Energy transfer in reconnection and turbulence

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.

Faster Form of Electron Magnetic Reconnection with a Finite Length X-Line

Observations in Earth's turbulent magnetosheath downstream of a quasiparallel bow shock reveal a prevalence of electron-scale current sheets favorable for electron-only reconnection where ions are not coupled to the reconnecting magnetic fields. In small-scale turbulence, magnetic structures associated with intense current sheets are limited in all dimensions. And since the coupling of ions are constrained by a minimum length scale, the dynamics of electron reconnection is likely to be 3D. Here, both 2D and 3D kinetic particle-in-cell simulations are used to investigate electron-only reconnection, focusing on the reconnection rate and associated electron flows. A new form of 3D electron-only reconnection spontaneously develops where the magnetic X-line is localized in the out-of-plane (z) direction. The consequence is an enhancement of the reconnection rate compared with two dimensions, which results from differential mass flux out of the diffusion region along z, enabling a faster inflow velocity and thus a larger reconnection rate. This outflow along z is due to the magnetic tension force in z just as the conventional exhaust tension force, allowing particles to leave the diffusion region efficiently along z unlike the 2D configuration.

Energy Flux Densities near the Electron Dissipation Region in Asymmetric Magnetopause Reconnection

Magnetic reconnection is of fundamental importance to plasmas because of its role in releasing and repartitioning stored magnetic energy. Previous results suggest that this energy is predominantly released as ion enthalpy flux along the reconnection outflow. Using Magnetospheric Multiscale data we find the existence of very significant electron energy flux densities in the vicinity of the magnetopause electron dissipation region, orthogonal to the ion energy outflow. These may significantly impact models of electron transport, wave generation, and particle acceleration.

Publisher Correction: Electron magnetic reconnection without ion coupling in Earth's turbulent magnetosheath

Change history: In this Letter, the y-axis values in Fig. 3f should go from 4 to -8 (rather than from 4 to -4), the y-axis values in Fig. 3h should appear next to the major tick marks (rather than the minor ticks), and in Fig. 1b, the arrows at the top and bottom of the electron-scale current sheet were going in the wrong direction; these errors have been corrected online.

Kinetic Range Spectral Features of Cross Helicity Using the Magnetospheric Multiscale Spacecraft

We study spectral features of ion velocity and magnetic field correlations in the magnetosheath and in the solar wind using data from the Magnetospheric Multiscale (MMS) spacecraft. High-resolution MMS observations enable the study of the transition of these correlations between their magnetofluid character at larger scales into the subproton kinetic range, previously unstudied in spacecraft data. Cross-helicity, angular alignment, and energy partitioning is examined over a suitable range of scales, employing measurements based on the Taylor frozen-in approximation as well as direct two-spacecraft correlation measurements. The results demonstrate signatures of alignment at large scales. As kinetic scales are approached, the alignment between v and b is destroyed by demagnetization of protons.

Electron-scale dynamics of the diffusion region during symmetric magnetic reconnection in space

Magnetic reconnection is an energy conversion process that occurs in many astrophysical contexts including Earth's magnetosphere, where the process can be investigated in situ by spacecraft. On 11 July 2017, the four Magnetospheric Multiscale spacecraft encountered a reconnection site in Earth's magnetotail, where reconnection involves symmetric inflow conditions. The electron-scale plasma measurements revealed (i) super-Alfvénic electron jets reaching 15,000 kilometers per second; (ii) electron meandering motion and acceleration by the electric field, producing multiple crescent-shaped structures in the velocity distributions; and (iii) the spatial dimensions of the electron diffusion region with an aspect ratio of 0.1 to 0.2, consistent with fast reconnection. The well-structured multiple layers of electron populations indicate that the dominant electron dynamics are mostly laminar, despite the presence of turbulence near the reconnection site.

