Ohm's Law, the Reconnection Rate, and Energy Conversion in Collisionless Magnetic Reconnection

Magnetic reconnection is a ubiquitous plasma process that transforms magnetic energy into particle energy during eruptive events throughout the universe. Reconnection not only converts energy during solar flares and geomagnetic substorms that drive space weather near Earth, but it may also play critical roles in the high energy emissions from the magnetospheres of neutron stars and black holes. In this review article, we focus on collisionless plasmas that are most relevant to reconnection in many space and astrophysical plasmas. Guided by first-principles kinetic simulations and spaceborne in-situ observations, we highlight the most recent progress in understanding this fundamental plasma process. We start by discussing the non-ideal electric field in the generalized Ohm's law that breaks the frozen-in flux condition in ideal magnetohydrodynamics and allows magnetic reconnection to occur. We point out that this same reconnection electric field also plays an important role in sustaining the current and pressure in the current sheet and then discuss the determination of its magnitude (i.e., the reconnection rate), based on force balance and energy conservation. This approach to determining the reconnection rate is applied to kinetic current sheets with a wide variety of magnetic geometries, parameters, and background conditions. We also briefly review the key diagnostics and modeling of energy conversion around the reconnection diffusion region, seeking insights from recently developed theories. Finally, future prospects and open questions are discussed.

Laboratory Study of Collisionless Magnetic Reconnection

A concise review is given on the past two decades' results from laboratory experiments on collisionless magnetic reconnection in direct relation with space measurements, especially by the Magnetospheric Multiscale (MMS) mission. Highlights include spatial structures of electromagnetic fields in ion and electron diffusion regions as a function of upstream symmetry and guide field strength, energy conversion and partitioning from magnetic field to ions and electrons including particle acceleration, electrostatic and electromagnetic kinetic plasma waves with various wavelengths, and plasmoid-mediated multiscale reconnection. Combined with the progress in theoretical, numerical, and observational studies, the physics foundation of fast reconnection in collisionless plasmas has been largely established, at least within the parameter ranges and spatial scales that were studied. Immediate and long-term future opportunities based on multiscale experiments and space missions supported by exascale computation are discussed, including dissipation by kinetic plasma waves, particle heating and acceleration, and multiscale physics across fluid and kinetic scales.

Energized Oxygen in the Magnetotail: Onset and Evolution of Magnetic Reconnection

Oxygen ions are a major constituent of magnetospheric plasma, yet the role of oxygen in processes such as magnetic reconnection continues to be poorly understood. Observations show that significant amounts of energized O+ can be present in a magnetotail current sheet (CS). A population of thermal O+ only has a relatively minor effect on magnetic reconnection. Despite this, published studies have so far only concentrated on the role of the low-energy thermal O+. We present a study of magnetic reconnection in a thinning CS with energized O+ present. Well-established, three-species, 2.5D particle-in-cell (PIC) kinetic simulations are used. Simulations of thermal H+ and thermal O+ validate our setup against published results. We then energize a thermal background O+ based on published in situ measurements. A range of energization is applied to the background O+. We discuss the effects of energized O+ on CS thinning and the onset and evolution of magnetic reconnection. The presence of energized O+ causes a two-regime onset response in a thinning CS. As energization increases in the lower-regime, reconnection develops at a single primary X-line, increases time-to-onset, and suppresses the rate of evolution. As energization continues to increase in the higher-regime, reconnection develops at multiple X-lines, forming a stochastic plasmoid chain; decreases time-to-onset; and enhances evolution via a plasmoid instability. Energized O+ drives a depletion of the background H+ around the central CS. As the energization increases, the CS thinning begins to slow and eventually reverses.

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.

