Formation Of Thin Current Sheets Research Articles

Current-driven kink instabilities in relativistic jets: dissipation properties

ABSTRACT We analyse the evolution of current-driven kink instabilities of a highly magnetized relativistic plasma column, focusing in particular on its dissipation properties. The instability evolution leads to the formation of thin current sheets where the magnetic energy is dissipated. We find that the total amount of dissipated magnetic energy is independent of the dissipation properties. Dissipation occurs in two stages: a peak when the instability saturates that is characterized by the formation of a helicoidal current sheet at the boundary of the deformed plasma column, followed by a weaker almost flat phase, in which turbulence develops. The detailed properties of these two phases depend on the equilibrium configuration and other parameters, in particular on the steepness of the pitch radial profile, on the presence of an external axial magnetic field and on the amount of magnetization. These results are relevant for high energy astrophysical sources, since current sheets can be the sites of magnetic reconnection where particles can be accelerated to relativistic energies and give rise to the observed radiation.

MMS Observations of Super Thin Electron‐Scale Current Sheets in the Earth's Magnetotail

AbstractFlapping of the current sheet (CS) associated with the propagation of high‐velocity bulk flows allowed to observe the super thin current sheet (STCS) in the magnetotail plasma sheet (PS). During the interval of interest, 111 crossings of the CS neutral plane were detected. In 95 crossings, the STCSs with a current density J ≥ 20 nA/m2 were observed. A half‐thickness (LSTCS) of the STCSs was about a few electron gyroradii or less. In a number of the STCSs the parameter of adiabaticity (κe) was <1.0 for suprathermal electron population (>1 keV). Our analysis has shown that the electric current in such STCSs is carried by unmagnetized electrons (κe < 1), and the stress balance is supported by the off‐diagonal terms of their pressure tensor. In this sense, the underlying physics of the formation of STCSs at electron scales by unmagnetized electrons is similar to the mechanism of ion‐scale thin CS formation by the quasi‐adiabatic ions. The low‐energy population of magnetized electrons is also crucially important since it keeps the STCS stable and allows their observation as a quasi‐stationary structure. We compare the observed half‐thickness of the STCS with that predicted by a new kinetic theory (λ) considering the coupling between ion‐scale TCS and electron‐scale STCS. We found a reasonable agreement between both values: LSTCS ∼ (0.3–1)λ. Further improvement in the theory taking into account the dynamics of unmagnetized electrons may provide better agreement with observations.

Global and local processes of thin current sheet formation during substorm growth phase

Formation of thin current sheets in Earth's magnetotail is a critical element of the magnetosphere dynamics. The configuration and stability of these thin current sheets control the onset of magnetic reconnection and particle acceleration in the magnetotail during substorms and other geomagnetic activities. In recent years, multipoint observations, kinetic and hybrid simulations have significantly improved our understanding of the structure and dynamics of thin current sheets, including their ion kinetic physics. Global hybrid simulations have also revealed many details of ion kinetics in thin current sheet physics. In this paper we review current understanding of current sheet physics and discuss our recent observational and simulation results on thin current sheet formation, emphasizing the kinetics of current sheet thinning, multi-component ion populations, the role of electron anisotropy and ion agyrotropy, and the role of the ionosphere.

Magnetic island merger as a mechanism for inverse magnetic energy transfer

Magnetic energy transfer from small to large scales due to successive magnetic island coalescence is investigated. A solvable analytical model is introduced and shown to correctly capture the evolution of the main quantities of interest, as borne out by numerical simulations. Magnetic reconnection is identified as the key mechanism enabling the inverse transfer, and setting its properties: magnetic energy decays as $\tilde t^{-1}$, where $\tilde t$ is time normalized to the (appropriately defined) reconnection timescale; and the correlation length of the field grows as $\tilde t^{1/2}$. The magnetic energy spectrum is self-similar, and evolves as $\propto \tilde t ^{-3/2}k^{-2}$, where the $k$-dependence is imparted by the formation of thin current sheets.

