Particle-in-cell simulations of low-β magnetic reconnection driven by laser interaction with a capacitor–coil target

Reconnection electric field is a key element of magnetic reconnection. It quantifies the change of magnetic topology and the dissipation of magnetic energy. In this work, two-dimensional (2D) particle-in-cell (PIC) simulations are performed to study the growth of the reconnection electric field in the electron diffusion region (EDR) during magnetic reconnection with a guide field. At first, a seed electric field is produced due to the excitation of the tearing-mode instability. Then, the reconnection electric field in the EDR, which is dominated by the electron pressure tensor term, suffers a spontaneous growth stage and grows exponentially until it saturates. A theoretical model is also proposed to explain such a kind of growth. The reconnection electric field in the EDR is found to be directly proportional to the electron outflow speed. The time derivative of electron outflow speed is proportional to the reconnection electric field in the EDR because the outflow is formed after the inflow electrons are accelerated by the reconnection electric field in the EDR and then directed away along the outflow direction. This kind of reinforcing process at last leads to the exponential growth of the reconnection electric field in the EDR.

We examine a rare and interesting observation of magnetic reconnection embedded in a large-scale region of strong turbulence in which magnetic field annihilation is energizing ions and electrons. The magnetic reconnection event is in Earth’s magnetotail and is associated with enhanced energetic particle fluxes indicating local particle acceleration. Despite substantial electric and magnetic field fluctuations throughout the surrounding, large-scale region, the ongoing magnetic reconnection has many similar properties to laminar, 2D magnetic reconnection including Hall electric fields, Hall magnetic fields, a thin electron current sheet, and ion and electron jets. Notably, the electron jet emerging from the electron diffusion region (EDR) appears to transport sufficient off-diagonal momentum to infer that off-diagonal electron stress can support the reconnection electric field in the EDR even in a turbulent environment. Although the electron jet appears to be briefly (∼1 s) deflected or possibly interrupted by an electromagnetic disturbance, the reconnection appears to otherwise continue for a long period (∼30 minutes) as evidenced by a persistent ion jet. This particular finding implies that the fundamental electron-scale processes inside of the EDR in turbulent magnetic reconnection are not necessarily distinct from those in laminar magnetic reconnection. These observations provide direct confirmation that magnetic reconnection can not only be responsible for but also can continue in regions of large-scale turbulence. Because the electric and magnetic fields of strong turbulence are linked to particle acceleration, it follows that particle acceleration also can continue as a consequence of turbulent magnetic reconnection.

Magnetic reconnection driven by a capacitor coil target is an innovative way to investigate low-β magnetic reconnection in the laboratory, where β is the ratio of particle thermal pressure to magnetic pressure. Low-β magnetic reconnection frequently occurs in the Earth’s magnetosphere, where the plasma is characterized by β ≲ 0.01. In this paper, we analyze electron acceleration during magnetic reconnection and its effects on the electron energy spectrum via particle-in-cell simulations informed by parameters obtained from experiments. We note that magnetic reconnection starts when the current sheet is down to about three electron inertial lengths. From a quantitative comparison of the different mechanisms underlying the electron acceleration in low-β reconnection driven by coil targets, we find that the electron acceleration is dominated by the betatron mechanism, whereas the parallel electric field plays a cooling role and Fermi acceleration is negligible. The accelerated electrons produce a hardened power-law spectrum with a high-energy bump. We find that injecting electrons into the current sheet is likely to be essential for further acceleration. In addition, we perform simulations for both a double-coil co-directional magnetic field and a single-coil one to eliminate the possibility of direct acceleration of electrons beyond thermal energies by the coil current. The squeeze between the two coil currents can only accelerate electrons inefficiently before reconnection. The simulation results provide insights to guide future experimental improvements in low-β magnetic reconnection driven by capacitor coil targets.

We present observations that suggest the X-line of guide-field magnetic reconnection is not necessarily orthogonal to the plane in which magnetic reconnection is occurring. The plane of magnetic reconnection is often referred to as the L–N plane, where L is the direction of the reversing and reconnecting magnetic field and N is normal to the current sheet. The X-line is often assumed to be orthogonal to the L–N plane (defined as the M-direction) in the majority of theoretical studies and numerical simulations. The four-satellite Magnetospheric Multiscale (MMS) mission, however, observes a guide-field magnetic reconnection event in Earth’s magnetotail in which the X-line may be oblique to the L–N plane. This finding is somewhat opportune as two of the MMS satellites at the same N location report nearly identical observations with no significant time delays in the electron diffusion region (EDR) even though they have substantial separation in L. A minimum directional derivative analysis suggests that the X-line is between 40° and 60° from M, adding support that the X-line is oblique. Furthermore, the measured ion velocity is inconsistent with the apparent motion of the MMS spacecraft in the L-direction through the EDR, which can be resolved if one assumes a shear in the L–N plane and motion in the M-direction. A nonorthogonal X-line, if somewhat common, would call for revisiting theory and simulations of guide-field magnetic reconnection, reexamination of how the reconnection electric field is supported in the EDR, and reconsidering the large-scale geometry of the X-line.

