Antiparallel Reconnection Research Articles

Kinetic entropy-based measures of distribution function non-Maxwellianity: theory and simulations

We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e. entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function with the same density, bulk flow and temperature as the local distribution. First, we consider a form previously employed by Kaufmann & Paterson (J. Geophys. Res., vol. 114, 2009, A00D04), assessing its properties and deriving equivalent forms. To provide a quantitative understanding of it, we derive analytical expressions for three common non-Maxwellian plasma distribution functions. We show that there are undesirable features of this non-Maxwellianity measure including that it can diverge in various physical limits and elucidate the reason for the divergence. We then introduce a new kinetic entropy-based non-Maxwellianity measure based on the velocity-space kinetic entropy density, which has a meaningful physical interpretation and does not diverge. We use collisionless particle-in-cell simulations of two-dimensional anti-parallel magnetic reconnection to assess the kinetic entropy-based non-Maxwellianity measures. We show that regions of non-zero non-Maxwellianity are linked to kinetic processes occurring during magnetic reconnection. We also show the simulated non-Maxwellianity agrees reasonably well with predictions for distributions resembling those calculated analytically. These results can be important for applications, as non-Maxwellianity can be used to identify regions of kinetic-scale physics or increased dissipation in plasmas.

Evolution of electron current layer during anti-parallel magnetic reconnection

Electron current layer (ECL) in the diffusion region plays an important role on energy dispassion and generation of a magnetic island during collisionless magnetic reconnection. In this study, kinetic simulations with high-resolution grids are performed to investigate the evolution of ECL during anti-parallel magnetic reconnection. It is found that ECL splits into two sublayers at the electron inertial scale, not long after the triggering of reconnection. The sublayers keep moving away from each other until reconnection rate reaches the maximum. We find the formation reason and maintaining mechanism of these sublayer structures of the ECL. When electrons flow toward the midplane, out-of-plane velocity is increased by the reconnection electric field. The deflection of magnetic field makes the out-of-plane component of velocity partly converted to the z direction. Electron flows pass through the mid-plane with super-Alfvenic speed. When they enter the other side, the increasing magnetic field makes velocity in the z direction gradually converted to the out-of-plane. Slowdown of the flows causes the density accumulation at the two sides of the mid-plane. The redistribution of electrons brings an extra pressure gradient to the ECS region, balancing the electric force and Ampere force.

Reconnection from a turbulence perspective

The spectral properties associated with laminar, anti-parallel reconnection are examined using a 2.5D kinetic particle in cell simulation. Both the reconnection rate and the energy spectrum exhibit three distinct phases: an initiation phase where the reconnection rate grows, a quasi-steady phase, and a declining phase where both the reconnection rate and the energy spectrum decrease. During the steady phase, the energy spectrum exhibits approximately a double power law behavior, with a slope near −5/3 at wave numbers smaller than the inverse ion inertial length and a slope steeper than −8/3 for larger wave numbers up to the inverse electron inertial length. This behavior is consistent with a Kolmogorov energy cascade and implies that laminar reconnection may fundamentally be an energy cascade process. Consistent with this idea is the fact that the reconnection rate exhibits a rough correlation with the energy spectrum at wave numbers near the inverse ion inertial length. The 2D spectrum is strongly anisotropic with most energy associated with the wave vector direction normal to the current sheet. Reconnection acts to isotropize the energy spectrum, reducing the Shebalin angle from an initial value of 70° to about 48° (nearly isotropic) by the end of the simulation. The distribution of energy over length scales is further analyzed by dividing the domain into spatial subregions and employing structure functions.

The Critical Role of Collisionless Plasma Energization on the Structure of Relativistic Magnetic Reconnection

Abstract During magnetically dominated relativistic reconnection, inflowing plasma depletes the initial relativistic pressure at the x-line and collisionless plasma heating inside the diffusion region is insufficient to overcome this pressure loss. The resulting significant pressure drop causes a collapse at the x-line, essentially a localization mechanism of the diffusion region necessary for fast reconnection. The extension of this low-pressure region (into the outflow) further explains the bursty nature of antiparallel reconnection because a once opened outflow exhaust can also collapse, which repeatedly triggers secondary tearing islands. However, a stable single x-line reconnection can be achieved when an external guide field exists, since the reconnecting magnetic field component rotates out of the reconnection plane at outflows, providing additional magnetic pressure to keep the exhaust open.

