Structure Of Current Sheet Research Articles

Two-dimensional self-similar plasma equilibria

Force-free plasma equilibria are expected to form in the solar corona, while in-situ spacecraft observations have shown that force-free equilibria are formed in the planetary magnetotails. In this paper, we develop fluid models of two-dimensional axially symmetric force-free equilibria and discuss similar slab equilibria. The group theory approach is used to find the symmetry groups and reduce the Grad-Shafranov equation with exponential and power law nonlinearities to ordinary differential equations for the self-similar (automodel) solutions that we analyze analytically and numerically. Force-free equilibria of the developed class have a magnetotail-type configuration with magnetic field lines stretched in the radial direction and represent nonlinear force-free equilibria, because rot B=α(r) B with α(r)≠const. Making use of the same symmetry groups, we generalize the developed force-free equilibria by including a finite plasma pressure gradient and compare different equilibria of the developed class. These models can be useful for describing the structure and stability of current sheets observed in planetary magnetotails and formed in the solar atmosphere.

New Analytical Solution of the Equilibrium Ampere’s Law Using the Walker’s Method: a Didactic Example

This work aims to demonstrate the analytical solution of the Grad-Shafranov (GS) equation or generalized Ampere’s law, which is important in the studies of self-consistent 2.5-D solution for current sheet structures. A detailed mathematical development is presented to obtain the generating function as shown by Walker (RSPSA 91, 410, 1915). Therefore, we study the general solution of the GS equation in terms of the Walker’s generating function in details without omitting any step. The Walker’s generating function g(ζ) is written in a new way as the tangent of an unspecified function K(ζ). In this trend, the general solution of the GS equation is expressed as exp(− 2Ψ) = 4|K ′(ζ)|2/cos2[K(ζ) − K(ζ ∗)]. In order to investigate whether our proposal would simplify the mathematical effort to find new generating functions, we use Harris’s solution as a test, in this case K(ζ) = arctan(exp(i ζ)). In summary, one of the article purposes is to present a review of the Harris’s solution. In an attempt to find a simplified solution, we propose a new way to write the GS solution using g(ζ) = tan(K(ζ)). We also present a new analytical solution to the equilibrium Ampere’s law using g(ζ) = cosh(b ζ), which includes a generalization of the Harris model and presents isolated magnetic islands.

The Temporal and Spatial Scales of Density Structures Released in the Slow Solar Wind During Solar Activity Maximum

Abstract In a recent study, we took advantage of a highly tilted coronal neutral sheet to show that density structures, extending radially over several solar radii (R s), are released in the forming slow solar wind approximately 4–5 R s above the solar surface. We related the signatures of this formation process to intermittent magnetic reconnection occurring continuously above helmet streamers. We now exploit the heliospheric imagery from the Solar Terrestrial Relation Observatory (STEREO) to map the spatial and temporal distribution of the ejected structures. We demonstrate that streamers experience quasi-periodic bursts of activity with the simultaneous outpouring of small transients over a large range of latitudes in the corona. This cyclic activity leads to the emergence of well-defined and broad structures. Derivation of the trajectories and kinematic properties of the individual small transients that make up these large-scale structures confirms their association with the forming slow solar wind (SSW). We find that these transients are released, on average, every 19.5 hr, simultaneously at all latitudes with a typical radial size of 12 R s. Their spatial distribution, release rate, and three-dimensional extent are used to estimate the contribution of this cyclic activity to the mass flux carried outward by the SSW. Our results suggest that, in interplanetary space, the global structure of the heliospheric current sheet is dominated by a succession of blobs and associated flux ropes. We demonstrate this with an example event using STEREO-A in situ measurements.

Suppression of Ion-Scale Microtearing Modes by Electron-Scale Turbulence via Cross-Scale Nonlinear Interactions in Tokamak Plasmas

Gyrokinetic turbulence simulations are applied for the first time to the cross-scale interactions of microtearing modes (MTMs) and electron-temperature-gradient (ETG) modes. The investigation of the fluctuation response in a multiscale simulation including both types of instabilities indicates that MTMs are suppressed by ETG turbulence. A detailed analysis of nonlinear mode coupling reveals that radially localized current-sheet structures of MTMs are strongly distorted by fine-scale E×B flows of ETG turbulence. Consequently, electron heat transport caused by the magnetic flutter of MTMs is significantly reduced and ETG turbulence dominates electron heat transport.