The two-fluid dynamics and energetics of the asymmetric magnetic reconnection in laboratory and space plasmas

Magnetic reconnection is a fundamental process in magnetized plasma where magnetic energy is converted to plasma energy. Despite huge differences in the physical size of the reconnection layer, remarkably similar characteristics are observed in both laboratory and magnetosphere plasmas. Here we present the comparative study of the dynamics and physical mechanisms governing the energy conversion in the laboratory and space plasma in the context of two-fluid physics, aided by numerical simulations. In strongly asymmetric reconnection layers with negligible guide field, the energy deposition to electrons is found to primarily occur in the electron diffusion region where electrons are demagnetized and diffuse. A large potential well is observed within the reconnection plane and ions are accelerated by the electric field toward the exhaust region. The present comparative study identifies the robust two-fluid mechanism operating in systems over six orders of magnitude in spatial scales and over a wide range of collisionality.

Magnetic energy in the plasma is transferred into particle energy by magnetic reconnection. Here the authors show the two-fluid dynamics of asymmetric magnetic reconnection in two different spatial scales of plasma, namely laboratory and astrophysical plasma.

How Accurately Can We Measure the Reconnection Rate M for the MMS Diffusion Region Event of 11 July 2017?

We investigate the accuracy with which the reconnection electric field E M can be determined from in situ plasma data. We study the magnetotail electron diffusion region observed by National Aeronautics and Space Administration's Magnetospheric Multiscale (MMS) on 11 July 2017 at 22:34 UT and focus on the very large errors in E M that result from errors in an L M N boundary normal coordinate system. We determine several L M N coordinates for this MMS event using several different methods. We use these M axes to estimate E M. We find some consensus that the reconnection rate was roughly E M = 3.2 ± 0.6 mV/m, which corresponds to a normalized reconnection rate of 0.18 ± 0.035. Minimum variance analysis of the electron velocity (MVA-v e), MVA of E, minimization of Faraday residue, and an adjusted version of the maximum directional derivative of the magnetic field (MDD-B) technique all produce reasonably similar coordinate axes. We use virtual MMS data from a particle-in-cell simulation of this event to estimate the errors in the coordinate axes and reconnection rate associated with MVA-v e and MDD-B. The L and M directions are most reliably determined by MVA-v e when the spacecraft observes a clear electron jet reversal. When the magnetic field data have errors as small as 0.5% of the background field strength, the M direction obtained by MDD-B technique may be off by as much as 35°. The normal direction is most accurately obtained by MDD-B. Overall, we find that these techniques were able to identify E M from the virtual data within error bars ≥20%.

Perspectives on magnetic reconnection

Magnetic reconnection is a topological rearrangement of magnetic field that occurs on time scales much faster than the global magnetic diffusion time. Since the field lines break on microscopic scales but energy is stored and the field is driven on macroscopic scales, reconnection is an inherently multi-scale process that often involves both magnetohydrodynamic (MHD) and kinetic phenomena. In this article, we begin with the MHD point of view and then describe the dynamics and energetics of reconnection using a two-fluid formulation. We also focus on the respective roles of global and local processes and how they are coupled. We conclude that the triggers for reconnection are mostly global, that the key energy conversion and dissipation processes are either local or global, and that the presence of a continuum of scales coupled from microscopic to macroscopic may be the most likely path to fast reconnection.

Laboratory study of magnetic reconnection with a density asymmetry across the current sheet

The effects of a density asymmetry across the current sheet on anti-parallel magnetic reconnection are studied systematically in a laboratory plasma. Despite a significant density ratio of up to 10, the in-plane magnetic field profile is not significantly changed. On the other hand, the out-of-plane Hall magnetic field profile is considerably modified; it is almost bipolar in structure with the density asymmetry, as compared to quadrupolar in structure with the symmetric configuration. Moreover, the ion stagnation point is shifted to the low-density side, and the electrostatic potential profile also becomes asymmetric with a deeper potential well on the low-density side. Nonclassical bulk electron heating together with electromagnetic fluctuations in the lower hybrid frequency range is observed near the low-density-side separatrix. The dependence of the ion outflow and reconnection electric field on the density asymmetry is measured and compared with theoretical expectations. The measured ion outflow speeds are about 40% of the theoretical values.

