Transition in electron physics of magnetic reconnection in weakly collisional plasma

The influence of Coulomb collisions on the structure of reconnection layers is examined in neutral sheet geometry using fully kinetic simulations with a Monte Carlo treatment of the Fokker–Planck operator. The algorithm is first carefully benchmarked against key predictions from transport theory, including the parallel and perpendicular resistivities as well as the thermal force. The results demonstrate that the collisionality is accurately specified, thus allowing the initial Lundquist number to be chosen as desired. For modest Lundquist numbers S≲1000, the classic Sweet–Parker solution is recovered. Furthermore, a distinct transition to a faster kinetic regime is observed when the thickness of the resistive layer δSP falls below the ion inertial length di. For higher Lundquist numbers S≳1000, plasmoids (secondary islands) are observed within the elongated resistive layers. These plasmoids give rise to a measurable increase in the reconnection rate and for certain cases induce a transition to kinetic regimes sooner than expected from the δSP≈di condition. During this transition, the reconnection electric field exceeds the runaway limit, leading to electron scale current layers in which the nonideal electric field is supported predominantly by off-diagonal components in the electron pressure tensor, along with a residual contribution from electron-ion momentum exchange. These weakly collisional electron layers are also unstable to the formation of new plasmoids.

The strong precipitating particle flux in the cusp regions is the consequence of magnetic reconnection between the interplanetary magnetic field and the geomagnetic field. Magnetic reconnection is thought to be the dominant process for mass, energy, and momentum transfer from the magnetosheath into the magnetosphere. Observations of downward precipitating cusp ions by polar orbiting satellites are instrumental in unlocking many questions about magnetic reconnection, e.g., their spatial and temporal nature and the location of the reconnection site at the magnetopause. In this study we combine cusp observations of structures in the precipitating ion‐energy dispersion by the Cluster satellites with Super Dual Auroral Radar Network radar observations to distinguish between the temporal and spatial magnetic reconnection processes at the magnetopause. The location of the cusp structures relative to the convection cells is interpreted as a temporal phenomenon caused by a change in the reconnection rate at the magnetopause. The 3‐D plasma observations of the Cluster Ion Spectrometry instruments onboard the Cluster spacecraft also provide the means to estimate the location of the reconnection site. While an earlier study of a spatial cusp structure event revealed bifurcated reconnection locations in different hemispheres as origins for the precipitating ions creating the cusp structures, the same method applied to the temporal cusp structures in this study shows only a single tilted reconnection line close to the subsolar point. Tracing the distance to the reconnection site provides not only the location of the reconnection line but can also be used to distinguish between spatial and temporal cusp structures.

In this study, we use fully kinetic Particle In Cell (PIC) simulations to investigate numerically the dispersion relation of the tearing instability in the kinetic regime, which is at the moment rather poorly explored by theoretical investigations. To reduce the computational cost of the simulations, we use the the semi-implicit, energy conserving ECsim code (Lapenta et al, 2017), that allows us to step over the smaller scales and fastest frequencies and focus on characteristic scales of interest, with excellent energy conservation.We run several simulations with current sheets of fixed length. The current sheet half-thickness is progressively increased from $\delta \sim d_i$ to significantly larger. The other simulation parameters are kept identical.In our simulations, the tearing instability grows without external perturbation from the particle noise of PIC simulations. Later onset times are (predictably) observed when the number of particles per cell is increased.Several modes grow unstable in each simulation. We plot the growth rates of the unstable modes as a function of the current sheet thickness. We obtain a spread around a curve decreasing with increasing current sheet thickness. 

The reconnection rate in relativistic magnetic reconnection driven by two relativistic intense femtosecond laser pulses is investigated using three-dimensional particle-in-cell (PIC) simulation. As the drive is enhanced, the current sheet is narrowed, and the reconnection rate is weakened. A new theoretical model is given to explain the rate observed in the PIC simulation. In addition, multi-scale reconnection is studied by setting a different ion mass in the simulation code. For mi=1836me , the current sheet is only at the electron scale, and only electron outflow jets are observed, which are super ion Alfvénic and close to the electron’s Alfvénic speed. The lengths of the electron outflow jets reach 100–200 times the length of the electron gyroradius and beyond the ion gyroradius. However, when mi=100me , more ions are coupled to electrons during the laser and plasma interaction, there are also electron outflow jets and no ion outflow jets in the current sheet, and the electron outflow jets are embedded in a wider ion-scale current layer.

