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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.

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., Competing Interests: Competing InterestsThe authors declare no competing interests., (© The Author(s) 2025.)

A common approach to assess the nature of energy conversion in a classical fluid or plasma is to compare power densities of the various possible energy conversion mechanisms. A leading research area is quantifying energy conversion for systems that are not in local thermodynamic equilibrium (LTE), as is common in a number of fluid and plasma systems. Here we introduce the "higher-order nonequilibrium term" (HORNET) effective power density, which quantifies the rate of change of departure of a phase space density from LTE. It has dimensions of power density, which allows for quantitative comparisons with standard power densities. We employ particle-in-cell simulations to calculate HORNET during two processes, magnetic reconnection and decaying kinetic turbulence in collisionless magnetized plasmas, that inherently produce non-LTE effects. We investigate the spatial variation of HORNET and the time evolution of its spatial average. By comparing HORNET with power densities describing changes to the internal energy (pressure dilatation, Pi-D, and divergence of the vector heat flux density), we find that HORNET can be a significant fraction of these other measures (8% and 35% for electrons and ions, respectively, for reconnection; up to 67% for both electrons and ions for turbulence), meaning evolution of the system towards or away from LTE can be dynamically important. Applications to numerous plasma phenomena are discussed.

Anisotropic electron heating during electron-only magnetic reconnection with a large guide magnetic field is directly measured in a laboratory plasma through in situ measurements of electron velocity distribution functions. Electron heating preferentially parallel to the magnetic field is localized to one separatrix, and anisotropies of 1.5 are measured. The mechanism for electron energization is identified as the parallel reconnection electric field because of the anisotropic nature of the heating and spatial localization. These characteristics are reproduced in a 2D particle-in-cell simulation and are also consistent with numerous magnetosheath observations. A measured increase in the perpendicular temperature along both separatrices is not reproduced by our 2D simulations. This work has implications for energy partition studies in magnetosheath and laboratory reconnection.

Weakly collisional and collisionless plasmas are typically far from local thermodynamic equilibrium (LTE), and understanding energy conversion in such systems is a forefront research problem. The standard approach is to investigate changes in internal (thermal) energy and density, but this omits energy conversion that changes any higher-order moments of the phase space density. In this Letter, we calculate from first principles the energy conversion associated with all higher moments of the phase space density for systems not in LTE. Particle-in-cell simulations of collisionless magnetic reconnection reveal that energy conversion associated with higher-order moments can be locally significant. The results may be useful in numerous plasma settings, such as reconnection, turbulence, shocks, and wave-particle interactions in heliospheric, planetary, and astrophysical plasmas.

Non-Maxwellian electron velocity distribution functions composed of a warm bulk population and a cold beam are directly measured during electron-only reconnection with a strong out-of-plane (guide) magnetic field in a laboratory plasma. Electron heating is localized to the separatrix, and the electron temperature increases continuously along the separatrix. The measured gain in enthalpy flux is 70% of the incoming Poynting flux. The electron beams are oppositely directed on either side of the X point, and their velocities are comparable to, and scale with, the electron Alfvén speed. Particle-in-cell simulations are consistent with the measurements. The experimental results are consistent with, and go beyond, recent observations in the magnetosheath.

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.

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.

Magnetic reconnection in current sheets is a magnetic-to-particle energy conversion process that is fundamental to many space and laboratory plasma systems. In the standard model of reconnection, this process occurs in a minuscule electron-scale diffusion region 1,2 . On larger scales, ions couple to the newly reconnected magnetic-field lines and are ejected away from the diffusion region in the form of bi-directional ion jets at the ion Alfvén speed 3-5 . Much of the energy conversion occurs in spatially extended ion exhausts downstream of the diffusion region 6 . In turbulent plasmas, which contain a large number of small-scale current sheets, reconnection has long been suggested to have a major role in the dissipation of turbulent energy at kinetic scales 7-11 . However, evidence for reconnection plasma jetting in small-scale turbulent plasmas has so far been lacking. Here we report observations made in Earth's turbulent magnetosheath region (downstream of the bow shock) of an electron-scale current sheet in which diverging bi-directional super-ion-Alfvénic electron jets, parallel electric fields and enhanced magnetic-to-particle energy conversion were detected. Contrary to the standard model of reconnection, the thin reconnecting current sheet was not embedded in a wider ion-scale current layer and no ion jets were detected. Observations of this and other similar, but unidirectional, electron jet events without signatures of ion reconnection reveal a form of reconnection that can drive turbulent energy transfer and dissipation in electron-scale current sheets without ion coupling.

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.