Guide Field Reconnection: Exhaust Structure and Heating

Magnetospheric Multiscale observations are used to probe the structure and temperature profile of a guide field reconnection exhaust ~100 ion inertial lengths downstream from the X-line in the Earth's magnetosheath. Asymmetric Hall electric and magnetic field signatures were detected, together with a density cavity confined near 1 edge of the exhaust and containing electron flow toward the X-line. Electron holes were also detected both on the cavity edge and at the Hall magnetic field reversal. Predominantly parallel ion and electron heating was observed in the main exhaust, but within the cavity, electron cooling and enhanced parallel ion heating were found. This is explained in terms of the parallel electric field, which inhibits electron mixing within the cavity on newly reconnected field lines but accelerates ions. Consequently, guide field reconnection causes inhomogeneous changes in ion and electron temperature across the exhaust.

On the Collisionless Asymmetric Magnetic Reconnection Rate

A prediction of the steady state reconnection electric field in asymmetric reconnection is obtained by maximizing the reconnection rate as a function of the opening angle made by the upstream magnetic field on the weak magnetic field (magnetosheath) side. The prediction is within a factor of 2 of the widely examined asymmetric reconnection model (Cassak & Shay, 2007, https://doi.org/10.1063/1.2795630) in the collisionless limit, and they scale the same over a wide parameter regime. The previous model had the effective aspect ratio of the diffusion region as a free parameter, which simulations and observations suggest is on the order of 0.1, but the present model has no free parameters. In conjunction with the symmetric case (Liu et al., 2017, https://doi.org/10.1103/PhysRevLett.118.085101), this work further suggests that this nearly universal number 0.1, essentially the normalized fast-reconnection rate, is a geometrical factor arising from maximizing the reconnection rate within magnetohydrodynamic-scale constraints.

PLAIN LANGUAGE SUMMARY

To understand the evolution of many space and astrophysical plasmas, it is imperative to know how fast magnetic reconnection processes the magnetic flux. Researchers found that reconnection in both symmetric and asymmetric geometries exhibits a normalized reconnection rate of order 0.1. In this work, we show that this nearly universal value in asymmetric geometry is also the maximal rate allowed in the magnetohydrodynamic scale. This result has applications to the transport process at plasma boundary layers like Earth's magnetopause.

Why does Steady-State Magnetic Reconnection have a Maximum Local Rate of Order 0.1?

Simulations suggest collisionless steady-state magnetic reconnection of Harris-type current sheets proceeds with a rate of order 0.1, independent of dissipation mechanism. We argue this long-standing puzzle is a result of constraints at the magnetohydrodynamic (MHD) scale. We predict the reconnection rate as a function of the opening angle made by the upstream magnetic fields, finding a maximum reconnection rate close to 0.2. The predictions compare favorably to particle-in-cell simulations of relativistic electron-positron and nonrelativistic electron-proton reconnection. The fact that simulated reconnection rates are close to the predicted maximum suggests reconnection proceeds near the most efficient state allowed at the MHD scale. The rate near the maximum is relatively insensitive to the opening angle, potentially explaining why reconnection has a similar fast rate in differing models.

Observations of Hall Reconnection Physics Far Downstream of the X Line

Observations made using the Wind spacecraft of Hall magnetic fields in solar wind reconnection exhausts are presented. These observations are consistent with the generation of Hall fields by a narrow ion inertial scale current layer near the separatrix, which is confirmed with an appropriately scaled particle-in-cell simulation that shows excellent agreement with observations. The Hall fields are observed thousands of ion inertial lengths downstream from the reconnection X line, indicating that narrow regions of kinetic dynamics can persist extremely far downstream.

Magnetospheric Multiscale Observations of the Electron Diffusion Region of Large Guide Field Magnetic Reconnection

We report observations from the Magnetospheric Multiscale (MMS) satellites of a large guide field magnetic reconnection event. The observations suggest that two of the four MMS spacecraft sampled the electron diffusion region, whereas the other two spacecraft detected the exhaust jet from the event. The guide magnetic field amplitude is approximately 4 times that of the reconnecting field. The event is accompanied by a significant parallel electric field (E_{∥}) that is larger than predicted by simulations. The high-speed (∼300  km/s) crossing of the electron diffusion region limited the data set to one complete electron distribution inside of the electron diffusion region, which shows significant parallel heating. The data suggest that E_{∥} is balanced by a combination of electron inertia and a parallel gradient of the gyrotropic electron pressure.