The reconnection rate which can be achieved in the steady-state flux-pile-up regime is severely limited by the gas pressure of the plasma. Using the family of solutions obtained previously by Priest and Forbes, we show that the Alfven Mach number of the plasma flowing towards the reconnection site cannot exceed πβe/(8 ln Rme), where βe and Rme are the plasma β and magnetic Reynolds numbers at large distance. This limit corresponds to a very weak flux-pile-up, and it is a factor of βe slower than the maximum Petschek rate. Thus the maximum flux-pile-up reconnection rate in the corona is at least two orders of magnitude smaller than the rate implied by flare observations.

This work investigates how magnetic reconnection affects the acceleration of coronal mass ejections (CMEs) and how the acceleration in turn affects the reconnection process. To model the CME process, we use a two‐dimensional flux rope model, which drives the ejection by means of a catastrophic loss of mechanical equilibrium. Our model provides a method for relating the motion of the ejected material to the reconnection rate in the current sheet created by the erupting field. In the complete absence of reconnection the tension force associated with the current sheet is always strong enough to prevent the flux rope from escaping from the Sun. However, our results imply that even a fairly small reconnection rate is sufficient to allow the flux rope to escape. Specifically, for a coronal density model that decreases exponentially with height we find that average Alfvén Mach number MA for the inflow into the reconnection site can be as small as MA = 0.005 and still be fast enough to give a plausible eruption. The best fit to observations is obtained by assuming an inflow rate on the order of MA ≈ 0.1. With this value the energy output matches the temporal behavior inferred for the long duration events often associated with CMEs. The model also suggests an explanation for the peculiar motion of giant X‐ray arches reported by Svestka et al. [1995, 1997]. X‐ray arches are the large loops associated with CMEs which are similar in form to “post”‐flare loops, but they have an upward motion that is often different. Instead of continually slowing with time, the arches move upward at a rate that remains nearly constant or may even increase with time. Here we show how the difference can be explained by reversal of the gradient of the coronal Alfvén speed with height.

Three flux transfer events (FTEs), observed by the AMPTE/IRM spacecraft in the southern hemisphere magnetosheath are studied by use of variance analysis of measured magnetic fields, B, and convection electric fields, Ec = −v × B, with the objective of determining the orientation and motion of the flux tube or magnetopause bulge causing the FTE signature. These FTEs preceded a series of magnetopause crossings during which the high plasma flow speeds, characteristic of quasi‐steady reconnection, were present. The main results are as follows: (1) For each FTE, a moving so‐called deHoffmann‐Teller (HT) frame of reference can be found, in which the local plasma velocities are nearly antiparallel to the local B vectors and have magnitudes in the range 70%–90% of the local nominal Alfvén speed (assuming all measured ions to be protons). The velocities of motion, vHT, of the HT frames for all three events, and for two subsequent magnetopause crossings, are sufficiently similar so that a single HT frame orders the data in this manner for one full hour. (2) In the first FTE, the spacecraft appears to have sampled fields and flow around a moving tube or elongated magnetopause bulge. The tube orientation and motion (given by the component of vHT perpendicular to the tube axis) could be determined along with impact parameter (ℓ ≃ 1.4a), tube diameter (2a ≃ 8000 km), and, with reasonable assumptions, tube length (L>20,000 km). The tube was found to move southward past the spacecraft, consistent with the observed negative‐positive signature in the component of B along the magnetopause normal. The ambient magnetosheath plasma moved in the opposite direction. (3) For the second and third FTEs, which were close encounters (ℓ/a<1), the tube orientation and therefore its motion could not be reliably determined. (4) On the whole, the observations are consistent with ongoing magnetopause reconnection with a time‐modulated reconnection rate that leads to repeated ejection of bulges in the magnetopause from the reconnection site.

