiation may also be relevant in the KHI

Correlation Scales of the Turbulent Cascade at 1 au

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Structure of the Current Sheet in the 11 July 2017 Electron Diffusion Region Event.

The structure of the current sheet along the Magnetospheric Multiscale (MMS) orbit is examined during the 11 July 2017 Electron Diffusion Region (EDR) event. The location of MMS relative to the X-line is deduced and used to obtain the spatial changes in the electron parameters. The electron velocity gradient values are used to estimate the reconnection electric field sustained by nongyrotropic pressure. It is shown that the observations are consistent with theoretical expectations for an inner EDR in 2-D reconnection. That is, the magnetic field gradient scale, where the electric field due to electron nongyrotropic pressure dominates, is comparable to the gyroscale of the thermal electrons at the edge of the inner EDR. Our approximation of the MMS observations using a steady state, quasi-2-D, tailward retreating X-line was valid only for about 1.4 s. This suggests that the inner EDR is localized; that is, electron outflow jet braking takes place within an ion inertia scale from the X-line. The existence of multiple events or current sheet processes outside the EDR may play an important role in the geometry of reconnection in the near-Earth magnetotail

The Turbulent Cascade for High Cross-helicity States at 1 au. II. Minor Energy

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Near-Earth plasma sheet boundary dynamics during substorm dipolarization.

We report on the large-scale evolution of dipolarization in the near-Earth plasma sheet during an intense (AL ~ -1000 nT) substorm on August 10, 2016, when multiple spacecraft at radial distances between 4 and 15 R E were present in the night-side magnetosphere. This global dipolarization consisted of multiple short-timescale (a couple of minutes) B z disturbances detected by spacecraft distributed over 9 MLT, consistent with the large-scale substorm current wedge observed by ground-based magnetometers. The four spacecraft of the Magnetospheric Multiscale were located in the southern hemisphere plasma sheet and observed fast flow disturbances associated with this dipolarization. The high-time-resolution measurements from MMS enable us to detect the rapid motion of the field structures and flow disturbances separately. A distinct pattern of the flow and field disturbance near the plasma boundaries was found. We suggest that a vortex motion created around the localized flows resulted in another field-aligned current system at the off-equatorial side of the BBF-associated R1/R2 systems, as was predicted by the MHD simulation of a localized reconnection jet. The observations by GOES and Geotail, which were located in the opposite hemisphere and local time, support this view. We demonstrate that the processes of both Earthward flow braking and of accumulated magnetic flux evolving tailward also control the dynamics in the boundary region of the near-Earth plasma sheet.Graphical AbstractMultispacecraft observations of dipolarization (left panel). Magnetic field component normal to the current sheet (BZ) observed in the night side magnetosphere are plotted from post-midnight to premidnight region: a GOES 13, b Van Allen Probe-A, c GOES 14, d GOES 15, e MMS3, g Geotail, h Cluster 1, together with f a combined product of energy spectra of electrons from MMS1 and MMS3 and i auroral electrojet indices. Spacecraft location in the GSM X-Y plane (upper right panel). Colorcoded By disturbances around the reconnection jets from the MHD simulation of the reconnection by Birn and Hesse (1996) (lower right panel). MMS and GOES 14-15 observed disturbances similar to those at the location indicated by arrows

Modeling Kelvin-Helmholtz instability-driven turbulence with hybrid simulations of Alfv\'enic turbulence

Magnetospheric Multiscale (MMS) observations of plasma turbulence generated by a Kelvin-Helmholtz (KH) event at the Earth's magnetopause are compared with a high-resolution two-dimensional (2D) hybrid direct numerical simulation (DNS) of decaying plasma turbulence driven by large-scale balanced Alfv\'enic fluctuations. The simulation, set up with four observation-driven physical parameters (ion and electron betas, turbulence strength, and injection scale) exhibits a quantitative agreement on the spectral, intermittency, and cascade-rate properties with in situ observations, despite the different driving mechanisms. Such agreement demonstrates a certain universality of the turbulent cascade from magnetohydrodynamic (MHD) to sub-ion scales, whose properties are mainly determined by the selected parameters, also indicating that the KH instability-driven turbulence has a quasi-2D nature. The validity of the Taylor hypothesis in the sub-ion spatial range suggests that the fluctuations at sub-ion scales have predominantly low frequencies, consistent with a kinetic Alfv\'en wave-like nature or with quasi-static structures. Finally, the third-order structure function analysis indicates that the cascade rate of the turbulence generated by a KH event in the magnetopause is an order of magnitude larger than in the ambient magnetosheath.Comment: 11 pages, 6 figures, submitted to The Astrophysical Journa

Multi-scale evolution of Kelvin–Helmholtz waves at the Earth's magnetopause during southward IMF periods

At the Earth's low-latitude magnetopause, the Kelvin-Helmholtz instability (KHI), driven by the velocity shear between the magnetosheath and magnetosphere, has been frequently observed during northward interplanetary magnetic field (IMF) periods. However, the signatures of the KHI have been much less frequently observed during southward IMF periods, and how the KHI develops under southward IMF has been less explored. Here, we performed a series of realistic 2D and 3D fully kinetic simulations of a KH wave event observed by the Magnetospheric Multiscale (MMS) mission at the dusk-flank magnetopause during southward IMF on September 23, 2017. The simulations demonstrate that the primary KHI bends the magnetopause current layer and excites the Rayleigh-Taylor instability (RTI), leading to penetration of high-density arms into the magnetospheric side. This arm penetration disturbs the structures of the vortex layer and produces intermittent and irregular variations of the surface waves which significantly reduces the observational probability of the periodic KH waves. The simulations further demonstrate that in the non-linear growth phase of the primary KHI, the lower-hybrid drift instability (LHDI) is induced near the edge of the primary vortices and contributes to an efficient plasma mixing across the magnetopause. The signatures of the large-scale surface waves by the KHI/RTI and the small-scale fluctuations by the LHDI are reasonably consistent with the MMS observations. These results indicate that the multi-scale evolution of the magnetopause KH waves and the resulting plasma transport and mixing as seen in the simulations may occur during southward IMF

Energy Partitioning Constraints at Kinetic Scales in Low- Turbulence

Turbulence is a fundamental physical process through which energy injected into a system at large scales cascades to smaller scales. In collisionless plasmas, turbulence provides a critical mechanism for dissipating electromagnetic energy. Here we present observations of plasma fluctuations in low- turbulence using data from NASAs Magnetospheric Multiscale mission in Earths magnetosheath. We provide constraints on the partitioning of turbulent energy density in the fluid, ion-kinetic, and electron-kinetic ranges. Magnetic field fluctuations dominated the energy density spectrum throughout the fluid and ion-kinetic ranges, consistent with previous observations of turbulence in similar plasma regimes. However, at scales shorter than the electron inertial length, fluctuation power in electron kinetic energy significantly exceeded that of the magnetic field, resulting in an electron-motion-regulated cascade at small scales. This dominance should be highly relevant for the study of turbulence in highly magnetized laboratory and astrophysical plasmas