Ion Inertial Length Research Articles

First Observations of Irregular Surface of Interplanetary Shocks at Ion Scales by Cluster

Abstract We present the first observational evidence of the irregular surface of interplanetary (IP) shocks by using multispacecraft observations of the Cluster mission. In total we discuss observations of four IP shocks that exhibit moderate Alfvénic Mach numbers (M A ≤ 6.5). Three of them are high-β shocks with upstream β = 2.2–3.7. During the times when these shocks were observed, the Cluster spacecraft formed constellations with inter-spacecraft separations ranging from less than one upstream ion inertial length (d i ) up to 100 d i . Expressed in kilometers, the distances ranged between 38 km and ∼104 km. We show that magnetic field profiles and the local shock normals of observed shocks are very similar when the spacecraft are of the order of one d i apart, but are strikingly different when the distances increase to 10 or more d i . We interpret these differences to be due to the irregular surface of IP shocks and discuss possible causes for such irregularity. We strengthen our interpretation by comparing observed shock profiles with profiles of simulated shocks. The latter had similar characteristics (M A, θ BN , upstream ion β) as observed shocks and the profiles were obtained at separations across the simulation domain equivalent to the Cluster inter-spacecraft distances.

Kinetic Simulations of Magnetic Reconnection in Partially Ionized Plasmas

Fast magnetic reconnection occurs in nearly all natural and laboratory plasmas and rapidly releases stored magnetic energy. Although commonly studied in fully ionized plasmas, if and when fast reconnection can occur in partially ionized plasmas, such as the interstellar medium or solar chromosphere, is not well understood. This Letter presents the first fully kinetic particle-in-cell simulations of partially ionized reconnection and demonstrates that fast reconnection can occur in partially ionized systems. In the simulations, the transition to fast reconnection occurs when the current sheet width thins below the ion-inertial length in contrast to previous analytic predictions. The peak reconnection rate is ≥0.08 when normalized to the bulk Alfvén speed (including both ion and neutral mass), consistent with previous experimental results. However, when the bulk Alfvén speed falls below the neutral sound speed, the rate becomes system size dependent. The normalized inflow velocity is ionization fraction dependent, which is shown to be a result of neutral momentum transport. A model for the inflow is developed which agrees well with the simulation results.

Small-scale dipolarization fronts in the Earth′s magnetotail

Previous studies suggest that dipolarization fronts (DFs) are 1 to 3RE (RE is the earth radius) wide in the dawn-dusk direction. Recent kinetic simulations have found that DFs may break up into small-scale structures after they are produced by reconnection. Motivated by this simulation, we revisited the scale size of DFs in the dawn-dusk direction by using Cluster observations during the years when the inter-distance among Cluster spacecraft was between 1000 and 2000 km. We selected the DFs that were detected by more than one spacecraft and estimated the radii of these DFs by a simple geometrical analysis, which is based on comparison of DF normals observed by different spacecraft. We found a few DFs that were only a few ion inertial lengths in the dawn-dusk direction. These results point out the importance of multi-scale coupling during the evolution of DFs.

Magnetosonic/whistler mode turbulence influences on ion dynamics

The development of decaying magnetosonic/whistler mode turbulence is investigated, employing a two-dimensional, fully kinetic, particle-in-cell simulation that covers scales at the end of the inertial range. The anisotropic wavenumber spectrum of magnetic fluctuations reaches electron kinetic scales through the forward cascade of the turbulence. The magnetic fluctuations have intermittency at scales shorter than the ion inertial length. The intermittent nature leads to a localized steepening of magnetic fluctuations which accelerates ions nonlinearly in the direction perpendicular to the background magnetic field. The non-thermal ions have the speed of several times faster than the ion thermal speed. The fully kinetic particle-in-cell simulation shows important implications for a fundamental understanding of the non-thermal ion production in magnetosonic/whistler mode turbulence.

Magnetoacoustic solitons in pair-ion fullerene plasma

ABSTRACT The propagation of magnetoacoustic (fast magnetohydrodynamic) waves in pair-ion (PI) fullerene plasma is studied in the linear and nonlinear regimes. The pair-ion (PI) fullerene plasma is theorized as homogeneous, magnetized, warm and collisionless. Employing multi-fluid magnetohydrodynamic model, the dispersion relation is obtained and wave dispersion effects which appear through ion inertial length are discussed. Using reductive perturbation technique (RPT), the Korteweg–de Vries (KdV) equation is derived and its solution for small but finite amplitude magnetoacoustic solitons propagating in the direction perpendicular to the external magnetic field is presented. The compressive magnetoacoustic soliton (i.e. positive potential pulse) propagating with super Alfvénic speed is obtained in magnetized PI fullerene plasma. The variations in the amplitude and width of the magnetoacoustic soliton structures are also illustrated by using numerical values of the plasma parameters such as ions' density, temperature difference between fullerene ions and magnetic field intensity, which have been taken from the PI plasma experiments already published in the literature.