Fully kinetic simulations of asymmetric magnetic reconnection reveal the presence of magnetic-field-aligned beams of electrons flowing toward the topological magnetic x line. Within the ∼6d_{e} electron-diffusion region, the beams become oblique to the local magnetic field, providing a unique signature of the electron-diffusion region where the electron frozen-in law is broken. The numerical predictions are confirmed by in situ Magnetospheric Multiscale spacecraft observations during asymmetric reconnection at Earth's dayside magnetopause.

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 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.

Supported by a kinetic simulation, we derive an exclusion energy parameter E_{X} providing a lower kinetic energy bound for an electron to cross from one inflow region to the other during magnetic reconnection. As by a Maxwell demon, only high-energy electrons are permitted to cross the inner reconnection region, setting the electron distribution function observed along the low-density side separatrix during asymmetric reconnection. The analytic model accounts for the two distinct flavors of crescent-shaped electron distributions observed by spacecraft in a thin boundary layer along the low-density separatrix.

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.

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.

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., (Copyright © 2016, American Association for the Advancement of Science.)

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.

A model for incomplete reconnection in sawtooth crashes is presented. The reconnection inflow during the crash phase of sawteeth self-consistently convects the high pressure core toward the reconnection site, raising the pressure gradient there. Reconnection shuts off if the diamagnetic drift speed at the reconnection site exceeds a threshold, which may explain incomplete reconnection. The relaxation of magnetic shear after reconnection stops may explain the destabilization of ideal interchange instabilities reported previously. Proof-of-principle two-fluid simulations confirm this basic picture. Predictions of the model compare favorably to data from the Mega Ampere Spherical Tokamak. Applications to transport modeling of sawteeth are discussed. The results should apply across tokamaks, including ITER., (© 2011 American Physical Society)

Large-scale resistive Hall-magnetohydrodynamic simulations of the transition from Sweet-Parker (collisional) to Hall (collisionless) magnetic reconnection are presented; the first to separate secondary islands from collisionless effects. Three main results are described. There exists a regime with secondary islands but without collisionless effects, and the reconnection rate is faster than Sweet-Parker, but significantly slower than Hall reconnection. This implies that secondary islands do not cause the fastest reconnection rates. The onset of Hall reconnection ejects secondary islands from the vicinity of the X line, implying that energy is released more rapidly during Hall reconnection. Coronal applications are discussed.

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.

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.

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.

Gas-phase structural parameters for ferrocenecarboxaldehyde have been determined using Fourier transform microwave spectroscopy. Rotational transitions due to a-, b-, and c-type dipole moments were measured. Eighteen rotational constants were determined by fitting the measured transitions of various isotopomers using a rigid rotor Hamiltonian with centrifugal distortion constants. Least-squares fit and Kraitchman analyses have been used to determine the gas-phase structural parameters and the atomic coordinates of the molecule using the rotational constants for various isotopomers. Structural parameters determined from the least-squares fit are the Fe-C bond lengths to the cyclopentadienyl rings, r(Fe-C)=2.047(4) A, and the distance between the carbon atoms of the cyclopentadienyl rings, r(C-C)=1.430(2) A and r(C1-C1')=1.46(1) A of ring carbon and aldehyde carbon atom. Structural parameters were also obtained using density-functional theory calculations, and these were quite helpful in resolving ambiguities in the structural fit analysis, and providing some fixed parameters for the structural analysis. The results of the least squares and the calculations indicate that the carbon atoms of the Cp groups for ferrocenecarboxaldehyde are in an eclipsed conformation in the ground vibrational state.

Rotational spectra for two isotopomers of chloroferrocene were measured using pulsed-beam Fourier transform microwave spectroscopy. Transitions were observed for (35)Cl and (37)Cl isotopomers in the 4-10 GHz range. Chlorine quadrupole coupling strengths and rotational constants were obtained from the data. The rotational constants and quadrupole coupling strengths for (35)Cl are A = 1370.009(8) MHz, B = 767.342(1) MHz, C = 634.8834(6) MHz, eQq(aa)() = -9.06(4) MHz, and eQq(bb)() = -28.43(6) MHz and for (37)Cl are A = 1362.23(2) MHz, B = 751.623(2) MHz, C = 622.324(1) MHz, eQq(aa)() = -8.78(18) MHz, and eQq(bb)() = -20.76(9) MHz. These measured rotational constants were used to determine the following structural parameters of chloroferrocene: r(Fe-(C(5)H(5))) = 1.594(20) Å, r(Fe-(C(5)H(4)Cl)) = 1.699(13) Å, r(C-Cl) =1.7204(9) Å, and r(C-C) = 1.4329(7) Å. No evidence for internal rotation was observed in the microwave spectrum.