Magnetospheric Multiscale Satellites Observations of Parallel Electric Fields Associated with Magnetic Reconnection

We report observations from the Magnetospheric Multiscale satellites of parallel electric fields (E_{∥}) associated with magnetic reconnection in the subsolar region of the Earth's magnetopause. E_{∥} events near the electron diffusion region have amplitudes on the order of 100  mV/m, which are significantly larger than those predicted for an antiparallel reconnection electric field. This Letter addresses specific types of E_{∥} events, which appear as large-amplitude, near unipolar spikes that are associated with tangled, reconnected magnetic fields. These E_{∥} events are primarily in or near a current layer near the separatrix and are interpreted to be double layers that may be responsible for secondary reconnection in tangled magnetic fields or flux ropes. These results are telling of the three-dimensional nature of magnetopause reconnection and indicate that magnetopause reconnection may be often patchy and/or drive turbulence along the separatrix that results in flux ropes and/or tangled magnetic fields.

Ion-scale secondary flux ropes generated by magnetopause reconnection as resolved by MMS

New Magnetospheric Multiscale (MMS) observations of small-scale (~7 ion inertial length radius) flux transfer events (FTEs) at the dayside magnetopause are reported. The 10 km MMS tetrahedron size enables their structure and properties to be calculated using a variety of multispacecraft techniques, allowing them to be identified as flux ropes, whose flux content is small (~22 kWb). The current density, calculated using plasma and magnetic field measurements independently, is found to be filamentary. Intercomparison of the plasma moments with electric and magnetic field measurements reveals structured non-frozen-in ion behavior. The data are further compared with a particle-in-cell simulation. It is concluded that these small-scale flux ropes, which are not seen to be growing, represent a distinct class of FTE which is generated on the magnetopause by secondary reconnection.

Electron-scale measurements of magnetic reconnection in space

Magnetic reconnection is a fundamental physical process in plasmas whereby stored magnetic energy is converted into heat and kinetic energy of charged particles. Reconnection occurs in many astrophysical plasma environments and in laboratory plasmas. Using measurements with very high time resolution, NASA's Magnetospheric Multiscale (MMS) mission has found direct evidence for electron demagnetization and acceleration at sites along the sunward boundary of Earth's magnetosphere where the interplanetary magnetic field reconnects with the terrestrial magnetic field. We have (i) observed the conversion of magnetic energy to particle energy; (ii) measured the electric field and current, which together cause the dissipation of magnetic energy; and (iii) identified the electron population that carries the current as a result of demagnetization and acceleration within the reconnection diffusion/dissipation region.

New electric field in asymmetric magnetic reconnection

We present a theory and numerical evidence for the existence of a previously unexplored in-plane electric field in collisionless asymmetric magnetic reconnection. This electric field, dubbed the "Larmor electric field," is associated with finite Larmor radius effects and is distinct from the known Hall electric field. Potentially, it could be an important indicator for the upcoming Magnetospheric Multiscale mission to locate reconnection sites as we expect it to appear on the magnetospheric side, pointing earthward, at the dayside magnetopause reconnection site.

Von Kármán energy decay and heating of protons and electrons in a kinetic turbulent plasma

Decay in time of undriven weakly collisional kinetic plasma turbulence in systems large compared to the ion kinetic scales is investigated using fully electromagnetic particle-in-cell simulations initiated with transverse flow and magnetic disturbances, constant density, and a strong guide field. The observed energy decay is consistent with the von Kármán hypothesis of similarity decay, in a formulation adapted to magnetohydrodyamics. Kinetic dissipation occurs at small scales, but the overall rate is apparently controlled by large scale dynamics. At small turbulence amplitudes the electrons are preferentially heated. At larger amplitudes proton heating is the dominant effect. In the solar wind and corona the protons are typically hotter, suggesting that these natural systems are in the large amplitude turbulence regime.

Energy partition in magnetic reconnection in Earth's magnetotail

The partition of energy flux in magnetic reconnection is examined experimentally using Cluster satellite observations of collisionless reconnection in Earth's magnetotail. In this plasma regime, the dominant component of the energy flux is ion enthalpy flux, with smaller contributions from the electron enthalpy and heat flux and the ion kinetic energy flux. However, the Poynting flux is not negligible, and in certain parts of the ion diffusion region the Poynting flux in fact dominates. Evidence for earthward-tailward asymmetry is ascribed to the presence of Earth's dipole fields.