Shock ripples observed by the MMS spacecraft: ion reflection and dispersive properties

Shock ripples are ion-inertial-scale waves propagating within the front region of magnetized quasi-perpendicular collisionless shocks. The ripples are thought to influence particle dynamics and acceleration at shocks. With the four magnetospheric multiscale (MMS) spacecraft, it is for the first time possible to fully resolve the small scale ripples in space. We use observations of one slow crossing of the Earth’s non-stationary bow shock by MMS. From multi-spacecraft measurements we show that the non-stationarity is due to ripples propagating along the shock surface. We find that the ripples are near linearly polarized waves propagating in the coplanarity plane with a phase speed equal to the local Alfvén speed and have a wavelength close to 5 times the upstream ion inertial length. The dispersive properties of the ripples resemble those of Alfvén ion cyclotron waves in linear theory. Taking advantage of the slow crossing by the four MMS spacecraft, we map the shock-reflected ions as a function of ripple phase and distance from the shock. We find that ions are preferentially reflected in regions of the wave with magnetic field stronger than the average overshoot field, while in the regions of lower magnetic field, ions penetrate the shock to the downstream region.

Magnetosheath Reconnection Before Magnetopause Reconnection Driven by Interplanetary Tangential Discontinuity: A Three‐Dimensional Global Hybrid Simulation With Oblique Interplanetary Magnetic Field

AbstractTerrestrial dayside dynamics associated with a southward turning, oblique interplanetary magnetic field (IMF) carried by an interplanetary tangential discontinuity (TD) is investigated by performing a three‐dimensional global‐scale hybrid simulation systematically for cases in which the incoming solar wind TD possesses various magnetic field rotation angles ΔΦ = 90° to 180° and half widths w = 2di0 to w = 30di0, where di0 is the ion inertial length in the solar wind. Overall, the TD is compressed while being transmitted into the magnetosheath, with different compression processes downstream of the quasi‐parallel (Q‐||) and quasi‐perpendicular (Q‐⊥) shocks. It is found that magnetosheath reconnection may take place downstream of both the Q‐|| and Q‐⊥ shocks due to interaction of the directional TD with the bow shock and magnetopause, but the existence of magnetosheath reconnection depends on w and ΔΦ. Magnetosheath flux ropes are formed through three‐dimensional patchy reconnection in the thinned current sheet, with a longer rope lengths under a larger ΔΦ. There exists a dawn‐dusk asymmetry in the spatial extent of the flux ropes, which becomes more significant as ΔΦ decreases. When ΔΦ decreases to 90°, no reconnection flux ropes are found. Magnetopause reconnection is initiated when the magnetic fluxes with a southward turning IMF (on the sunward side) reach the magnetopause, and the magnetopause flux ropes can be mixed with the magnetosheath ones. Our simulation demonstrates that the effects of a southward turning of the IMF may not be a simple field direction change that leads to reconnection only at the magnetopause.

Incompressive Energy Transfer in the Earth’s Magnetosheath: Magnetospheric Multiscale Observations

Abstract Using observational data from the Magnetospheric Multiscale mission in the Earth’s magnetosheath, we estimate the energy cascade rate at three ranges of length scale, employing a single data interval, 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 length scale, where we expect a reduction due to involvement of other channels of transfer. The computed inertial range cascade rate is almost equal to the von Kármán–MHD law at the energy-containing scale, while the incompressive cascade rate evaluated at the kinetic scale is somewhat lower, as anticipated in theory. In agreement with a recent study, we find that the incompressive cascade rate in the Earth’s magnetosheath is about 1000 times larger than the cascade rate in the pristine solar wind.

Solar Wind Turbulence Studies Using MMS Fast Plasma Investigation Data

Abstract 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 Plasma Investigation (FPI) instrument on board the Magnetospheric Multiscale 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 properties of solar wind turbulence extending into the kinetic range. Magnetic field fluctuations dominate electron and ion-velocity fluctuation spectra throughout the energy-containing and inertial ranges. However, a multispacecraft analysis indicates that at scales shorter than the ion inertial length, electron velocity fluctuations become larger than ion-velocity and magnetic field fluctuations. The kurtosis of ion-velocity peaks around a few ion inertial lengths and returns to a near Gaussian value at sub-ion scales.