Influence of 3D plasmoid dynamics on the transition from collisional to kinetic reconnection

Within the resistive magnetohydrodynamic model, high-Lundquist number reconnection layers are unstable to the plasmoid instability, leading to a turbulent evolution where the reconnection rate can be independent of the underlying resistivity. However, the physical relevance of these results remains questionable for many applications. First, the reconnection electric field is often well above the runaway limit, implying that collisional resistivity is invalid. Furthermore, both theory and simulations suggest that plasmoid formation may rapidly induce a transition to kinetic scales, due to the formation of thin current sheets. Here, this problem is studied for the first time using a first-principles kinetic simulation with a Fokker-Planck collision operator in 3D. The low-β reconnecting current layer thins rapidly due to Joule heating before the onset of the oblique plasmoid instability. Linear growth rates for standard (ky = 0) tearing modes agree with semicollisional boundary layer theory, but the angular spectrum of oblique (|ky|>0) modes is significantly narrower than predicted. In the nonlinear regime, flux-ropes formed by the instability undergo complex interactions as they are advected and rotated by the reconnection outflow jets, leading to a turbulent state with stochastic magnetic field. In a manner similar to previous 2D results, super-Dreicer fields induce a transition to kinetic reconnection in thin current layers that form between flux-ropes. These results may be testable within new laboratory experiments.

Hall Effect in Laboratory and Space Current Sheets

The role of the Hall effect in the formation of thin current sheets (CSs) is analyzed by comparing results of laboratory and satellite experiments. In spite of the strong difference in the plasma parameters, both laboratory and space CSs are characterized by the hot ion component and cold isotropic electron component. Such a relation between the ion and electron components would have to guarantee the predominant contribution of the ion diamagnetic drift current to the total current density. However, the Cluster spacecraft observations of thin CSs in the Earth’s magnetotail have revealed the predominance of a strong electron (rather than ion) current. This may be due to the Hall effect, which causes generation of electric fields, which redistribute the CS currents in favor of the electron currents at the expense of the ion currents. Observations demonstrate that the thinner the CS, the stronger this effect. A similar tendency was also observed in laboratory experiments on CS formation in plasma with ions of different mass, which made it possible to vary the CS relative thickness and monitor the consequences of the Hall effect. Comparison of results of satellite and laboratory experiments indicates that the Hall effect plays an important role in the formation of thin CSs in both magnetospheric and laboratory plasmas.

Generalized magnetotail equilibria: Effects of the dipole field, thin current sheets, and magnetic flux accumulation

AbstractGeneralizations of the class of quasi‐1‐D solutions of the 2‐D Grad‐Shafranov equation, first considered by Schindler in 1972, are investigated. It is shown that the effect of the dipole field, treated as a perturbation, can be included into the original 1972 class solution by modification of the boundary conditions. Some of the solutions imply the formation of singularly thin current sheets. Equilibrium solutions for such sheets resolving their singular current structure on the scales comparable to the thermal ion gyroradius can be obtained assuming anisotropic and nongyrotropic plasma distributions. It is shown that one class of such equilibria with the dipole‐like boundary perturbation describes bifurcation of the near‐Earth current sheet. Another class of weakly anisotropic equilibria with thin current sheets embedded into a thicker plasma sheet helps explain the formation of thin current sheets in a relatively distant tail, where such sheets can provide ion Landau dissipation for spontaneous magnetic reconnection. The free energy for spontaneous reconnection can be provided due to accumulation of the magnetic flux at the tailward end of the closed field line region. The corresponding hump in the normal magnetic field profile Bz(x,z = 0) creates a nonzero gradient along the tail. The resulting gradient of the equatorial magnetic field pressure is shown to be balanced by the pressure gradient and the magnetic tension force due to the higher‐order correction of the latter in the asymptotic expansion of the tail equilibrium in the ratio of the characteristic tail current sheet variations across and along the tail.

Thin current sheet formation in response to the loading and the depletion of magnetic flux during the substorm growth phase

AbstractThe physics of geomagnetic substorms has been under debate for a long time. Although the growth phase has received less attention than the spectacular expansion phase, the state of the magnetotail at the end of the growth phase, i.e., a thin current sheet (CS) formation is of central importance because it provides the magnetotail conditions for the expansion phase onset. This study investigates CSs evolution during the substorm growth phase. The growth phase physics considered here includes the removal of closed magnetic flux in the near‐Earth tail and the addition of magnetic flux into the tail lobes. It is found that two separate CSs evolve at distinct locations in the near‐Earth and the midtail region in response to the depletion and the loading of magnetic flux. The relative current densities in the dual‐current‐sheet configuration depends strongly on whether the depleted or the added magnetic flux dominates. The presented results suggest that substorm expansion onset may be associated only with reconnection onset in the near‐Earth CS, while midtail reconnection causes bursty bulk flows or bubbles.