Bulk ion acceleration and particle heating during magnetic reconnection are studied in the collisionless plasma of the Magnetic Reconnection Experiment (MRX). The plasma is in the two-fluid regime, where the motion of the ions is decoupled from that of the electrons within the ion diffusion region. The reconnection process studied here is quasi-symmetric since plasma parameters such as the magnitude of the reconnecting magnetic field, the plasma density, and temperature are compatible on each side of the current sheet. Our experimental data show that the in-plane (Hall) electric field plays a key role in ion heating and acceleration. The electrostatic potential that produces the in-plane electric field is established by electrons that are accelerated near the electron diffusion region. The in-plane profile of this electrostatic potential shows a “well” structure along the direction normal to the reconnection current sheet. This well becomes deeper and wider downstream as its boundary expands along the separatrices where the in-plane electric field is strongest. Since the in-plane electric field is 3–4 times larger than the out-of-plane reconnection electric field, it is the primary source of energy for the unmagnetized ions. With regard to ion acceleration, the Hall electric field causes ions near separatrices to be ballistically accelerated toward the outflow direction. Ion heating occurs as the accelerated ions travel into the high pressure downstream region. This downstream ion heating cannot be explained by classical, unmagnetized transport theory; instead, we conclude that ions are heated by re-magnetization of ions in the reconnection exhaust and collisions. Two-dimensional (2-D) simulations with the global geometry similar to MRX demonstrate downstream ion thermalization by the above mechanisms. Electrons are also significantly heated during reconnection. The electron temperature sharply increases across the separatrices and peaks just outside of the electron diffusion region. Unlike ions, electrons acquire energy mostly from the reconnection electric field, and the energy gain is localized near the X-point. However, the increase in the electron bulk flow energy remains negligible. These observations support the assertion that efficient electron heating mechanisms exist around the electron diffusion region and that the heat generated there is quickly transported along the magnetic field due to the high parallel thermal conductivity of electrons. Classical Ohmic dissipation based on the perpendicular Spitzer resistivity is too small to balance the measured heat flux, indicating the presence of anomalous electron heating.

<p>Magnetic reconnection is a fundamental energy conversion process in plasmas. It occurs in thin current sheets, where a change in the magnetic field topology leads to rapid heating of plasma, plasma bulk acceleration and acceleration of plasma particles. To allow for magnetic field reconfiguration, both ions and electrons must be demagnetized. The ion and electron demagnetization  take place in the ion and electron diffusion regions respectively, in both cases at kinetic scales. For the first time, Magnetospheric Multiscale (MMS) spacecraft observations, at inter-spacecraft separation comparable to the electron inertial length, allow for a multi-point analysis of the electron diffusion region (EDR). A key question is whether the EDR has a homogeneous or patchy structure. </p><p>Here we report MMS observations at the magnetopause providing evidence of inhomogeneous current densities and energy conversion over a few (∼ 3 d<sub>e</sub>) electron inertial lengths suggesting that the EDR can be structured at electron scales. In particular, the energy conversion is patchy and changing sign in the vicinity of the reconnection site implying that the EDR comprises regions where energy is transferred from the field to the plasma and regions with the opposite energy transition, which is unexpected during reconnection. The origin of the patchy energy conversion appears to be connected to the large v<sub>e,N</sub> ∼ v<sub>e,M</sub> directed from the magnetosphere to magnetosheath. These observations are consistent with recent high-resolution and low-noise kinetic simulations of asymmetric reconnection. Patchy energy conversion is observed also in an EDR at the magnetotail, where the inter-spacecraft separation was ∼ 1 d<sub>e</sub>. Electric field measurements are different among the spacecraft suggesting inhomogeneities at the electron scale. However, in this case the current density appear homogeneous in the EDR suggesting that the structuring may be sourced from a different kind of electron dynamics in the magnetotail.</p>