On singularity formation via viscous vortex reconnection

Recognizing the fact that the finite-time singularity of the Navier–Stokes equations is widely accepted as a key issue in fundamental fluid mechanics, and motivated by the recent model of Moffatt & Kimura (J. Fluid Mech., vol. 861, 2019a, pp. 930–967; J. Fluid Mech., vol. 870, 2019b, R1) on this issue, we have performed direct numerical simulation (DNS) for two colliding slender vortex rings of radius . The separation between the two tipping points and the scale of the core cross-section are chosen as ; the vortex Reynolds number ( ) ranges from 1000 to 4000. In contrast to the claim that the core remains compact and circular, there is notable core flattening and stripping, which further increases with – akin to our previous finding in the standard anti-parallel vortex reconnection. Furthermore, the induced motion of bridges arrests the curvature growth and vortex stretching at the tipping points; consequently, the maximum vorticity grows with substantially slower than the exponential scaling predicted by the model – implying that, for this configuration, even physical singularity is unlikely. Our simulations not only shed light on the longstanding question of finite-time singularities, but also further delineate the detailed mechanisms of reconnection. In particular, we show for the first time that the separation distance before reconnection follows 1/2 scaling exactly – a significant DNS result.

Influence of parallel shearing flow on the switch-off effect of magnetic reconnection

Parallel shearing flows significantly affect the structure of the magnetic reconnection layer and generate new shock structures such as intermediate shock (IS) and time-dependent IS. The strength of shock waves (such as slow shock) can be changed and result in the switch-off of magnetic reconnection under certain conditions. In this study, we perform numerical simulations of one-dimensional resistive magnetohydrodynamic equations by using the total variation diminishing algorithm to investigate the influence of parallel shear flow on the switch-off effect of magnetic reconnection on both asymmetric and symmetric magnetic reconnection layers. Numerical results show that there exists a critical shear velocity Vzc that equals VA in symmetrical antiparallel magnetic reconnection, where VA denotes the inflow Alfvén velocity. For symmetric component magnetic reconnection, Vzc drops with the increase in guide magnetic field strength, which also equals the component of inflow Alfvén velocity along the z-axis. In regard to asymmetric magnetic reconnection, the critical shear velocity, Vzc, that leads to the switch-off of magnetic reconnection, ranging between the z-axis components of inflow Alfvén velocity in the magentosheath and in the magnetosphere. A new parameter associated with the Alfvén velocity on both sides is proposed; for both antiparallel reconnection and component reconnection, this new parameter equals the critical shear velocities.

A physical model of turbulence cascade via vortex reconnection sequence and avalanche

Viscous anti-parallel vortex reconnection is studied by means of direct numerical simulation for vortex Reynolds numbers ( , circulation/viscosity) up to 40 000. To suppress the inherent symmetry breaking due to the Kelvin–Helmholtz (planar jet) instability, as prevalent in prior studies, and to better explore the progression of the mechanism details, the simulation is performed by imposing symmetry and using double-precision arithmetic. We show, for the first time, the evidence of vortex reconnection cascade scenario initially proposed by Melander and Hussain (CTR Report, 1988), who suggested that the remnant threads, following the first reconnection, undergo successive reconnections in a cascade. Secondary reconnection (the details distinctly captured and visualized at a lower ) leads to the successive generation of numerous small-scale structures, including vortex rings, hairpin-like vortex packets and vortex tangles. As increases, the third and higher generations of reconnection form a turbulent cloud avalanche consisting of a tangle of fine vortices. The energy is rapidly transferred to finer scales during reconnection, and a distinct - 5/3 inertial range is observed for the kinetic energy spectrum, associated with numerous resulting fine-scale bridgelets and thread filaments. In addition, we also discover an inverse cascade at large scales through the accumulation of bridgelets. The separation distance before the first reconnection is found to scale as , which is different from the typical 1/2 scaling for classical and quantum vortex filament reconnections. Both peak enstrophy and its production rate grow with faster than the power law suggested by Hussain and Duraisamy (Phys. Fluids, vol. 23, 2011, 021701). Our simulations not only reveal the detailed mechanisms of high- reconnection, but also shed light on the physics of turbulence cascade and present the reconnection avalanche as a realistic physical model for turbulence cascade.