Formation of self‐organized shear structures in thin current sheets

AbstractSelf‐consistent kinetic (particle‐in‐cell) model of magnetotail thin current sheet (TCS) is used to understand the formation of self‐consistent sheared magnetic structures. It is shown that shear configurations appear in TCS as a result of self‐consistent evolution of some initial magnetic perturbation at the current sheet center. Two general shapes of shear TCS components are found as a function of the transverse coordinate: symmetric and antisymmetric. We show that TCS formation goes together with the emergence of field‐aligned currents in the center of the current sheet, as a result of north‐south asymmetry of quasi‐adiabatic ion motions. Ion drift currents can also contribute to the magnetic shear evolution, but their role is much less significant, their contribution depending upon the normal component Bz and the amplitude of the initial perturbation in TCS. Parametric maps illustrating different types of TCS equilibria are presented that show a higher probability of formation of symmetric shear TCS configuration at lower values of the normal magnetic component.

Accelerated ions ahead of earthward propagating dipolarization fronts

We report on the evolving ion distributions associated with the arrival of an earthward propagating dipolarization front in the near‐Earth magnetotail using Time History of Events and Macroscale Interactions during Substorms (THEMIS). Ion distributions exhibit steady duskward anisotropy well before the front arrival, suggesting thin current sheet formation at ∼11 RE, during the growth phase of a moderate geomagnetic substorm. As the dipolarization front moves closer, an additional, earthward streaming ion population appears, resulting in an earthward velocity moment. This population eventually overwhelms the preexisting duskward anisotropy and merges with the earthward convecting bulk flow once the dipolarization front arrives. Test‐particle simulations show that the observed ion evolution is consistent with a picture of ions reflected and accelerated by the approaching front and moving ahead of it.

Linear theory of anisotropy driven modes in a Harris neutral sheet

There are several sources of electron and ion anisotropies that can have a profound effect on the stability of the current sheets in the magnetosphere. A new semianalytical approach is introduced and utilized to develop the linear theory of anisotropy driven modes in a neutral sheet. This technique is intermediary between analytical models and those that solve the exact linear Vlasov equation. Its advantage is in its accuracy and speed. Both the parallel and perpendicular limits are considered, and improved stability criteria and growth rates for Weibel, anisotropic tearing, and Fried–Weibel modes are obtained. For the same anisotropy levels, electron anisotropy is much more effective in modifying the stability of the modes, but the presence of large ion anisotropy in the magnetosheath can still have a significant effect on the growth of the tearing mode. Effects of ion anisotropy are more pronounced for thicker sheets, whereas the electron anisotropy is weakly dependent on the current sheet thickness. Although the current expectation is that magnetic reconnection in the magnetosphere is associated with the formation of thin current sheets, our results suggest an interesting possibility of fast growth rates for thick sheets in the presence of sufficient electron and/or ion anisotropies.

Dynamics of equilibrium upset and electromagnetic energy transformation in the geomagnetotail: A theory and simulation using particles. 3. Versions of formation of thin current sheets

The final part of the study is devoted to the process of rapid reconfiguration of the geomagnetotail after the upset of the equilibrium, i.e., to substorm activation. Such a version of spontaneous formation of nonlinear kinetic small-scale structures at the site occupied by an initial current sheet (CS), which results in the formation of a specific equilibrium current structure with strong ion anisotropy (forced kinetic current sheet, FKCS), has been revealed in the course of numerical simulation. This reconfiguration “channel” is realized when the relative value of the magnetic field component normal to CS is smaller than a certain critical value. In this case the disturbance intensity is SPONTANEOUSLY settled at a certain final level at the late stages. The obtained results are compared with the previous study of the system evolution under the action of the external trigger. The physical causes and specific features of different CS evolution regimes are considered. The studied plasma mechanisms are responsible for the effects of rapid energy transformation—magnetic field “annihilation”—that took place in the geomagnetotail.

Modeling of the Magnetospheric Response to the Dynamic Solar Wind

We discuss quasi-static and dynamic models of the magnetotail response to perturbations imposed by the solar wind, focusing particularly on the formation of thin current sheets, their structure and breakup.