The interaction between the solar wind and Jupiter's magnetic field confines the planetary field to the largest magnetosphere in the Solar System. However, the full picture of when and where key processes operate at the magnetopause boundary of the system remains unclear. This is essential for testing understanding with observations and for determining the relative importance of different drivers of Jovian magnetospheric dynamics. Here we present a global analytical model of Jovian magnetopause conditions under steady state, which forms the basis of boundary process assessments. Sites of magnetic reconnection at Jupiter's magnetopause are expected to be in regions of sufficiently high magnetic shear across the boundary, controlled by the orientation of the interplanetary magnetic field. Reconnection rates are also most sensitive to changes in the highly variable IMF, followed by changes in the solar wind plasma mass density. The largest plasma flow shear across the boundary is in the equatorial dawn region, producing a region that is typically unstable to growth of the Kelvin‐Helmholtz (K‐H) instability. Compared to magnetopause reconnection site locations, this K‐H‐unstable region at dawn is less sensitive to changing conditions. Motion of K‐H boundary perturbations typically includes dawn‐to‐dusk motion across the subsolar region. Model‐predicted reconnection voltages are typically hundreds of kV but rely on steady solar wind conditions on a time scale that is longer than typical at Jupiter's orbit. How the reconnection voltage compares to the voltage applied due to the “viscous‐like” interaction involving K‐H instability remains unclear.

Recent magnetospheric observations and three‐dimensional (3D) kinetic simulations have shown that plasma wave activities are significantly enhanced around the reconnection x‐line, implying that the reconnection process is fully 3D. However, how the turbulence affects the local reconnection process has been poorly understood so far. We find by means of large‐scale particle‐in‐cell simulation in 3D system that the local reconnection rate can be significantly enhanced, reaching 0.4, which is much larger than theoretical predictions for two‐dimensional (2D) reconnection. The large reconnection rate is associated with large energy conversion rate and strong electron acceleration. The enhancement of the reconnection rate is caused by local increases of electron momentum transport and pressure gradient force induced by turbulence, which can not occur in 2D system. The result is expected to give better interpretations to in‐situ satellite observations where magnetic reconnection proceeds in 3D system.

The electron inertia and the off‐diagonal electron pressure terms are well‐known for the frozen‐in condition breakdown in collisionless magnetic reconnection, which are naturally kinetic and difficult to employ in magnetohydrodynamic (MHD) simulations. Considering the limitations of MHD and Hall MHD in neglecting the important electron dynamics such as the inertia and the nongyrotropic pressure, the kinetic characteristics of electrons and ions in the diffusion region are studied and an effective resistivity model involving dynamics of charged particles is proposed (Ma et al. 2018, https://doi.org/10.1038/s41598‐018‐28851‐7 Sci. Rep. 8 10521), where the guide field is omitted to simplify the model by primarily considering the out‐of‐plane velocity of charged particles and the in‐plane reconnecting field. The amplitude of the effective resistivity is mainly determined by electrons in most realistic situations with large ion‐electron mass ratios. In this work, the effective resistivity model for collisionless magnetic reconnection is successfully applied in the 2.5D MHD and Hall MHD simulations, which remarkably improves the simulation results compared with traditional MHD models. For the MHD case, the effective resistivity significantly increases the reconnection rate to a reasonable value of . For the Hall MHD case with effective resistivity, the peak reconnection rate is , and the major structures of the reconnecting field and the current sheet agree well with the particle‐in‐cell (PIC) simulations. Meanwhile, a more general effective resistivity model incorporating guide field corrections for MHD simulations is under development.

We identify the electron diffusion region (EDR) of a guide field dayside reconnection site encountered by the Magnetospheric Multiscale (MMS) mission and estimate the terms in generalized Ohm's law that controlled energy conversion near the X‐point. MMS crossed the moderate‐shear (∼130°) magnetopause southward of the exact X‐point. MMS likely entered the magnetopause far from the X‐point, outside the EDR, as the size of the reconnection layer was less than but comparable to the magnetosheath proton gyroradius, and also as anisotropic gyrotropic “outflow” crescent electron distributions were observed. MMS then approached the X‐point, where all four spacecraft simultaneously observed signatures of the EDR, for example, an intense out‐of‐plane electron current, moderate electron agyrotropy, intense electron anisotropy, nonideal electric fields, and nonideal energy conversion. We find that the electric field associated with the nonideal energy conversion is (a) well described by the sum of the electron inertial and pressure divergence terms in generalized Ohms law though (b) the pressure divergence term dominates the inertial term by roughly a factor of 5:1, (c) both the gyrotropic and agyrotropic pressure forces contribute to energy conversion at the X‐point, and (d) both out‐of‐the‐reconnection‐plane gradients (∂/∂M) and in‐plane (∂/∂L,N) in the pressure tensor contribute to energy conversion near the X‐point. This indicates that this EDR had some electron‐scale structure in the out‐of‐plane direction during the time when (and at the location where) the reconnection site was observed.