Numerical study of the cascading energy conversion of the reconnection current sheet in solar eruptions

Magnetic reconnection plays an important role in the energy conversion during solar eruptions. In this work, we present a resistive magnetohydrodynamical study (2.5D) of a flux rope eruption based on the Lin and Forbes model regarding cascading reconnection. We use a second-order Godunov scheme code, to better understand the physical mechanisms responsible for high reconnection rates and the internal structure, particularly in chaotic or turbulent regions, of the coronal mass ejection (CME)/flare current sheet (CS). Two sets of simulations with Lundquist numbers of 1.18 x 10(5) and 2.35 x 10(5) in the vicinity of the CS, generating a slow CME and a moderate one, show global dynamic features largely consistent with the flare model. Looking into the fine structure of the CS, magnetic reconnection employs simultaneously the Sweet-Parker mode and time-dependent small-scale Petschek patterns in the early stage. As the flux rope rises, the outflow region becomes turbulent, which further enhances the reconnection rates. Our results show that coalescence and fusion processes of plasmoids provide a large number of small, transient local diffusion regions to dissipate magnetic energy, and confirm that the dissipation starts at macro-MHD scales rather than ion inertial lengths. The two runs have the same range of the local reconnection rates (10(-4)-0.3) relevant to CMEs. The fast rates are closely proportional to the square of the aspect ratio of multiple small-scale CSs. The topology of the magnetic field and the turbulence spectrum of the energy cascade are statistically addressed as well.

Oblique Ion‐Scale Magnetotail Flux Ropes Generated by Secondary Tearing Modes

AbstractWe examine Magnetospheric Multiscale observations of three ion‐scale magnetic flux ropes (diameter ~6–9 ion inertial lengths) in the Earth's magnetotail reconnection diffusion region with a small guide field. During the event, the electron reconnection exhaust reversed direction together with the reversal of normal magnetic field component. After that, the three ion‐scale flux ropes were observed near the ion diffusion region, in which flat‐top distributions were found at the field‐aligned electrons (<2 keV). The axis orientation and motion velocity of the flux ropes are determined by minimum variance analysis of the electric field component along the flux rope axis, using single‐spacecraft measurements. Results show that the three flux rope axes form 13°, 55°, and 55° to the guide field direction and are mostly tilted toward the direction of the reconnecting field. These results are also validated by multiple‐spacecraft analysis methods. It is found that the tilted angles agree reasonably well with the predicted angles for secondary tearing modes, suggesting that these ion‐scale flux ropes are likely generated by secondary tearing instabilities as those recently found in the three‐dimensional kinetic simulations of turbulent magnetic reconnection.

Small‐Scale Flux Transfer Events Formed in the Reconnection Exhaust Region Between Two X Lines

AbstractWe report MMS observations of the ion‐scale flux transfer events (FTEs) that may involve two main X lines and tearing instability between the two X lines. The four spacecraft detected multiple isolated regions with enhanced magnetic field strength and bipolar Bn signatures normal to the nominal magnetopause, indicating FTEs. The currents within the FTEs flow mostly parallel to B, and the magnetic tension force is balanced by the total pressure gradient force. During these events, the plasma bulk flow velocity was directed southward. Detailed analysis of the magnetic and electric field and plasma moments variations suggests that the FTEs were initially embedded within the exhaust region north of an X line but were later located southward/downstream of a subsequent X line. The cross sections of the individual FTEs are in the range of ~2.5–6.8 ion inertial lengths. The observations suggest the formation of multiple secondary FTEs. The presence of an X line in the exhaust region southward of a second X line results from the southward drift of an old X line and the reformation of a new X line. The current layer between the two X lines is unstable to the tearing instability, generating multiple ion‐scale flux‐rope‐type secondary islands.

Intense Electric Fields and Electron‐Scale Substructure Within Magnetotail Flux Ropes as Revealed by the Magnetospheric Multiscale Mission

AbstractThree flux ropes associated with near‐Earth magnetotail reconnection are analyzed using Magnetospheric Multiscale observations. The flux ropes are Earthward propagating with sizes from ∼3 to 11 ion inertial lengths. Significantly different axial orientations are observed, suggesting spatiotemporal variability in the reconnection and/or flux rope dynamics. An electron‐scale vortex, associated with one of the most intense electric fields (E) in the event, is observed within one of the flux ropes. This E is predominantly perpendicular to the magnetic field (B); the electron vortex is frozen‐in with E × B drifting electrons carrying perpendicular current and causing a small‐scale magnetic enhancement. The vortex is ∼16 electron gyroradii in size perpendicular to B and potentially elongated parallel to B. The need to decouple the frozen‐in vortical motion from the surrounding plasma implies a parallel E at the structure's ends. The formation of frozen‐in electron vortices within reconnection‐generated flux ropes may have implications for particle acceleration.