Generalized phase mixing: Turbulence-like behaviour from unidirectionally propagating MHD waves

We present the results of three-dimensional (3D) ideal magnetohydrodynamics (MHD) simulations on the dynamics of a perpendicularly inhomogeneous plasma disturbed by propagating Alfvénic waves. Simpler versions of this scenario have been extensively studied as the phenomenon of phase mixing. We show that, by generalizing the textbook version of phase mixing, interesting phenomena are obtained, such as turbulence-like behavior and complex current-sheet structure, a novelty in longitudinally homogeneous plasma excited by unidirectionally propagating waves. This study is in the setting of a coronal hole. However, it constitutes an important finding for turbulence-related phenomena in astrophysics in general, relaxing the conditions that have to be fulfilled in order to generate turbulent behavior.

Imprints of Quasi‐Adiabatic Ion Dynamics on the Current Sheet Structures Observed in the Martian Magnetotail by MAVEN

AbstractNumerous studies of the current sheets (CS) in the Earth's magnetotail showed that quasi‐adiabatic ion dynamics plays an important role in the formation of complicated multilayered current structures. In order to check whether the similar mechanisms operate in the Martian magnetotail, we analyzed 80 CS crossings using MAVEN measurements on the nightside of Mars at radial distances ~1.0–2.8RM. We found that CS structures experience similar dependence on the value of the normal component of the magnetic field at the neutral plane (BN) and on the ratio of the ion drift velocity outside the CS to the thermal velocity (VT/VD) as it was observed for the CSs in the Earth's magnetotail. For the small values of BN, a thin and intense CS embedded in a thicker one is observed. The half‐thickness L of this layer is ~30–100 km ≤ ρH+ (ρH+ is a gyroradius of thermal protons outside the CS). With the increase of BN, the L also increases up to several hundred kilometers (~ρO+, ρO2+), the current density decreases, and the embedding feature disappears. Our statistical analysis showed a good agreement between L values observed by MAVEN and the CS scaling obtained from the quasi‐adiabatic model, if the plasma characteristics in Martian CSs are used as input parameters. Thus, we may conclude that in spite of the differences in magnetic topology, ion composition, and plasma thermal characteristics observed in the Earth's and Martian magnetotails, similar quasi‐adiabatic mechanisms contribute to the formation of the CSs in the magnetotails of both planets.

Experimental Verification of the Role of Electron Pressure in Fast Magnetic Reconnection with a Guide Field.

We report detailed laboratory observations of the structure of a reconnection current sheet in a two-fluid plasma regime with a guide magnetic field. We observe and quantitatively analyze the quadrupolar electron pressure variation in the ion-diffusion region, as originally predicted by extended magnetohydrodynamics simulations. The projection of the electron pressure gradient parallel to the magnetic field contributes significantly to balancing the parallel electric field, and the resulting cross-field electron jets in the reconnection layer are diamagnetic in origin. These results demonstrate how parallel and perpendicular force balance are coupled in guide field reconnection and confirm basic theoretical models of the importance of electron pressure gradients for obtaining fast magnetic reconnection.

Numerical study of Hall effects on counter-helicity spheromak merging by two-dimensional Hall-MHD simulations

Hall effects on counter-helicity spheromak merging were investigated by two-dimensional MHD and Hall-MHD simulations of merging two axisymmetric toroidal flux tubes. In Hall-MHD cases, the structure of the reconnection current sheet and reconnection outflow are modified from the MHD case due to the Hall effect. We compared two cases (called “case-O” and “case-I”) of counter-helicity merging, which are distinguished by the polarity of toroidal magnetic fluxes. Radial motion of the reconnection X-point is controlled by poloidal electron flow accompanying the toroidal flux of the merging two spheromaks, and this creates a large difference in the current sheet and flow structure between the two cases of the Hall-MHD regime. The radial shift of the reconnection X-point depending on the polarity of toroidal magnetic flux of the spheromaks breaks the symmetry between the two cases. It was also found that there widely exists separation of ion and electron flow which are affected by the modification of the current sheet structure due to the radial shift of the X-point in the downstream side of the merging, and its spatial scale of the distribution of the Hall electric field is larger than the ion skin depth.

Structure of current and plasma in current sheets depending on the conditions of sheet formation

The structure of current sheets created under laboratory conditions is characterized by a large variety, which depends substantially on the conditions under which the sheet if formed. In this work, we present the results of an experimental study of the structure and evolution of current sheets that were formed in magnetic configurations with a singular line of the X type. It has been shown that the change in the transverse magnetic field gradient, the strength of the longitudinal magnetic field, and the mass of the ions in plasma makes it possible to significantly vary the main parameters of the current sheets. This offers the challenges of using laboratory experimental results for analyzing and simulating the cosmophysical processes.