Direct evidence for a three-dimensional magnetic flux rope flanked by two active magnetic reconnection X lines at Earth's magnetopause

We report the direct detection by three THEMIS spacecraft of a magnetic flux rope flanked by two active X lines producing colliding plasma jets near the center of the flux rope. The observed density depletion and open magnetic field topology inside the flux rope reveal important three-dimensional effects. There was also evidence for nonthermal electron energization within the flux rope core where the fluxes of 1-4 keV superthermal electrons were higher than those in the converging reconnection jets. The observed ion and electron energizations differ from current theoretical predictions.

Super-Alfvénic propagation of substorm reconnection signatures and Poynting flux

The propagation of reconnection signatures and their associated energy are examined using kinetic particle-in-cell simulations and Cluster satellite observations. It is found that the quadrupolar out-of-plane magnetic field near the separatrices is associated with a kinetic Alfvén wave. For magnetotail parameters, the parallel propagation of this wave is super-Alfvénic (V(∥) ∼ 1500-5500 km/s) and generates substantial Poynting flux (S ∼ 10(-5)-10(-4) W/m(2)) consistent with Cluster observations of magnetic reconnection. This Poynting flux substantially exceeds that due to frozen-in ion bulk outflows and is sufficient to generate white light aurora in Earth's ionosphere.

Asymmetry of the ion diffusion region Hall electric and magnetic fields during guide field reconnection: observations and comparison with simulations

In situ measurements of magnetic reconnection in the Earth's magnetotail are presented showing that even a moderate guide field (20% of the reconnecting field) considerably distorts ion diffusion region structure. The Hall magnetic and electric fields are asymmetric and shunted away from the current sheet; an appropriately scaled particle-in-cell simulation is found to be in excellent agreement with the data. The results show the importance of correctly accounting for the effects of the magnetic shear when attempting to identify and study magnetic reconnection diffusion regions in nature.

Magnetic reconnection in two-dimensional magnetohydrodynamic turbulence

Systematic analysis of numerical simulations of two-dimensional magnetohydrodynamic turbulence reveals the presence of a large number of X-type neutral points where magnetic reconnection occurs. We examine the statistical properties of this ensemble of reconnection events that are spontaneously generated by turbulence. The associated reconnection rates are distributed over a wide range of values and scales with the geometry of the diffusion region. Locally, these events can be described through a variant of the Sweet-Parker model, in which the parameters are externally controlled by turbulence. This new perspective on reconnection is relevant in space and astrophysical contexts, where plasma is generally in a fully turbulent regime.

Evidence for an elongated (>60 ion skin depths) electron diffusion region during fast magnetic reconnection

Observations of an extremely elongated electron diffusion region occurring during fast reconnection are presented. Cluster spacecraft in situ observations of an expanding reconnection exhaust reveal a broad current layer ( approximately 10 ion skin depths thick) supporting the reversal of the reconnecting magnetic field together with an intense current embedded at the center that is due to a super-Alfvénic electron outflow jet with transverse scale of approximately 9 electron skin depths. The electron jet extends at least 60 ion skin depths downstream from the X-line.

Two-scale structure of the electron dissipation region during collisionless magnetic reconnection

Particle-in-cell simulations of collisionless magnetic reconnection are presented that demonstrate that reconnection remains fast in very large systems. The electron dissipation region develops a distinct two-scale structure along the outflow direction. Consistent with fast reconnection, the length of the electron current layer stabilizes and decreases with decreasing electron mass, approaching the ion inertial length for a proton-electron plasma. Surprisingly, the electrons form a super-Alfvénic outflow jet that remains decoupled from the magnetic field and extends large distances downstream from the x line.

