Antiparallel Magnetic Reconnection Research Articles

On a plasma sheath with a small normal magnetic field separating regions of oppositely directed magnetic field

The Harris-sheet model provides an elegant solution to the kinetic plasma equation for a steady state 1D current sheet geometry separating regions with oppositely directed magnetic field. However, adding just a small normal magnetic field to the Harris configuration yields thermal streaming of particles into and out of the current sheet, fundamentally changing the form of its kinetic description. The action variable, Jz, associated with the oscillatory orbit motion perpendicular to the current sheet is well conserved and can be applied for solving the kinetic equation in the 1D sheet geometry that includes a small normal magnetic field. Revisiting this problem, we develop a new formalism that permits numerical solutions to be readily obtained for general upstream/asymptotic electron and ion distributions. In particular, we consider the case of isotropic ion pressure and anisotropic bi-Maxwellian electrons. The current sheets are then supported by electron pressure anisotropy. Furthermore, the total current across a particular sheet is set by the fire-hose condition based on the electron pressures normalized by the asymptotic magnetic field pressure. Analytical approximations are obtained for the numerical solutions expressed in terms of the asymptotic electron temperature anisotropy and the ion temperature. We discuss a preliminary application of the framework to the electron diffusion region of anti-parallel magnetic reconnection.

Phase-space Analysis of Ordered and Disordered Nonthermal Ion Energization during Magnetic Reconnection

Anomalous ion heating is frequently observed to accompany magnetic reconnection, yet there is little consensus on its origin. Instead of the usual velocity-space analysis, we use phase-space analysis to exhaustively explain how ions are nonthermally energized during collisionless, antiparallel magnetic reconnection. There are both ordered and disordered aspects in the process; the former is explained in terms of conservative quantities, and the latter is explained by demonstrating chaos through a direct calculation of Lyapunov exponents. The former induces “multibeam-like heating” in all three directions, whereas the latter induces stochastic bulk heating. Profiles of the ion temperature tensor components during reconnection can be easily understood by the phase-space distributions of ions in different motional stages.

The force balance of electrons during kinetic anti-parallel magnetic reconnection

Fully kinetic simulations are applied to the study of 2D anti-parallel reconnection, elucidating the dynamics by which the electron fluid maintains force balance within both the ion diffusion region (IDR) and the electron diffusion region (EDR). Inside the IDR, magnetic field-aligned electron pressure anisotropy (pe∥≫pe⊥) develops upstream of the EDR. Compared to previous investigations, the use of modern computer facilities allows for simulations at the natural proton to electron mass ratio mi/me=1836. In this high-mi/me-limit, the electron dynamics change qualitatively, as the electron inflow to the EDR is enhanced and mainly driven by the anisotropic pressure. Using a coordinate system with the x-direction aligned with the reconnecting magnetic field and the y-direction aligned with the central current layer, it is well known that for the much studied 2D laminar anti-parallel and symmetric scenario the reconnection electric field at the X-line must be balanced by the ∂pexy/∂x and ∂peyz/∂z off-diagonal electron pressure stress components. We find that the electron anisotropy upstream of the EDR imposes large values of ∂pexy/∂x within the EDR, and along the direction of the reconnection X-line, this stress cancels with the stress of a previously determined theoretical form for ∂peyz/∂z. The electron frozen-in law is instead broken by pressure tensor gradients related to the direct heating of the electrons by the reconnection electric field. The reconnection rate is free to adjust to the value imposed externally by the plasma dynamics at larger scales.

The Role of a Strong Out‐Of‐Plane Magnetic Field at the X‐Line in Antiparallel Magnetic Reconnection as a Guide Field

AbstractThe magnetic reconnection process substantially changes the configuration of the magnetic field in plasma and explosively releases magnetic energy. The asymptotic magnetic field lines during magnetic reconnection events can be strictly antiparallel or only have one antiparallel component, and the magnetic reconnection features are distinct under different asymptotic magnetic fields. Here, we provide the first observational evidence demonstrating the existence of a strong out‐of‐plane magnetic field at the X‐line in antiparallel reconnection. The analyses described herein show that this strong out‐of‐plane magnetic field significantly changes the structure of the diffusion region, thereby altering the reconnection features in terms of particle dynamics and energy dissipation by way of a guide field. A new pattern of the normal electric field near the X‐line is responsible for producing this out‐of‐plane magnetic field. Our findings suggest that, in addition to asymptotic conditions, local processes inside the diffusion region can also determine whether magnetic reconnection events develop as antiparallel reconnection or component reconnection.