Partitioning of integrated energy fluxes in four tail reconnection events observed by Cluster

AbstractWe present the partitioning of integrated energy flux from four tail reconnection events observed by Cluster, focusing on the relative contributions of Poynting flux, electron, H+ and O+ enthalpy, and kinetic energy flux in the tailward and earthward directions in order to study temporal and spatial features of each event. We further subdivide the Poynting flux into three frequency bands to examine the possible structures and waves that contribute most significantly to the total Poynting flux from the reconnection region. Our results indicate that H+ enthalpy flux is often dominant, but O+ enthalpy, electron enthalpy, Poynting flux, and H+ kinetic energy flux can contribute significant or greater total energy flux depending on spacecraft location with respect the current sheet, flow direction, temporal scale, and local conditions. We observe integrated H+ enthalpy fluxes that differ by factors of 3–4 between satellites, even over ion inertial length scales. We observe strong differences in behavior between H+ and O+ enthalpy fluxes in all events, highlighting the importance of species‐specific energization mechanisms. We find tailward‐earthward asymmetry in H+ enthalpy flux, possibly indicative of the influence of the closed earthward boundary of the magnetotail system. Frequency filtering of the Poynting flux shows that current sheet surface waves and structures on the timescale of current sheet flapping contribute significantly, while large‐scale structure contributions are relatively small. We observe that the direction and behavior of the Poynting flux differs between bands, indicating that the observed flux originates from multiple distinct sources or processes.

Full particle-in-cell simulations of kinetic equilibria and the role of the initial current sheet on steady asymmetric magnetic reconnection

Tangential current sheets are ubiquitous in space plasmas and yet hard to describe with a kinetic equilibrium. In this paper, we use a semi-analytical model, the BAS model, which provides a steady ion distribution function for a tangential asymmetric current sheet and we prove that an ion kinetic equilibrium produced by this model remains steady in a fully kinetic particle-in-cell simulation even if the electron distribution function does not satisfy the time independent Vlasov equation. We then apply this equilibrium to look at the dependence of magnetic reconnection simulations on their initial conditions. We show that, as the current sheet evolves from a symmetric to an asymmetric upstream plasma, the reconnection rate is impacted and the X line and the electron flow stagnation point separate from one another and start to drift. For the simulated systems, we investigate the overall evolution of the reconnection process via the classical signatures discussed in the literature and searched in the Magnetospheric MultiScale data. We show that they seem robust and do not depend on the specific details of the internal structure of the initial current sheet.

Earth's distant magnetotail current sheet near and beyond lunar orbit

AbstractWe analyze the structure of the Earth magnetotail current sheet (CS) in middle, X∈[−50,−20] RE, and distant, X∈[−100,−80] RE, regions using data set of 573 CS crossings by Geotail in 1994–1995. For a subset of 213 CSs we determine the CS thickness L, average current density j0, and velocity vD=j0/en0 (n0 is the ion number density). We find similar dawn‐dusk distributions of CS parameters for middle and distant tail: L is about 3000 km at the dusk flank and grows up to 12,000 km toward the dawn flank; j0 grows toward the dusk flank by a factor of 2–3; and the most intense CSs (with higher vD) are observed near midnight. We show that ion‐scale CSs with the thickness of several ion thermal gyroradii (say less than seven) are observed in middle and distant tail in more than 50% of crossings. For observed CSs electrons likely provide the dominant contribution to the current density. We divide the subset into intense and weak CSs (using parameter vD). Weak CSs have thickness of about 20 ion thermal gyroradii and Bz of about 1.5 nT. Intense CSs have thickness of about 3–7 thermal gyroradii and much smaller Bz implying more stretched field line configuration. Intense CSs are accompanied by fast ion flows: vD is larger for larger amplitudes of ion bulk velocity vx that is likely due to larger contribution of Speiser ions. The properties of the CS in middle and distant tail are compared with those found for the near‐Earth tail.

THEMIS two-point measurements of the cross-tail current density: A thick bifurcated current sheet in the near-Earth plasma sheet.