Drag force on ions in magnetized electron plasmas

Ion heating during a substorm on 15 February 2008, starting at 0348 UT, is studied with a new approach recently described in Ashour‐Abdalla et al. (2015). The general conditions of the magnetotail are obtained from a global magnetohydrodynamic (MHD) model and are used to drive a full kinetic particle‐in‐cell (PIC) simulation of a 3‐D region of the tail. Within the kinetic box, the ions, the electrons, and the fields evolve self‐consistently. The large scales are captured by the MHD model and the small scales by the PIC model based on the MHD state. This approach is used to study ion heating. Different heating mechanisms were analyzed by examining the velocity distributions at different locations. In the x direction heating occurs as the reconnection‐generated ion jet interacts with the environment in which it propagates. The heating is found mostly in the separatrices and increases downstream of the reconnection region. In the y direction the heating is less intense and is found near the dipolarization fronts. It occurs as ions become magnetized and gyrotropize the distribution function. In addition, ions can be heated in the y direction by the reconnection electric field near the reconnection site. In the z direction the ions are heated by the formation of beams moving along z between the separatrices.

During magnetospheric substorms, plasma from magnetic reconnection in the magnetotail is thought to reach the inner magnetosphere and form a partial ring current. We simulate this process using a fully kinetic 3D particle‐in‐cell (PIC) numerical code along with a global magnetohydrodynamics (MHD) model. The PIC simulation extends from the solar wind outside the bow shock to beyond the reconnection region in the tail, while the MHD code extends much further and is run for nominal solar wind parameters and a southward interplanetary magnetic field. By the end of the PIC calculation, ions and electrons from the tail reconnection reach the inner magnetosphere and form a partial ring current and diamagnetic current. The primary source of particles to the inner magnetosphere is bursty bulk flows (BBFs) that originate from a complex pattern of reconnection in the near‐Earth magnetotail at to . Most ion acceleration occurs in this region, gaining from 10 to 50 keV as they traverse the sites of active reconnection. Electrons jet away from the reconnection region much faster than the ions, setting up an ambipolar electric field allowing the ions to catch up after approximately 10 ion inertial lengths. The initial energy flux in the BBFs is mainly kinetic energy flux from the ions, but as they move earthward, the energy flux changes to enthalpy flux at the ring current. The power delivered from the tail reconnection in the simulation to the inner magnetosphere is W, which is consistent with observations.

Magnetic reconnection under a strong guide field B G / B y 0 ≫ 1 , as in solar wind and laboratory plasmas, is investigated using the gyrokinetic electron and fully kinetic ion (GeFi) particle simulation model, where B y 0 is the antiparallel component of the magnetic field and B G is the guide field. Cases with two-dimensional force-free current sheets are presented in conditions with a large guide field and low plasma beta, similar to the reconnection events associated with solar flares. To gain insights into how the ion-to-electron mass ratio ( m i / m e ) and normalized guide field ( B G / B y 0 ) affect the rate and structures of reconnection, we present a series of simulations by varying m i / m e from 100 to 1836 and B G / B y 0 from 5 to 15. First, linear eigenmode analysis is performed for the collisionless tearing mode. We find that the eigenmode structure and growth rate of the tearing mode obtained from the GeFi simulation are in excellent agreement with the eigenmode theory for strong B G . Subsequently, we employ GeFi simulations to explore the reconnection rate and current sheet structure across a wide range of m i / m e and B G / B y 0 . Intriguingly, it is found that the reconnection rate is insensitive to m i / m e . The growth rate of the tearing mode, however, has a strong dependence on m i / m e . The reconnection rate exhibits a clear increase with decreasing B G / B y 0 and also strongly depends on B G / B y 0 . Furthermore, the length of the electron diffusion region increases with m i / m e . These findings advance understanding of the reconnection dynamics in solar flares and other astrophysical phenomena.