Two-dimensional stationary configurations of the current-carrying plasma sheet and their usage in describing physical effects of disturbance development in the nightside magnetosphere

It has been indicated that the previously proposed two-dimensional model of collisionless isotropic current-carrying plasma sheet makes it possible to reproduce and physically clearly describe many phenomena in the observed process of disturbance development in the nighttime magnetosphere. The formation of thin current sheets in the near zone, the characteristic scale of these sheets (the current sheet thickness and a change in this scale along the magnetotail), and the formation of the configuration with a neutral point in the near zone have been considered in the work. The latter is possible since the solution of the model problem includes the solution with a change in the magnetic field topology. The initial stage of the disturbance development in the magnetotail in the case when the electric field is switched on at the northern and southern boundaries has been considered within the scope of the MHD description where the Ohm’s law has been used in the generalized form (∂/∂ ≠ 0) in the inertial term. The problem of current sheet intensification is analyzed (approximately) by considering two competitive processes: an increase in the current velocity in the plasma sheet and a development of convection.

Thin current sheets and loss of equilibrium: Three‐dimensional theory and simulations

Using quasi‐static equilibrium theory and three‐dimensional MHD simulations, we confirm earlier two‐dimensional results that finite boundary deformations of magnetotail equilibria can lead to large local current density enhancements, that is, the formation of thin current sheets. Equilibrium configurations that satisfy flux, entropy, and topology conservation cease to exist when the boundary deformations exceed critical limits. This provides a strong argument for onset of instability or the loss of equilibrium, regardless of the dissipation mechanism. Catastrophe points can be reached for relatively modest perturbations of the boundary. The most important internal property that influences the critical limit is the variation of the lobe magnetic field strength with distance from the Earth, related to the overall tail flaring. Stronger flaring, corresponding to a more rapid decrease of the lobe field with distance downtail, tends to stabilize the tail. That means such configurations require stronger perturbations to reach the critical limit or show less significant thinning and current density intensification for a given perturbation. Due to the nonlinearity of the tail response to the perturbations, the current intensification tends to be more localized than the perturbation.

Formation of thin current sheets in the magnetotail: Effects of propagating boundary deformations

Observations and simulations have demonstrated the important role of thin current sheet formation in the course of substorms. Previously, using two‐dimensional magnetohydrostatic equilibrium theory together with magnetic flux, entropy, and topology conservation, we demonstrated that a finite boundary deformation of magnetotail equilibria can lead to a loss of equilibrium; that is, equilibrium configurations that satisfy the constraints cease to exist when the boundary deformation exceeds a critical value. When the critical threshold is approached, locally the current density becomes infinite; that is, a thin current sheet is formed. Using time‐dependent MHD simulations, we confirm the basic theoretical results. We further extend this work to study the effects of tailward propagating boundary perturbations, corresponding to the rise and subsequent reduction of a duskward electric field (rise and subsequent northward turning of southward IMF Bz). We demonstrate that these boundary conditions again can lead to thin current sheet formation and the possible loss of equilibrium (catastrophe) or onset of instability. Finite perturbations of magnitudes consistent with those observed can produce a strong local increase of the current density and a local reduction of the magnetic field component Bz in the center of the plasma sheet, so that kinetic instabilities and a dynamic evolution may be triggered. The current sheet formation is influenced not only by the magnitude and the duration of the applied electric field but also by the temporal profile: A sudden decrease of the driving electric field following a more gradual increase is more effective than a gradual decrease following a sudden increase. This may provide a clue for the apparent substorm triggering by sudden northward turning of the IMF.

Birkeland currents in the plasma sheet

Geotail particle and magnetic field measurements were combined to generate long‐term‐averaged 3‐D models of the plasma sheet. Ampere's law was used to calculate the Birkeland current j∥ in the −30 < x < −16RE, ∣z∣ > 1RE region. Current diversion, or the growth of current in a unit flux tube j∥/B, took place throughout the region studied. This suggests that electron scattering is broadly distributed. No substantial change in j∥/B could be detected between the plasma sheet boundary layer and the ionosphere. Birkeland currents were strongest and exhibited a dawn‐dusk asymmetry when the interplanetary magnetic field (IMF) was southward. This asymmetry may be associated with the formation of thin current sheets on the dusk side during disturbed periods. Symmetries were apparent above and below the neutral sheet when the IMF was northward or southward, but these symmetries were not present when the IMF pointed dawnward or duskward. For these latter cases, separate surfaces were found on which Bx = 0, By = 0, and j∥ = 0. This apparently complex structure could be understood as a consequence of the tendency for By in the neutral sheet to have the same sign as the IMF By. The observed Birkeland currents were in the region 1 sense when leaving the plasma sheet for all IMF orientations. Current diversion was analyzed in an MHD framework. The analysis suggested that the reduction of gradient and curvature guiding center drifts, and the presence of polarization currents in the diversion region can provide sources of electrons to sustain a steady j∥. It also was noted that the formation of an E∥ region in the topside ionosphere can make it appear to the conducting ionosphere as if it is being driven by a current source rather than by the plasma sheet electric field.