Inner and outer electron diffusion region of antiparallel collisionless reconnection: Density dependence

We study inflow density dependence of substructures within electron diffusion region (EDR) of collisionless symmetric magnetic reconnection. We perform a set of 2.5D particle-in-cell simulations which start from a Harris current layer with a uniform background density nb. A scan of nb ranging from 0.02 n0 to 2 n0 of the peak current layer density (n0) is studied keeping other plasma parameters the same. Various quantities measuring reconnection rate, EDR spatial scales, and characteristic velocities are introduced. We analyze EDR properties during quasisteady stage when the EDR length measures saturate. Consistent with past kinetic simulations, electrons are heated parallel to the B field in the inflow region. The presence of the strong parallel anisotropy acts twofold: (1) electron pressure anisotropy drift gets important at the EDR upstream edge in addition to the E×B drift speed and (2) the pressure anisotropy term −∇·P(e)/(ne) modifies the force balance there. We find that the width of the EDR demagnetization region and EDR current are proportional to the electron inertial length ∼de and ∼denb0.22, respectively. Magnetic reconnection is fast with a rate of ∼0.1 but depends weakly on density as ∼nb−1/8. Such reconnection rate proxies as EDR geometrical aspect or the inflow-to-outflow electron velocity ratio are shown to have different density trends, making electric field the only reliable measure of the reconnection rate.

Decomposition of plasma kinetic entropy into position and velocity space and the use of kinetic entropy in particle-in-cell simulations

We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particle-in-cell (PIC) simulations and use it to interpret plasma physics processes in heliospheric, planetary, and astrophysical systems. First, we calculate kinetic entropy in two forms—the “combinatorial” form related to the logarithm of the number of microstates per macrostate and the “continuous” form related to flnf, where f is the particle distribution function. We discuss the advantages and disadvantages of each and discuss subtleties about implementing them in PIC codes. Using collisionless PIC simulations that are two-dimensional in position space and three-dimensional in velocity space, we verify the implementation of the kinetic entropy diagnostics and discuss how to optimize numerical parameters to ensure accurate results. We show the total kinetic entropy is conserved to three percent in an optimized simulation of antiparallel magnetic reconnection. Kinetic entropy can be decomposed into a sum of a position space entropy and a velocity space entropy, and we use this to investigate the nature of kinetic entropy transport during collisionless reconnection. We find the velocity space entropy of both electrons and ions increases in time due to plasma heating during magnetic reconnection, while the position space entropy decreases due to plasma compression. This project uses collisionless simulations, so it cannot address physical dissipation mechanisms; nonetheless, the infrastructure developed here should be useful for studies of collisional or weakly collisional heliospheric, planetary, and astrophysical systems. Beyond reconnection, the diagnostic is expected to be applicable to plasma turbulence and collisionless shocks.

Formation of electron depletion layer and parallel electric field in the separatrix region of anti-parallel magnetic reconnection**Project supported by the National Natural Science Foundation of China (Grant Nos. 41774169, 41527804, and 41804159), the Key Research Program of Frontier Sciences, Chinese Academy of Sciences (Grant No. QYZDJ-SSW-DQC010), and the Youth Innovation Promotion Association of the Chinese Academy of Sciences (Grant No.