Ion and electron acoustic bursts during anti-parallel magnetic reconnection driven by lasers

Ion and electron acoustic bursts during anti-parallel magnetic reconnection driven by lasers

Evidence of the Hall Effect Providing the Core Field inside a Magnetic Flux Rope in an Antiparallel Magnetic Reconnection

The observations from the Magnetospheric Multiscale mission on 2015 November 12 showed the existence of tripolar Hall magnetic fields north of the X line in a quasi-antiparallel reconnection at the dayside of the magnetopause. The bipolar variation in the normal component of the magnetic field inside the middle polar region of the tripolar Hall fields indicated the presence of an ion-scale magnetic flux rope. The coexistence of Hall fields and a magnetic flux rope provides the first evidence that the Hall effect in quasi-antiparallel magnetic reconnection can generate the core field inside a magnetic flux rope. There is one dip in the core field of the observed magnetic flux rope. We interpret the core field and the dip with the Hall effect associated with sequential multiple-X-line reconnection. The results of this study shed light on the mechanism of the generation of the core field inside the magnetic flux rope.

Pressure–strain interaction. III. Particle-in-cell simulations of magnetic reconnection

How energy is converted into thermal energy in weakly collisional and collisionless plasma processes, such as magnetic reconnection and plasma turbulence, has recently been the subject of intense scrutiny. The pressure–strain interaction has emerged as an important piece, as it describes the rate of conversion between bulk flow and thermal energy density. In two companion studies, we presented an alternate decomposition of the pressure–strain interaction to isolate the effects of converging/diverging flow and flow shear instead of compressible and incompressible flow, and we derived the pressure–strain interaction in magnetic field-aligned coordinates. Here, we use these results to study pressure–strain interaction during two-dimensional anti-parallel magnetic reconnection. We perform particle-in-cell simulations and plot the decompositions in both Cartesian and magnetic field-aligned coordinates. We identify the mechanisms contributing to positive and negative pressure–strain interaction during reconnection. This study provides a roadmap for interpreting numerical and observational data of the pressure–strain interaction, which should be important for studies of reconnection, turbulence, and collisionless shocks.

On the Presence and Thermalization of Cold Ions in the Exhaust of Antiparallel Symmetric Reconnection

Using fully kinetic 2.5 dimensional particle-in-cell simulations of anti-parallel symmetric magnetic reconnection, we investigate how initially cold ions are captured by the reconnection process, and how they evolve and behave in the exhaust. We find that initially cold ions can remain cold deep inside the exhaust. Cold ions that enter the exhaust downstream of active separatrices, closer to the dipolarization front, appear as cold counter-streaming beams behind the front. In the off-equatorial region, these cold ions generate ion-acoustic waves that aid in the thermalization both of the incoming and outgoing populations. Closest to the front, due to the stronger magnetization, the ions can remain relatively cold during the neutral plane crossing. In the intermediate exhaust, the weaker magnetization leads to enhanced pitch angle scattering and reflection. Cold ions that enter the exhaust closer to the X line, at active separatrices, evolve into a thermalized exhaust. Here, the cold populations are heated through a combination of thermalization at the separatrices and pitch angle scattering in the curved magnetic field around the neutral plane. Depending on where the ions enter the exhaust, and how long time they have spent there, they are accelerated to different energies. The superposition of separately thermalized ion populations that have been accelerated to different energies form the hot exhaust population.