Whistler‐mediated magnetic reconnection in large systems: Magnetic flux pileup and the formation of thin current sheets

We compute numerical solutions of the resistive Hall MHD equations corresponding to pairwise magnetic island coalescence. The simulation results can be organized according to the relative sizes of three length scales: the electron dissipation length, ℓe; the ion inertial length, di; and the island wavelength, λ. We identify three qualitatively distinct regimes of magnetic island coalescence: (1) the resistive MHD limit, di ≲ ℓe ≪ λ; (2) the “whistler‐mediated” limit, ℓe ≪ di ≪ λ; and (3) the “whistler‐driven” limit, ℓe ≪ λ ≲ di. In the resistive MHD limit, magnetic flux piles up outside thin current sheets between the islands. The upstream Alfvén speed increases with increasing Lundquist number, and the reconnection rate is insensitive to the Lundquist number. In the whistler‐driven limit, the electron and ion bulk flows decouple on the island wavelength scale. Magnetic flux pileup does not occur, and the coalescence proceeds on a whistler timescale that is much shorter than the Alfvén time. In the whistler‐mediated limit, electron and ion bulk flows decouple in spatially localized “ion inertial sheets” around the island separatrices. Flux pileup is reduced, and the upstream Alfvén speed approaches a nearly constant value as the Lundquist number is increased. The maximum reconnection rate in the whistler‐mediated limit is comparable to that observed in the resitive MHD limit over the Lundquist number range 500 < Sλ < 10000.

Models of two‐dimensional embedded thin current sheets from Vlasov theory

This paper uses the steady state Vlasov theory to obtain an explicit description of the properties of thin current sheets in two space dimensions. The method is general; in particular, it is not restricted to local Maxwellian distribution functions. The treatment includes chaotic particle motion, and the plasma is treated as quasi‐neutral. Such general equilibria are necessary for modeling observed structures in the Earth's magnetotail. In particular, this applies to thin current sheets embedded in wider sheets. Abandoning local Maxwellian distribution functions implies that the electric potential can no longer be transformed to zero such that additional efforts are required to include the electric field. Critical input parameters are the gyroscales of the different particle species and the ion/electron temperature ratio. The results illustrate how finite ion gyroscales affect the current sheet structure. Further aspects that are analyzed include the contributions of electrons and ions to the total current density, Hall currents, the occurrence of significant electric fields and the role of the ion/electron temperature ratio. The necessity of electric potentials in the self‐consistent structure of thin current sheets of the present type may provide a link between the presence or formation of thin current sheets and auroral arcs.

On the quasistatic development of thin current sheets in magnetotail‐like magnetic fields

The mechanism for the formation of thin current sheets in magnetotail‐like magnetic fields is investigated by numerical experiments using topology conserving equilibrium sequences. Motivated by the magnetotail magnetic field in the midnight meridian plane, a two‐dimensional model field is computed including a line dipole‐like (inner) part and a tail‐like part. The plasma is modeled as a polytropic gas and the total amount of plasma in each flux tube is fixed during an equilibrium sequence. Topology conservation is ensured by the use of inverse coordinates. The resulting set of nonlinear partial integrodiiferential equations is solved numerically using a continuation method. Starting from a current‐free field, stretching and compressing deformations are applied at the boundaries to mimic the analogue of a quasistatic substorm growth phase in our model. To investigate whether the process of thin current sheet formation is robust and to understand better the basic properties of that process, the boundary deformations are chosen such that there is no preferred location of compression of the field which would predetermine the site of thin current sheet formation. Current sheets are only found to form if a transition region between dipolar and tail‐like field exists in the equilibrium, and the current density exhibits two different cross‐tail length scales showing the importance of the transition region between the dipolar and the tail‐like field. However, the thin current component is much smaller than in other models of thin current sheet formation in the magnetotail. This result can be attributed to the chosen type of boundary deformations. The results are consistent with the gradient‐of‐flux‐volume mechanism which has been proposed as an explanation for the formation of thin current sheets in the Earth's magnetotail.