It is generally accepted that during collisionless magnetic reconnection, electrons flow toward the X line in the separatrix region, and then an electron depletion layer is formed. In this paper, with two-dimensional (2D) particle-in-cell (PIC) simulation, we investigate the characteristics of the separatrix region during magnetic reconnection. In addition to the electron depletion layer, we find that there still exists an electric field parallel to the magnetic field in the separatrix region. Because a reduced ion-to-electron mass ratio and light speed are usually used in PIC simulation models, we also change these parameters to analyze the characteristics of the separatrix region. It is found that the increase in the ion-to-electron mass ratio makes the electron depletion layer and the parallel electric field more obvious, while the influence of light speed is less pronounced.

A Parametric Study of the Structure of Hall Magnetic Field Based on Kinetic Simulations. I. Anti-parallel Magnetic Reconnection in an Asymmetric Current Sheet

Abstract The generation of the Hall magnetic field is considered one of the most important characteristics in collisionless magnetic reconnection. Here, in this paper, with two-dimensional particle-in-cell simulations, we study the structure of the Hall magnetic field generated during anti-parallel magnetic reconnection in an asymmetric current sheet. A quadrupolar structure of the Hall magnetic field is first formed, and then it evolves into a hexapolar structure with the proceeding magnetic reconnection. In the quadrupolar structure of the Hall magnetic field, the quadrants on the side of the current sheet with the weaker magnetic field (the dominant Hall magnetic field) are much stronger than those on the other side, and they can cross the center of the current sheet. With the increase of the ratio of the magnetic fields or the decrease of the density ratio (here, the ratio is defined as the values between the side with the stronger magnetic field to that with the weaker magnetic field), the tendency will become more salient. However, with a decrease of the temperature ratio, the tendency reverses. With the proceeding reconnection, two ribbons with an enhanced Hall magnetic field are generated in the region below the dominant Hall magnetic field, and then a hexapolar structure of the Hall magnetic field is formed, which will become stronger with an increase of the ratio of the magnetic field or decrease of the density, while the effect of the temperature asymmetry is much weaker than that of the magnetic field and density asymmetry. The generation of the Hall magnetic field can be explained by the in-plane current carried mainly by the electrons.

The Transition Between Antiparallel and Component Magnetic Reconnection at Earth's Dayside Magnetopause

AbstractMagnetic reconnection at Earth's magnetopause is usually described by two different scenarios, antiparallel and component reconnection. The Maximum Magnetic Shear model combines these two scenarios at specific connection points known as the Knee regions. Using a database of confirmed magnetopause reconnection locations observed during Phase 1a of the Magnetospheric Multiscale mission, a recent study showed that the model predicts the reconnection locations correctly within 2 Earth radii 80% of the time. The study also revealed and confirmed the existence of anomalies, that is, a specific set of conditions/parameters for which the observed reconnection locations are significantly different than the predicted locations. The first anomaly, described in an earlier study, occurs during the equinoxes for events with interplanetary magnetic field (IMF) clock angles around 120° and 240°. Another previously unknown anomaly was found for events observed around December that also occurs for the same IMF clock angle ranges as the first anomaly. Several of the anomalous December events were observed in the dawn sector Knee region and show that a combination of a large dipole tilt with an IMF clock angle of about 140° causes the magnetopause antiparallel reconnection region to line up along the draped IMF. That causes a deflection of the Knee points and the predicted reconnection location. These events demonstrate that magnetic reconnection at the Earth's dayside magnetopause preferentially occurs in the antiparallel locations and only occurs along component reconnection line segments when the draped IMF field lines at the magnetopause no longer contact an antiparallel reconnection region.

The Role of the Parallel Electric Field in Electron‐Scale Dissipation at Reconnecting Currents in the Magnetosheath

AbstractWe report observations from the Magnetospheric Multiscale satellites of reconnecting current sheets in the magnetosheath over a range of out‐of‐plane “guide” magnetic field strengths. The currents exhibit nonideal energy conversion in the electron frame of reference, and the events are within the ion diffusion region within close proximity (a few electron skin depths) to the electron diffusion region. The study focuses on energy conversion on the electron scale only. At low guide field (antiparallel reconnection), electric fields and currents perpendicular to the magnetic field dominate the energy conversion. Additionally, electron distributions exhibit significant nongyrotropy. As the guide field increases, the electric field parallel to the background magnetic field becomes increasingly strong, and the electron nongyrotropy becomes less apparent. We find that even with a guide field less than half the reconnecting field, the parallel electric field and currents dominate the dissipation. This suggests that parallel electric fields are more important to energy conversion in reconnection than previously thought and that at high guide field, the physics governing magnetic reconnection are significantly different from antiparallel reconnection.