Plasma heating and current sheet structure in anti-parallel magnetic reconnection

A theoretical model and an analytic theory of current sheet structure are presented for understanding anti-parallel driven magnetic reconnection in 2-1/2 dimension in collisionless plasmas. The theoretical model provides formulation to compute the current sheet y-profiles by specifying the profiles of electron and ion flow velocities Vex(x,y) and Vix(x,y). The current sheet solutions depend on the plasma density nin, merging magnetic field B0, ion velocity vi, and electron velocity ve in the upstream and the Sevz=Vez/Vdz parameter where Vez is the electron velocity accelerated by the reconnection electric field Ez in the electron orbit meandering region, Vdz≃cEy/Bx is the E→×B→ drift velocity as electrons enter the orbit meandering region, Bx is the merging magnetic field, and Ey is the electrostatic electric field. With simplifying assumptions on the y-profiles of Vex and Vix, we have also developed an analytic theory of the current sheet structure. Analytic expressions for the anomalous resistivity, the electrostatic potential drop, and the maximum Ey amplitude Emax are obtained. The analytic results agree reasonably well with both the particle-in-cell simulation results and the numerical solutions of the theoretical model. The ions energy gain due to the potential drop is ∝B02/nin. The electron energy gain is ∝(B02/8πnin)Sevz. The B02/nin scaling of the average ion and electron energy gains are consistent with laboratory experiments and space plasma observations.

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.

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.

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.

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.

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.

Three‐dimensional development of front region of plasma jets generated by magnetic reconnection

AbstractA three‐dimensional fully kinetic particle‐in‐cell simulation of antiparallel magnetic reconnection is performed to investigate the three‐dimensional development of reconnection jet fronts treating three instabilities: the lower hybrid drift instability (LHDI), the ballooning/interchange instability (BICI), and the ion‐ion kink instability. Sufficiently large system size and high ion‐to‐electron mass ratio of the simulation allow us to see the coupling among the three instabilities in the fully kinetic regime for the first time. As the jet fronts develop, the LHDI and BICI become dominant over the ion‐ion kink instability. The rapid growth of the LHDI enhances the BICI growth and the resulting formation of finger‐like structures. The small‐scale front structures produced by these instabilities are similar to recent high‐resolution field observations of the dipolarization fronts in the near‐Earth magnetotail using Time History of Events and Macroscale Interactions during Substorms (THEMIS) and Cluster spacecraft and pose important questions for a future full high‐resolution observation by the Magnetospheric Multiscale (MMS) mission.

Experimental Demonstration of the Collisionless Plasmoid Instability below the Ion Kinetic Scale during Magnetic Reconnection.

The spontaneous formation of magnetic islands is observed in driven, antiparallel magnetic reconnection on the Terrestrial Reconnection Experiment. We here provide direct experimental evidence that the plasmoid instability is active at the electron scale inside the ion diffusion region in a low collisional regime. The experiments show the island formation occurs at a smaller system size than predicted by extended magnetohydrodynamics or fully collisionless simulations. This more effective seeding of magnetic islands emphasizes their importance to reconnection in naturally occurring 3D plasmas.

Reconstruction of the electron diffusion region

AbstractWe discuss mathematical tools for the reconstruction of two‐dimensional, time‐independent magnetic field and flow in the electron diffusion region, at a site of antiparallel magnetic reconnection. The basic assumptions are that the ions are stationary and have constant density. The width of the reconnection layer is of the order of the electron gyroradius or the electron inertial length. Our model includes the axial electron pressure term in Ohm's law developed by M. Hesse and coworkers. We demonstrate the feasibility of doing reconstruction of electron magnetohydrodynamic (EMHD) structures for a simplified system with zero electron inertia. The code is benchmarked using an exact solution that has antiparallel unidirectional magnetic fields, plus out‐of‐plane quadrupolar Hall fields, as well as the expected slow electron inflow and rapid exit jets. The inertialess reconstruction is then applied to synthetic data from a 2‐D, particle‐in‐cell, simulation of antiparallel reconnection. We find that the inertialess reconstruction of its electron diffusion region works reasonably well only when the spacecraft path passes close to the center of the reconnection site where the magnetic field is zero and the electron flow has a stagnation point. When the path is located farther away, the effects of electron inertia, and probably also deviations from the Hesse formula, cause the quality of the reconstruction to deteriorate. Electron inertia is included in the theoretical development presented here but requires a more complicated numerical reconstruction code. The development and testing of such a code is underway and will be presented separately.