The basic properties of the near‐Earth current sheet from 8 RE to 12 RE were determined based on Time History of Events and Macroscale Interactions during Substorms (THEMIS) observations from 2007 to 2013. Ampere's law was used to estimate the current density when the locations of two spacecraft were suitable for the calculation. A total of 3838 current density observations were obtained to study the vertical profile. For typical solar wind conditions, the current density near (off) the central plane of the current sheet ranged from 1 to 2 nA/m2 (1 to 8 nA/m2). All the high current densities appeared off the central plane of the current sheet, indicating the formation of a bifurcated current sheet structure when the current density increased above 2 nA/m2. The median profile also showed a bifurcated structure, in which the half thickness was about 3 RE. The distance between the peak of the current density and the central plane of the current sheet was 0.5 to 1 RE. High current densities above 4 nA/m2 were observed in some cases that occurred preferentially during substorms, but they also occurred in quiet times. In contrast to the commonly accepted picture, these high current densities can form without a high solar wind dynamic pressure. In addition, these high current densities can appear in two magnetic configurations: tail‐like and dipolar structures. At least two mechanisms, magnetic flux depletion and new current system formation during the expansion phase, other than plasma sheet compression are responsible for the formation of the bifurcated current sheets.

Intermittent Dissipation and Heating in 3D Kinetic Plasma Turbulence.

High resolution, fully kinetic, three dimensional (3D) simulation of collisionless plasma turbulence shows the development of turbulence characterized by sheetlike current density structures spanning a range of scales. The nonlinear evolution is initialized with a long wavelength isotropic spectrum of fluctuations having polarizations transverse to an imposed mean magnetic field. We present evidence that these current sheet structures are sites for heating and dissipation, and that stronger currents signify higher dissipation rates. The analyses focus on quantities such as J·E, electron, and proton temperatures, and conditional averages of these quantities based on local electric current density. Evidently, kinetic scale plasma, like magnetohydrodynamics, becomes intermittent due to current sheet formation, leading to the expectation that heating and dissipation in astrophysical and space plasmas may be highly nonuniform. Comparison with previous results from 2D kinetic simulations, as well as high frequency solar wind observational data, are discussed.

Energy dynamics and current sheet structure in fluid and kinetic simulations of decaying magnetohydrodynamic turbulence

Simulations of decaying magnetohydrodynamic (MHD) turbulence are performed with a fluid and a kinetic code. The initial condition is an ensemble of long-wavelength, counter-propagating, shear-Alfvén waves, which interact and rapidly generate strong MHD turbulence. The total energy is conserved and the rate of turbulent energy decay is very similar in both codes, although the fluid code has numerical dissipation, whereas the kinetic code has kinetic dissipation. The inertial range power spectrum index is similar in both the codes. The fluid code shows a perpendicular wavenumber spectral slope of k⊥−1.3. The kinetic code shows a spectral slope of k⊥−1.5 for smaller simulation domain, and k⊥−1.3 for larger domain. We estimate that collisionless damping mechanisms in the kinetic code can account for the dissipation of the observed nonlinear energy cascade. Current sheets are geometrically characterized. Their lengths and widths are in good agreement between the two codes. The length scales linearly with the driving scale of the turbulence. In the fluid code, their thickness is determined by the grid resolution as there is no explicit diffusivity. In the kinetic code, their thickness is very close to the skin-depth, irrespective of the grid resolution. This work shows that kinetic codes can reproduce the MHD inertial range dynamics at large scales, while at the same time capturing important kinetic physics at small scales.

MODULATION OF GALACTIC COSMIC RAYS OBSERVED AT L1 IN SOLAR CYCLE 23

We analyze a unique 15 yr record of galactic cosmic-ray (GCR) measurements made by the SOHO Coronal Diagnostic Spectrometer NIS detectors, recording integrated GCR numbers with energies above 1.0 GeV between 1996 July and 2011 June. We are able to closely reproduce the main features of the SOHO/CDS GCR record using the modulation potential calculated from neutron monitor data by Usoskin et al. The GCR numbers show a clear solar cycle modulation: they decrease by 50% from the 1997 minimum to the 2000 maximum of the solar cycle, then return to the 1997 level in 2007 and continue to rise, in 2009 December reaching a level 25% higher than in 1997. This 25% increase is in contrast with the behavior of Ulysses/KET GCR protons extrapolated to 1 AU in the ecliptic plane, showing the same level in 2008-2009 as in 1997. The GCR numbers are inversely correlated with the tilt angle of the heliospheric current sheet. In particular, the continued increase of SOHO/CDS GCRs from 2007 until 2009 is correlated with the decrease of the minimum tilt angle from 30° in mid-2008 to 5° in late 2009. The GCR level then drops sharply from 2010 January, again consistent with a rapid increase of the tilt angle to over 35°. This shows that the extended 2008 solar minimum was different from the 1997 minimum in terms of the structure of the heliospheric current sheet.