Trefoil knot timescales for reconnection and helicity

Three-dimensional images of evolving numerical trefoil vortex knots are used to study the growth and decay of the enstrophy and helicity. Negative helicity density () plays several roles. First, during anti-parallel reconnection, sheets of oppositely signed helicity dissipation of equal magnitude on either side of the maximum of the enstrophy dissipation allow the global helicity to be preserved through the first reconnection, as suggested theoretically (Laing et al 2015 Sci. Rep. 5 9224) and observed experimentally (Scheeler et al 2014a Proc. Natl Acad. Sci. 111 15350–5). Next, to maintain the growth of the enstrophy and positive helicity within the trefoil while is preserved, forms in the outer parts of the trefoil so long as the periodic boundaries do not interfere. To prevent that, the domain size is increased as the viscosity . Combined, this allows two sets of trefoils to form a new scaling regime with linearly decreasing up to common ν-independent times tx that the graphics show is when the first reconnection ends. During this phase there is good correspondence between the evolution of the simulated vortices and the reconnecting experimental trefoil of Kleckner and Irvine (2017 Nat. Phys. 9 253–8) when time is scaled by their respective nonlinear timescales tf. The timescales tf are based upon by the radii rf of the trefoils and their circulations Γ, so long as the strong camber of the experimental hydrofoil models is used to correct the published experimental circulations Γ that use only the flat-plate approximation.

Super‐Alfvénic Propagation and Damping of Reconnection Onset Signatures

AbstractThe quadrupolar out‐of‐plane Hall magnetic field generated during collisionless reconnection propagates away from the x line as a kinetic Alfvén wave (KAW). While it has been shown that this KAW carries substantial Poynting flux and propagates super‐Alfvenically, how this KAW damps as it propagates away from the x line is not well understood. In this study, this damping is examined using kinetic particle‐in‐cell simulations of antiparallel symmetric magnetic reconnection in a one‐dimensional current sheet equilibrium. In the reconnection simulations, the KAW wave vector has a typical magnitude comparable to an inverse fluid Larmor radius (effectively an inverse ion Larmor radius) and a direction of 85–89° relative to the local magnetic field. We find that the damping of the reconnection KAW is consistent with linear Landau damping results from a numerical Vlasov dispersion solver. This knowledge allows us to generalize our damping predictions to regions in the magnetotail and solar corona where the magnetic geometry can be approximated as a current sheet. For the magnetotail, the KAW from reconnection will not damp away before propagating the approximately 20 Earth radii associated with global magnetotail distances. For the solar corona, on the other hand, these KAWs will completely damp before reaching the distances comparable to the flare loop length.

Simulations of anti-parallel reconnection using a nonlocal heat flux closure

The integration of kinetic effects in fluid models is important for global simulations of the Earth's magnetosphere. In particular, it has been shown that ion kinetics play a crucial role in the dynamics of large reconnecting systems, and that higher-order fluid moment models can account for some of these effects. Here, we use a ten-moment model for electrons and ions, which includes the off diagonal elements of the pressure tensor that are important for magnetic reconnection. Kinetic effects are recovered by using a nonlocal heat flux closure, which approximates linear Landau damping in the fluid framework. The closure is tested using the island coalescence problem, which is sensitive to ion dynamics. We demonstrate that the nonlocal closure is able to self-consistently reproduce the structure of the ion diffusion region, pressure tensor, and ion velocity without the need for fine-tuning of relaxation coefficients present in earlier models.