Electron Energization at a Reconnecting Magnetosheath Current Sheet

AbstractWe present observations of electron energization within a sub‐ion‐scale magnetosheath current sheet (CS). A number of signatures indicate ongoing reconnection, including the thickness of the CS (∼0.7 ion inertial length), nonzero normal magnetic field, Hall magnetic fields with electrons carrying the Hall currents, and electron heating. We observe localized electron acceleration and heating parallel to the magnetic field at the edges of the CS. Electrostatic waves observed in these regions have low phase velocity and small wave potentials and thus cannot provide the observed acceleration and heating. Instead, we find that the electrons are accelerated by a parallel potential within the separatrix regions. Similar acceleration has been reported based on magnetopause and magnetotail observations. Thus, despite the different plasma conditions in magnetosheath, magnetopause, and magnetotail, the acceleration mechanism and corresponding heating of electrons is similar.

Magnetic depression and electron transport in an ion-scale flux rope associated with Kelvin–Helmholtz waves

Abstract. We report an ion-scale magnetic flux rope (the size of the flux rope is ∼ 8.5 ion inertial lengths) at the trailing edge of Kelvin–Helmholtz (KH) waves observed by the Magnetospheric Multiscale (MMS) mission on 27 September 2016, which is likely generated by multiple X-line reconnection. The currents of this flux rope are highly filamentary: in the central flux rope, the current flows are mainly parallel to the magnetic field, supporting a local magnetic field increase at about 7 nT, while at the edges the current filaments are predominantly along the antiparallel direction, which induce an opposing field that causes a significant magnetic depression along the axis direction (> 20 nT), meaning the overall magnetic field of this flux rope is depressed compared to the ambient magnetic field. Thus, this flux rope, accompanied by the plasma thermal pressure enhancement in the center, is referred to as a crater type. Intense lower hybrid drift waves (LHDWs) are found at the magnetospheric edge of the flux rope, and the wave potential is estimated to be ∼ 17 % of the electron temperature. Though LHDWs may be stabilized by the mechanism of electron resonance broadening, these waves could still effectively enable diffusive electron transports in the cross-field direction, corresponding to a local density dip. This indicates LHDWs could play important roles in the evolution of crater flux ropes. Keywords. Magnetospheric physics (magnetopause, cusp, and boundary layers; solar wind–magnetosphere interactions)

Dynamics of Intense Currents in the Solar Wind

Abstract Transient currents in the solar wind are carried by various magnetic field discontinuities that contribute significantly to the magnetic field fluctuation spectrum. Internal instabilities and dynamics of these discontinuities are believed to be responsible for magnetic field energy dissipation and corresponding charged particle acceleration and heating. Accurate modeling of these phenomena requires detailed investigation of transient current formation and evolution. By examining such evolution using a unique data set compiled from observations of the same solar wind flow by two spacecraft at Earth’s and Mars’s orbits, we show that it consists of several processes: discontinuity thinning (decrease in thickness normalized by the ion inertial length), intensification of currents normalized to the proton thermal current (i.e., the product of proton charge, density, and thermal velocity), and increase in the compressional component of magnetic field variations across discontinuities. The significant proton temperature variation around most observed discontinuities indicates possible proton heating. Plasma velocity jumps across the discontinuities are well correlated with Alfvén velocity changes. We discuss possible explanations of the observed discontinuity evolution. We also compare the observed evolution with predictions of models describing discontinuity formation due to Alfvén wave steepening. Our results show that discontinuity modeling likely requires taking into account both the effects of nonlinear Alfvén wave dynamics and solar wind expansion.