A possible mechanism of the enhancement and maintenance of the shear magnetic field component in the current sheet of the Earth’s magnetotail

The influence of the shear magnetic field component, which is directed along the electric current in the current sheet (CS) of the Earth’s magnetotail and enhanced near the neutral plane of the CS, on the nonadiabatic dynamics of ions interacting with the CS is studied. The results of simulation of the nonadiabatic ion motion in the prescribed magnetic configuration similar to that observed in the magnetotail CS by the CLUSTER spacecraft demonstrated that, in the presence of some initial shear magnetic field, the north-south asymmetry in the ion reflection/refraction in the CS is observed. This asymmetry leads to the formation of an additional current system formed by the oppositely directed electric currents flowing in the northern and southern parts of the plasma sheet in the planes tangential to the CS plane and in the direction perpendicular to the direction of the electric current in the CS. The formation of this current system perhaps is responsible for the enhancement and further maintenance of the shear magnetic field near the neutral plane of the CS. The CS structure and ion dynamics observed in 17 intervals of the CS crossings by the CLUSTER spacecraft is analyzed. In these intervals, the shear magnetic field was increased near the neutral plane of the CS, so that the bell-shaped spatial distribution of this field across the CS plane was observed. The results of the present analysis confirm the suggested scenario of the enhancement of the shear magnetic field near the neutral plane of the CS due to the peculiarities of the nonadiabatic ion dynamics.

Thin current sheets with strong bell-shape guide field: Cluster observations and models with beams

Abstract. We study the kinetic structure of intense ion-scale current sheets with strong electron currents and the guide field having a bell-shape profile. We consider four crossings of the Earth magnetotail current sheet by the Cluster mission in 2003. The thickness of these current sheets is about the ion inertial length and significantly smaller than the characteristic ion gyroradius. We analyze the asymmetry of the electron velocity distribution functions and show that the electron current is provided by the small electron subpopulation interpreted as an electron beam or two counter-streaming electron beams. The beam (counter-streaming beams) has a bulk velocity of the order of the electron thermal velocity and a density (difference of beam densities) of about 1–5% of the plasma density. To describe the observed current sheets we develop a kinetic model with particle beams. The model predicts different thickness of the current sheet for different types of current carriers (one electron beam or two counter-streaming electron beams). The observed ion-scale current sheets can be explained assuming that the current is carried by one electron beam and a co-streaming ion beam. Although the ion beam does not carry a significant current, this beam is required to balance the electron current perpendicular to the current sheet neutral plane. The developed model explains the dominance of the electron current and the ion scales of the current sheets.

Vertical displacements of the current sheet and Hall currents

Vertical displacements of the peripheral regions of the current sheet with respect to its mean plane have been detected in the case of the sheet formation in the three-dimensional configuration with the X line and longitudinal component of the magnetic field. It has been shown that this effect is due to the generation of Hall currents and the appearance of vertically directed forces. Change in the sign of vertical displacements at the late stage of the sheet evolution has been detected, indicating the generation of opposite Hall currents when the direction of the main current near the side edges of the sheet changes. It has been shown that Hall currents significantly affect the structure of current sheets, and vertical oscillations of the peripheral regions of the current sheet, which appear owing to oppositely directed Hall currents, are involved in the dynamic processes in current sheets.

TEMPERATURE FLUCTUATIONS DRIVEN BY MAGNETOROTATIONAL INSTABILITY IN PROTOPLANETARY DISKS

The magnetorotational instability (MRI) drives magnetized turbulence in sufficiently ionized regions of protoplanetary disks, leading to mass accretion. The dissipation of the potential energy associated with this accretion determines the thermal structure of accreting regions. Until recently, the heating from the turbulence has only been treated in an azimuthally averaged sense, neglecting local fluctuations. However, magnetized turbulence dissipates its energy intermittently in current sheet structures. We study this intermittent energy dissipation using high resolution numerical models including a treatment of radiative thermal diffusion in an optically thick regime. Our models predict that these turbulent current sheets drive order unity temperature variations even where the MRI is damped strongly by Ohmic resistivity. This implies that the current sheet structures where energy dissipation occurs must be well resolved to correctly capture the flow structure in numerical models. Higher resolutions are required to resolve energy dissipation than to resolve the magnetic field strength or accretion stresses. The temperature variations are large enough to have major consequences for mineral formation in disks, including melting chondrules, remelting calcium-aluminum rich inclusions, and annealing silicates; and may drive hysteresis: current sheets in MRI active regions could be significantly more conductive than the remainder of the disk.