The rate of magnetic reconnection is of the utmost importance in a variety of processes because it controls, for example, the rate energy is released in solar flares, the speed of the Dungey convection cycle in Earth’s magnetosphere, and the energy release rate in harmful geomagnetic substorms. It is known from numerical simulations and satellite observations that the rate is approximately 0.1 in normalized units, but despite years of effort, a full theoretical prediction has not been obtained. Here, we present a firstprinciples theory for the reconnection rate in nonrelativistic electronion collisionless plasmas, and show that the same prediction explains why SweetParker reconnection is considerably slower. The key consideration of this analysis is the pressure at the reconnection site (i.e., the xline). We show that the Hall electromagnetic fields in antiparallel reconnection cause an energy void, equivalently a pressure depletion, at the xline, so the reconnection exhaust opens out, enabling the fast rate of 0.1. If the energy can reach the xline to replenish the pressure, the exhaust does not open out. In addition to heliospheric applications, these results are expected to impact reconnection studies in planetary magnetospheres, magnetically confined fusion devices, and astrophysical plasmas.
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Abstract 
Abstract Magnetic reconnection converts, often explosively, stored magnetic energy to particle energy in space and in the laboratory. Through processes operating on length scales that are tiny, it facilitates energy conversion over dimensions of, in some cases, hundreds of Earth radii. In addition, it is the mechanism behind large current disruptions in fusion machines, and it can explain eruptive behavior in astrophysics. We have known about the importance of magnetic reconnection for quite some time based on space observations. Theory and modeling employed magnetized fluids, a very simplistic description. While successful at modeling the large‐scale consequences of reconnection, it is ill suited to describe the engine itself. This is because, at its heart, magnetic reconnection in space is kinetic, that is, governed by the intricate interaction of charged particles with the electromagnetic fields they create. This complex interaction occurs in very localized regions and involves very short temporal variations. Researching reconnection requires the ability to measure these processes as well as to express them in models vastly more complex than fluid approaches. Until very recently, neither of these capabilities existed. With the advent of NASA's Magnetospheric Multiscale mission and modern modeling advances, this has now changed, and we have now determined its small‐scale structure in exquisite detail. In this paper, we review recent research results to predict what will be achieved in the future. We discuss how reconnection contributes to the evolution of larger‐scale systems, and its societal impacts in the context of threatening space hazards, customarily referred to as “space weather.”

Using incoherent Thomson scattering, electron heating and acceleration at the electron velocity distribution function (EVDF) level are investigated during electrononly reconnection in the PHAse Space MApping (PHASMA) facility. Reconnection arises during the merger of two kinkfree flux ropes. Both push and pull type reconnection occur in a single discharge. Electron heating is localized around the separatrix, and the electron temperature increases continuously along the separatrix with distance from the Xline. The local measured gain in enthalpy flux is up to 70% of the incoming Poynting flux. Notably, nonMaxwellian EVDFs comprised of a warm bulk population and a cold beam are directly measured during the electrononly reconnection. The electron beam velocity is comparable to, and scales with, electron Alfvén speed, revealing the signature of electron acceleration caused by electrononly reconnection. The observation of oppositely directed electron beams on either side of the Xpoint provides “smokinggun” evidence of the occurrence of electrononly reconnection in PHASMA. 2D particleincell simulations agree well with the laboratory measurements. The measured conversion of Poynting flux into electron enthalpy is consistent with recent observations of electrononly reconnection in the magnetosheath [Phan et al., Nature 557, 202 (2018)] at similar dimensionless parameters as in the experiments. The laboratory measurements go beyond the magnetosheath observations by directly resolving the electron temperature gain.

Observations in Earth’s turbulent magnetosheath downstream of a quasiparallel bow shock reveal a prevalence of electronscale current sheets favorable for electrononly reconnection where ions are not coupled to the reconnecting magnetic fields. In smallscale 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 particleincell simulations are used to investigate electrononly reconnection, focusing on the reconnection rate and associated electron flows. A new form of 3D electrononly reconnection spontaneously develops where the magnetic Xline is localized in the outofplane (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.more » « less

Using 2.5 dimensional kinetic particleincell (PIC) simulations, we simulate reconnection conditions appropriate for the magnetosheath and solar wind, i.e., plasma beta (ratio of gas pressure to magnetic pressure) greater than 1 and low magnetic shear (strong guide field). Changing the simulation domain size, we find that the ion response varies greatly. For reconnecting regions with scales comparable to the ion inertial length, the ions do not respond to the reconnection dynamics leading to “electrononly” reconnection with very large quasisteady reconnection rates. Note that in these simulations the ion Larmor radius is comparable to the ion inertial length. The transition to more traditional “ioncoupled” reconnection is gradual as the reconnection domain size increases, with the ions becoming frozenin in the exhaust when the magnetic island width in the normal direction reaches many ion inertial lengths. During this transition, the quasisteady reconnection rate decreases until the ions are fully coupled, ultimately reaching an asymptotic value. The scaling of the ion outflow velocity with exhaust width during this electrononly to ioncoupled transition is found to be consistent with a theoretical model of a newly reconnected field line. In order to have a fully frozenin ion exhaust with ion flows comparable to the reconnection Alfven speed, an exhaust width of at least several ion inertial lengths is needed. In turbulent systems with reconnection occurring between magnetic bubbles associated with fluctuations, using geometric arguments we estimate that fully ioncoupled reconnection requires magnetic bubble length scales of at least several tens of ion inertial lengths.more » « less

We describe a systematic development of kinetic entropy as a diagnostic in fully kinetic particleincell (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 f ln f, 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 twodimensional in position space and threedimensional 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 plasmamore » « less