Electron‐Scale Measurements of Dipolarization Front

AbstractDipolarization front (DF)—a sharp boundary with scale of ion inertial length (c/ωpi) in the Earth's magnetotail—can also have fine structures at electron scale (c/ωpe). Such electron‐scale structures, determining the local energy conversion, have not been revealed by multispacecraft observations so far, due to the large separation of spacecraft in previous studies. Here we report the first electron‐scale multispacecraft measurements of DF, using data from the recent Magnetospheric Multiscale mission. We find strong parallel currents only in the high‐density side of the DF but strong perpendicular currents across the whole DF. We find no parallel electric fields during the DF interval. Although DF is primarily an energy‐load region (E·J > 0), the electron‐scale currents could lead to a localized energy generation (E·J < 0). Such features are different from those reported in previous multispacecraft studies, where the currents, electric fields, and energy conversion are uniform across the DF; they also shed lights on the study of substorm current wedge, which is crucial in the magnetosphere‐ionosphere coupling.

Guide Field Reconnection: Exhaust Structure and Heating.

Magnetospheric Multiscale observations are used to probe the structure and temperature profile of a guide field reconnection exhaust ~100 ion inertial lengths downstream from the X‐line in the Earth's magnetosheath. Asymmetric Hall electric and magnetic field signatures were detected, together with a density cavity confined near 1 edge of the exhaust and containing electron flow toward the X‐line. Electron holes were also detected both on the cavity edge and at the Hall magnetic field reversal. Predominantly parallel ion and electron heating was observed in the main exhaust, but within the cavity, electron cooling and enhanced parallel ion heating were found. This is explained in terms of the parallel electric field, which inhibits electron mixing within the cavity on newly reconnected field lines but accelerates ions. Consequently, guide field reconnection causes inhomogeneous changes in ion and electron temperature across the exhaust.

On the Importance of Spatial and Velocity Resolution in the Hybrid-Vlasov Modeling of Collisionless Shocks

In hybrid-Vlasov plasma modeling, the ion velocity distribution function is propagated using the Vlasov equation while electrons are considered a charge-neutralizing fluid. It is an alternative to particle-in-cell methods, one advantage being the absence of sampling noise in the moments of the distribution. However, the discretization requirements in up to six dimensions (3D position, 3V velocity) make the computational cost of hybrid-Vlasov models higher. This is why hybrid-Vlasov modeling has only recently become more popular and available to model large-scale systems. The hybrid-Vlasov model Vlasiator is the first to have been successfully applied to model the solar-terrestrial interaction. It includes in particular the bow shock and magnetosheath regions, albeit in 2D-3V configurations so far. The purpose of this study is to investigate how Vlasiator parameters affect the modeling of a plasma shock in a 1D-3V simulation. The setup is similar to the Earth's bow shock in previous simulations, so that the present results can be related to existing and future magnetospheric simulations. The parameters investigated are the spatial and velocity resolution, as well as the phase space density threshold, which is the key parameter of the so-called sparse velocity space. The role of the Hall term in Ohm's law is also studied. The evaluation metrics used are the convergence of the final state, the complexity of spatial profiles and ion distributions as well as the position of the shock front. In agreement with previous Vlasiator studies it is not necessary to resolve the ion inertial length and gyroradius in order to obtain kinetic phenomena. While the code remains numerically stable with all combinations of resolutions, it is shown that significantly increasing the resolution in one space but not the other leads to unphysical results. Past a certain level, decreasing the phase space density threshold bears a large computational weight without clear physical improvement in the setup used here. Finally, the inclusion of the Hall term shows only minor effects in this study, mostly because of the 1D configuration and the scales studied, at which the Hall term is not expected to play a major role.

On the Full-range β Dependence of Ion-scale Spectral Break in the Solar Wind Turbulence

Abstract The power spectrum of magnetic fluctuations has a break at the high-frequency end of the inertial range. Beyond this break, the spectrum becomes steeper than the Kolmogorov law f −5/3. The break frequency was found to be associated with plasma beta (β). However, the full-range β dependence of the ion-scale spectral break has not been presented before in observational studies. Here we show the continuous variation of the break frequency on full-range β in the solar wind turbulence. By using measurements from the WIND and Ulysses spacecraft, we show the break frequency (f b ) normalized, respectively, by the frequencies corresponding to ion inertial length (f di ), ion gyroradius ( ), and cyclotron resonance scale (f ri ) as a function of β for 1306 intervals. Their β values spread from 0.005 to 20, which nearly covers the full β range of the observed solar wind turbulence. It is found that ( ) generally decreases (increases) with β, while is nearly a constant. We perform a linear fit on the statistical result, and obtain the empirical formulas , , and to describe the relation between f b and β. We also compare our observations with a numerical simulation and the prediction by ion cyclotron resonance theory. Our result favors the idea that the cyclotron resonance is an important mechanism for energy dissipation at the spectral break. When β ≪ 1 and β ≫ 1, the break at f di and may also be associated with other processes.