Onset of fast magnetic reconnection

We demonstrate the existence of a new steady-state magnetic reconnection configuration which lies at the boundary of the basins of attraction between the Sweet-Parker and Hall reconnection configurations. The solution is linearly unstable to small perturbations and its identification required a novel iterative numerical technique. The eigenmodes of the unstable solution are localized near the X line, suggesting that the onset of fast reconnection in a weakly collisional plasma is initiated locally at the X line as opposed to remotely at the boundaries.

Electron acceleration from contracting magnetic islands during reconnection

A long-standing problem in the study of space and astrophysical plasmas is to explain the production of energetic electrons as magnetic fields 'reconnect' and release energy. In the Earth's magnetosphere, electron energies reach hundreds of thousands of electron volts (refs 1-3), whereas the typical electron energies associated with large-scale reconnection-driven flows are just a few electron volts. Recent observations further suggest that these energetic particles are produced in the region where the magnetic field reconnects. In solar flares, upwards of 50 per cent of the energy released can appear as energetic electrons. Here we show that electrons gain kinetic energy by reflecting from the ends of the contracting 'magnetic islands' that form as reconnection proceeds. The mechanism is analogous to the increase of energy of a ball reflecting between two converging walls--the ball gains energy with each bounce. The repetitive interaction of electrons with many islands allows large numbers to be efficiently accelerated to high energy. The back pressure of the energetic electrons throttles reconnection so that the electron energy gain is a large fraction of the released magnetic energy. The resultant energy spectra of electrons take the form of power laws with spectral indices that match the magnetospheric observations.

Catastrophe model for fast magnetic reconnection onset

A catastrophe model for the onset of fast magnetic reconnection is presented that suggests why plasma systems with magnetic free energy remain apparently stable for long times and then suddenly release their energy. For a given set of plasma parameters there are generally two stable reconnection solutions: a slow (Sweet-Parker) solution and a fast (Alfvénic) Hall reconnection solution. Below a critical resistivity the slow solution disappears and fast reconnection dominates. Scaling arguments predicting the two solutions and the critical resistivity are confirmed with two-fluid simulations.

Production of energetic electrons during magnetic reconnection

The production of energetic electrons during magnetic reconnection is explored with full particle simulations and analytic analysis. Density cavities generated along separatrices bounding growing magnetic islands support parallel electric fields that act as plasma accelerators. Electrons because of their low mass are fast enough to make multiple passes through these acceleration cavities and are therefore capable of reaching relativistic energies.

Three-species collisionless reconnection: effect of O+ on magnetotail reconnection

The nature of collisionless reconnection in a three-species plasma composed of a heavy species, protons, and electrons is examined. In addition to the usual two length scales present in two-species reconnection, there are two additional larger length scales in the system: one associated with a "heavy whistler" which produces a large scale quadrupolar out-of-plane magnetic field, and one associated with the "heavy Alfvén" wave which can slow the outflow speed and thus the reconnection rate. The consequences for reconnection with O+ present in the magnetotail are discussed.

Impact of frustrated singularities on magnetic island evolution

The growth of magnetic islands is explored using the magnetohydrodynamic model in a simple slab system in which the value of the tearing mode stability parameter Delta' can be varied continuously. Unless the system is close to marginal stability reconnection is controlled by Sweet-Parker current layers, whose formation is a consequence of the inherent singular structure of magnetic island equilibria.

Formation of electron holes and particle energization during magnetic reconnection

Three-dimensional particle simulations of magnetic reconnection reveal the development of turbulence driven by intense electron beams that form near the magnetic x-line and separatrices. The turbulence collapses into localized three-dimensional nonlinear structures in which the electron density is depleted. The predicted structure of these electron holes compares favorably with satellite observations at Earth's magnetopause. The birth and death of these electron holes and their associated intense electric fields lead to strong electron scattering and energization, whose understanding is critical to explaining why magnetic explosions in space release energy so quickly and produce such a large number of energetic electrons.

Role of dispersive waves in collisionless magnetic reconnection

Simulations of collisionless magnetic reconnection show a dramatic enhancement of the nonlinear reconnection rate due to the formation of an open outflow region. We link the formation of this open configuration to dispersive whistler and kinetic Alfvén wave dynamics at small scales. The roles of these two waves are controlled by two dimensionless parameters, which allow us to identify regions of fast and slow reconnection.