Occurrence frequency and location of magnetic islands at the dayside magnetopause

AbstractSimulations of magnetic reconnection often predict the formation of magnetic islands forming and propagating out through the reconnection exhaust region. However, to date, only a few observations of magnetic islands at the Earth's magnetopause have been identified and analyzed. Crossings near reconnection sites at the dayside magnetopause by Cluster from 2001 to 2009 are examined in a systematic effort to determine the frequency and location of magnetic islands. Using the maximum magnetic shear model as a guide for the distance to the reconnection site, 47 magnetopause crossings within 3 RE of the predicted reconnection site are examined. The occurrence of island structures in the reconnection exhaust is investigated in the context of how the type of reconnection, antiparallel or component, affects the frequency of formation of the islands. For Cluster magnetopause crossings confirmed to be near reconnection sites, island signatures, primarily bidirectional streaming electrons in the magnetosheath boundary layer, are seen for approximately 85% of the crossings and are common features for both antiparallel and component reconnection.

RISR‐N observations of the IMF By influence on reverse convection during extreme northward IMF

AbstractPrevious studies have demonstrated that the high‐latitude ionospheric convection is strongly influenced by the interplanetary magnetic field (IMF) direction. However, the temporal details of how the convection transitions from one state to another are still not understood completely. In this study, we analyze an interval on 12 September 2014 which provided a rare opportunity to examine dynamic variations in the dayside convection throat as the IMF transitioned from strong By+ to strong Bz+. Between 18:00 and 20:00 UT the northward face of the Resolute Bay Incoherent Scatter Radar (RISR‐N) rotated through the noon sector and directly measured strengthening reverse convection flows in the dayside throat region that peaked at ∼2800 m/s. Near‐simultaneous measurements from DMSP satellites confirm the magnitude of the reverse convection and its proximity to the cusp. Time series comparison of the RISR‐N north‐south flows with the IMF Bz component shows a remarkably high correlation, suggestive of strong linear coupling, with no sign of velocity saturation. Likewise, the east‐west flow variations were highly correlated with the changes in IMF By. However, time‐lagged correlation analysis reveals that the IMF By influence acted on a time scale 10 min shorter than that of the Bz component. As a consequence, the manner in which the convection transitioned from the strong By+ condition to the strong Bz+ condition is inconsistent with either the antiparallel or component reconnection models. Instead, we suggest that these particular observations are consistent with two separate reconnection sites on the magnetopause driven independently by the IMF By and Bz components.

Processes setting the structure of the electron distribution function within the exhausts of anti-parallel reconnection

In situ spacecraft observations within the exhausts of magnetic reconnection document a large variation in the velocity space structure of the electron distribution function. Multiple mechanisms help govern the underlying electron dynamics, yielding a range of signatures for collisionless reconnection. These signatures include passing beams of electrons separated by well-defined boundaries from betatron heated/cooled trapped electrons. The present study emphasizes how localized regions of non-adiabatic electron dynamics can mix electrons across the trapped/passing boundaries and impact the form of the electron distributions in the full width of the exhaust. While our study is based on 2D simulations, the described principles shaping the velocity space distributions also apply to 3D geometries making our findings relevant to spacecraft observation of reconnection in the Earth's magnetosphere.

A new model for the electron pressure nongyrotropy in the outer electron diffusion region

AbstractWe present a new model to describe the electron pressure nongyrotropy inside the electron diffusion region (EDR) in an antiparallel magnetic reconnection scenario. A combination of particle‐in‐cell simulations and analytical estimates is used to identify such a component of the electron pressure tensor in the rotated coordinates, which is nearly invariant along the outflow direction between the X line and the electron remagnetization points in the outer EDR. It is shown that the EDR two‐scale structure (inner and outer parts) is formed due to superposition of the nongyrotropic meandering electron population and gyrotropic electron population with large anisotropy parallel to the magnetic field upstream of the EDR. Inside the inner EDR the influence of the pressure anisotropy can largely be ignored. In the outer EDR, a thin electron layer with electron flow speed exceeding the E × B drift velocity is supported by large‐momentum flux produced by the electron pressure anisotropy upstream of the EDR. We find that this fast electron exhaust flow with |Ve×B|>|E| is in fact a constituent part of the EDR, a finding which will steer the interpretation of the Magnetospheric Multiscale Mission (MMS) data.