Observation of ion acceleration and heating during collisionless magnetic reconnection in a laboratory plasma

The ion dynamics in a collisionless magnetic reconnection layer are studied in a laboratory plasma. The measured in-plane plasma potential profile, which is established by electrons accelerated around the electron diffusion region, shows a saddle-shaped structure that is wider and deeper towards the outflow direction. This potential structure ballistically accelerates ions near the separatrices toward the outflow direction. Ions are heated as they travel into the high-pressure downstream region.

Plasmoid-induced turbulence in collisionless magnetic reconnection

The dissipation mechanism in collisionless magnetic reconnection in a quasisteady period is investigated for the antiparallel field configuration. A three-dimensional simulation in a fully kinetic system reveals that a current-aligned electromagnetic mode produces turbulent electron flow that facilitates the transport of the momentum responsible for the current density. It is found that the electromagnetic turbulence is drastically enhanced by plasmoid formations and has a significant impact on the dissipation at the magnetic x-line. The linear analyses confirm that the mode survives in the real ion-to-electron mass ratio, which assures the importance of the turbulence in collisionless reconnection.

Evolution of an electron current layer prior to reconnection onset

Electron current layers (ECLs) are the sites where magnetic reconnection initiates in a current sheet. Using three-dimensional particle-in-cell simulations, we study the plasma processes that occur in an ECL as it evolves rapidly over a short time scale much shorter than the ion cyclotron period. The processes include its thinning, generation of electrostatic instabilities, trapping and heating of electrons in growing waves, its rebroadening, generation of anomalous resistivity, and eventually the generation of large-amplitude magnetic fluctuations. These fluctuations could be interpreted in terms of electron tearing and/or Weibel instabilities, which are commonly invoked as mechanisms for the magnetic reconnection onset. The widths of the broadened ECL are compared with those measured in the magnetic reconnection experiment, showing excellent agreement.

Finite dissipation and intermittency in magnetohydrodynamics

We present an analysis of data stemming from numerical simulations of decaying magnetohydrodynamic (MHD) turbulence up to grid resolution of 1536(3) points and up to Taylor Reynolds number of approximately 1200 . The initial conditions are such that the initial velocity and magnetic fields are helical and in equipartition, while their correlation is negligible. Analyzing the data at the peak of dissipation, we show that the dissipation in MHD seems to asymptote to a constant as the Reynolds number increases, thereby strengthening the possibility of fast reconnection events in the solar environment for very large Reynolds numbers. Furthermore, intermittency of MHD flows, as determined by the spectrum of anomalous exponents of structure functions of the velocity and the magnetic field, is stronger than that of fluids, confirming earlier results; however, we also find that there is a measurable difference between the exponents of the velocity and those of the magnetic field, reminiscent of recent solar wind observations. Finally, we discuss the spectral scaling laws that arise in this flow.

Collisionless magnetic reconnection via Alfvén eigenmodes

We propose an analytic approach to the problem of collisionless magnetic reconnection formulated as a process of Alfvén eigenmodes' generation and dissipation. Alfvén eigenmodes are confined by the current sheet in the same way that quantum mechanical waves are confined by the tanh;{2} potential. The dynamical time scale of reconnection is the system scale divided by the eigenvalue propagation velocity of the n = 1 mode. The prediction of the n = 1 mode shows good agreement with the in situ measurement of the reconnection-associated Hall fields.

The science of space weather

The basic physics underpinning space weather is reviewed, beginning with a brief overview of the main causes of variability in the near-Earth space environment. Although many plasma phenomena contribute to space weather, one of the most important is magnetic reconnection, and recent cutting edge research in this field is reviewed. We then place this research in context by discussing a number of specific types of space weather in more detail. As society inexorably increases its dependence on space, the necessity of predicting and mitigating space weather will become ever more acute. This requires a deep understanding of the complexities inherent in the plasmas that fill space and has prompted the development of a new generation of scientific space missions at the international level.