Magnetic reconnection is a fundamental physical process of rapidly converting magnetic energy into particles in space physics. The electron diffusion region (EDR), which can be split into the inner EDR and outer EDR, is the crucial region during magnetic reconnection. The inner EDR, where the magnetic field is dissipated, is responsible for the heating and acceleration of the electrons. The outer EDR also plays a crucial role where the electrons are decelerated and return the energy to the magnetic field in the pileup region behind the reconnection front (RF). Here we present the studies associated with energy conversions around EDR using fully kinetic particle-in-cell (PIC) simulations of advanced GPU-accelerated computing and Magnetospheric Multiscale (MMS) mission observations. It is found that part of the electrons in the outer EDR are forced backward to the inner EDR by the magnetic tension force to be accelerated again, which we name it by magnetic Marangoni effect. And we also report a novel crater structure of magnetic field behind the RF caused by the continuous impact of the high-speed outflow electron jets. Our PIC simulation scheme based on the GPU architecture can achieve high performance computing and fast accessibility to the simulation results. The scientific findings in our studies propose various approaches for the particle acceleration and energy conversion during magnetic reconnection.

Results from particle‐in‐cell simulations of reconnection with asymmetric upstream conditions are reported to elucidate electron energization and structure of the electron diffusion region (EDR). Acceleration of unmagnetized electrons results in discrete structures in the distribution functions and supports the intense current and perpendicular heating in the EDR. The accelerated electrons are cyclotron turned by the reconnected magnetic field to produce the outflow jets, and as such, the acceleration by the reconnection electric field is limited, leading to resistivity without particle‐particle or particle‐wave collisions. A map of electron distributions is constructed, and its spatial evolution is compared with quantities previously proposed to be EDR identifiers to enable effective identifications of the EDR in terrestrial magnetopause reconnection.

Magnetic reconnection underlies the physical mechanism of explosive phenomena in the solar atmosphere and planetary magnetospheres, where plasma is usually collisionless. In the standard model of collisionless magnetic reconnection, the diffusion region consists of two substructures: an electron diffusion region is embedded in an ion diffusion region, in which their scales are based on the electron and ion inertial lengths. In the ion diffusion region, ions are unfrozen in the magnetic fields while electrons are magnetized. The resulted Hall effect from the different motions between ions and electrons leads to the production of the in-plane currents, and then generates the quadrupolar structure of out-of-plane magnetic field. In the electron diffusion region, even electrons become unfrozen in the magnetic fields, and the reconnection electric field is contributed by the off-diagonal electron pressure terms in the generalized Ohm’s law. The reconnection rate is insensitive to the specific mechanism to break the frozen-in condition, and is on the order of 0.1. In recent years, the launching of Cluster, THEMIS, MMS, and other spacecraft has provided us opportunities to study collisionless magnetic reconnection in the Earth’s magnetosphere, and to verify and extend more insights on the standard model of collisionless magnetic reconnection. In this paper, we will review what we have learned beyond the standard model with the help of observations from these spacecraft as well as kinetic simulations.

Magnetic field reconnection plays a key role in determining the magnetic field topology and in the conversion of magnetic energy into kinetic energy in cosmic plasmas. Magnetic reconnection was proposed by solar physicists in an attempt to explain solar flares. The concept of magnetic reconnection was extended to Earth’s magnetosphere to explain auroral substorms. In this review, we first briefly review the classical fluid steady models with small separatrix angle. We then report magnetic reconnection with a large separatrix angle, and the time-dependent multiple X line reconnection (MXR) associated with flux transfer events. The transition from a single X line reconnection to MXR is examined. Global three-dimensional (3-D) magnetic reconnection is reviewed. The particle pressure gradient associated mainly with the electron (ion) off-diagonal pressure tensor terms, $$P_{xy}$$ and $$P_{zy}$$ , is shown to play an important role for electron (ion) dynamics to balance the reconnection electric field ( $$E_{y}$$ ) near the X line. In addition, various plasma waves and instabilities may occur near the ion diffusion and electron diffusion regions, including the upper hybrid drift waves, lower hybrid drift waves, ion-ion beam instability, electron beam instability, whistler waves and kinetic Alfven waves. The layered structure of outflow region of magnetic reconnection is examined. These layered structures include slow shocks, rotation discontinuities, expansion waves and plasma jets. Recent satellite observations of magnetic reconnection in the Earth and planetary magnetospheres are also discussed. The polar cap electric field associated with magnetic reconnection at the Earth's magnetopause and the energy flow in the polar cap region are examined.

The structure of the electron diffusion region (EDR) in different plasma regimes is an outstanding question related to magnetic reconnection. Here we report a long EDR that extended at least 20 ion inertial lengths downstream of an X line at the Earth’s magnetopause, which was observed by the Magnetospheric Multiscale mission. This EDR was detected in the exhaust of an asymmetric magnetic reconnection with a moderate guide field, the reconnection rate of which was ∼0.1. It corresponds to strong positive energy dissipation ( ) and enhancement of electron nongyrotropy. The energy dissipation was contributed by the electron jet and non-ideal electric field along the outflow direction, which suggests that the EDR probably plays more important roles in the energy conversion in magnetic reconnection than previously thought. Our result could be a significant step toward fully understanding the structure of the EDR.

Magnetic reconnection experiments in high-energy-density (HED) laser-produced plasmas have recently been conducted at the Shenguang-II (SG-II) facility. Two plasma bubbles and a ‘frozen-in’ magnetic field are generated by irradiating an Al foil using two laser beams. As the two bubbles with opposing magnetic fields expand and squeeze each other, magnetic reconnection occurs. In the experiments, three well-collimated high-speed electron jets are observed in the fanlike outflow region of the laser-driven magnetic reconnection. Based on two-dimensional (2D) particle-in-cell (PIC) simulations, we demonstrate that the three electron jets in the outflow region of laser-driven magnetic reconnection are super-Alfvénic, and their formation mechanism is also revealed in this paper. The two super-Alfvénic jets at the edge are formed by the outflow electrons, which move along magnetic field lines after they are accelerated in the vicinity of the X-line by the reconnection electric field. The super-Alfvénic jet at the center is formed by the electrons that come from the outside of the plasma bubbles. These electrons are reflected by the magnetic field in the pileup region and are meanwhile accelerated by the resulting electric field.

The twisted local magnetic field at the front or rear regions of the magnetic clouds (MCs) associated with interplanetary coronal mass ejections (ICMEs) is often nearly opposite to the direction of the ambient interplanetary magnetic field. There is also observational evidence for magnetic reconnection (MR) outflows occurring within the boundary layers of MCs. In this study, a MR event located at the western flank of the MC occurring on October 3, 2000 is studied in detail. Both the large‐scale geometry of the helical MC and the MR outflow structure are scrutinized in a detailed multipoint study. The ICME sheath is of hybrid propagation‐expansion type. Here, the freshly reconnected open field lines are expected to slip slowly over the MC resulting in plasma mixing at the same time. As for MR, the current sheet geometry and the vertical motion of the outflow channel between ACE‐Geotail‐WIND spacecraft were carefully studied and tested. The main findings on MR include (a) first‐time observation of non‐Petschek‐type slow‐shock‐like discontinuities in the inflow regions; (b) observation of turbulent Hall magnetic field associated with a Lorentz‐force‐deflected electron jet; (c) acceleration of protons by reconnection electric field and their back‐scatter from the slow‐shock‐like discontinuity; (d) observation of relativistic electron near the MC inflow boundary/separatrix; these electron populations can presumably appear as a result of nonadiabatic acceleration, gradient B drift, and via acceleration in the electrostatic potential well associated with the Hall current system; and (e) observation of Doppler‐shifted ion‐acoustic and Langmuir waves in the MC inflow region.

The onset of collisionless magnetic reconnection is considered to be controlled by electron dynamics in the electron diffusion region, where the reconnection electric field is balanced mainly by the off-diagonal electron pressure tensor term. Two-dimensional particle-in-cell simulations are employed in this paper to investigate the self-reinforcing process of the reconnection electric field in the electron diffusion region, which is found to grow exponentially. A theoretical model is proposed to demonstrate such a process in the electron diffusion region. In addition the reconnection electric field in the pileup region, which is balanced mainly by the electromotive force term, is also found to grow exponentially and its growth rate is twice that in the electron diffusion region.

Magnetic reconnection and plasma turbulence are ubiquitous and key processes in the Universe. These two processes are suggested to be intrinsically related: magnetic reconnection can develop turbulence, and, in turn, turbulence can influence or excite magnetic reconnection. In this study, we report a rare and unique electron diffusion region (EDR) observed by the Magnetospheric Multiscale mission in the Earth’s magnetotail with significantly enhanced energetic particle fluxes. The EDR is in a region of strong turbulence within which the plasma density is dramatically depleted. We present three salient features. (1) Despite the turbulence, the EDR behaves nearly the same as that in 2D quasi-planar reconnection; the observations suggest that magnetic reconnection continues for several minutes. (2) The observed reconnection electric field and inferred energy transport are exceptionally large. However, the aspect ratio of the EDR (one definition of reconnection rate) is fairly typical. Instead, extraordinarily large-amplitude Hall electric fields appear to enable the strong energy transport. (3) We hypothesize that the high-energy transport rate, density depletion, and the strong particle acceleration are related to a near-runaway effect, which is due to the combination of low-plasma-density inflow (from lobes) and possible positive feedback between turbulence and reconnection. The detailed study on this EDR gives insight into the interplay between reconnection and turbulence, and the possible near-runaway effect, which may play an important role in other particle acceleration in astrophysical plasma.