Magnetic reconnection releases energy explosively as field lines break and reconnect in plasmas ranging from the Earth's magnetosphere to solar eruptions and astrophysical applications. Collisionless kinetic simulations have shown that this process involves both ion and electron kinetic-scale features, with electron current layers forming nonlinearly during the onset phase and playing an important role in enabling field lines to break 1-4 . In larger two-dimensional studies, these electron current layers become highly extended, which can trigger the formation of secondary magnetic islands 5-10 , but the influence of realistic three-dimensional dynamics remains poorly understood. Here we show that, for the most common type of reconnection layer with a finite guide field, the three-dimensional evolution is dominated by the formation and interaction of helical magnetic structures known as flux ropes. In contrast to previous theories 11 , the majority of flux ropes are produced by secondary instabilities within the electron layers. New flux ropes spontaneously appear within these layers, leading to a turbulent evolution where electron physics plays a central role.Thin current layers are the preferred locations for magnetic reconnection to develop. The most common configuration in nature is guide-field geometry, where the rotation of magnetic field across the layer is less than 180 • . Present theoretical ideas of how reconnection proceeds in these configurations are deeply rooted in early analytical work 11 that, if correct, would imply a direct transition to three-dimensional (3D) turbulence due to a broad spectrum of interacting tearing instabilities. At the core of this idea is the notion that a spectrum of tearing instabilities develops across the initial current sheet for perturbations satisfying the local resonance condition. As these modes grow, the resulting magnetic islands would overlap, leading to stochastic magnetic-field lines and a turbulent evolution. Recently, this type of scenario was proposed as a mechanism for accelerating energetic particles during reconnection 12 . Similar ideas for generating turbulence have been studied in fusion plasmas 13 using resistive magnetohydrodynamics (MHD) and two-fluid 14 models. Alternatively, other researchers have imposed turbulent fluctuations within MHD models in an attempt to understand the consequences 15 . In either case, these results are not applicable to the highly collisionless environment of the magnetosphere, where reconnection is initiated within kinetic ion-scale current layers. The ability to study the self-consistent generation of turbulence during magnetic reconnection with first-principles 3D simulations has only become feasible in the past year.1 Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA, 2 University of California San Diego, La Jolla, California 92093, USA. *e-mail: daughton@lanl.gov. tearing instability gives rise to flux ropes as illustrated by an isosurface of the particle density coloured by the magnitude of the curr...

The electron diffusion region during magnetic reconnection lies in different regimes depending on the pressure anisotropy, which is regulated by the properties of thermal electron orbits. In kinetic simulations at the weakest guide fields, pitch angle mixing in velocity space causes the outflow electron pressure to become nearly isotropic. Above a threshold guide field that depends on a range of parameters, including the normalized electron pressure and the ion-to-electron mass ratio, electron pressure anisotropy develops in the exhaust and supports extended current layers. This new regime with electron current sheets extending to the system size is also reproduced by fluid simulations with an anisotropic closure for the electron pressure. It offers an explanation for recent spacecraft observations.

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Results of the first validation of large guide field, B g /δB 0 1, gyrokinetic simulations of magnetic reconnection at a fusion and solar corona relevant β i = 0.01 and solar wind relevant β i = 1 are presented, where δB 0 is the reconnecting field. Particle-in-cell (PIC) simulations scan a wide range of guide magnetic field strength to test for convergence to the gyrokinetic limit. The gyrokinetic simulations display a high degree of morphological symmetry, to which the PIC simulations converge when β i B g /δB 0 1 and B g /δB 0 1. In the regime of convergence, the reconnection rate, relative energy conversion, and overall magnitudes are found to match well between the PIC and gyrokinetic simulations, implying that gyrokinetics is capable of making accurate predictions well outside its regime of formal applicability. These results imply that in the large guide field limit many quantities resulting from the nonlinear evolution of reconnection scale linearly with the guide field.

We have developed the linear theory of collisionless ion tearing in a two‐dimensional magnetotail equilibrium for a single resonant species. We have solved the normal mode problem for tearing instability by an algorithm that employs particle‐in‐cell simulation to calculate the orbit integrals in the Maxwell‐Vlasov eigenmode equation. The results of our single‐species tearing analysis can be applied to ion tearing where electron effects are not included. We have calculated the tearing growth rate as a function of the magnetic field component Bn normal to the current sheet for thick and thin current sheets, and we show that marginal stability occurs when the normal gyrofrequency Ωn is comparable to the Harris neutral sheet growth rate. A cross‐tail By component has little effect on the growth rate for By ≃ Bn. Even in the limit By ≫ Bn, the mode is strongly stabilized by Bn. We report that random pitch angle scattering can overcome the stabilizing effect of Bn and drive the growth rate up toward the Harris neutral sheet (Bn = 0) value when the pitch angle diffusion rate is comparable to Ωn.

[1] This paper is the first in a series of three with the aim of addressing one of the controversial issues at the magnetopause, namely the location where reconnection first occurs during periods of a large interplanetary magnetic field B y . In this first paper, the linear properties of the collisionless tearing mode are reexamined as a function of the guide field B y using a formally exact approach for computing the nonlocal Vlasov stability of a current layer. Three distinct parameter regimes are identified depending on the degree to which electron orbits are modified by the guide field in the central region of the current layer. In the limit of both weak and strong guide field, the fastest-growing tearing mode has a wave vector k x perpendicular to the direction of the current, in agreement with previous theoretical treatments. However, for intermediate values of the guide field where the electrons begin to transition to magnetized orbits, the fastest-growing modes have a finite wave vector k y in the direction of the current. In this newly discovered regime, the so-called drift tearing modes have finite real frequency and propagate in the direction of the electron diamagnetic drift with growth rates 10-50% larger than the conventional tearing instability. Maximum growth occurs for a propagation angle in the range q = tan À1 (k y /k x ) % 6-10°. These new predictions are confirmed using fully kinetic particle-in-cell simulations. The structure of the out-of-plane magnetic field perturbation predicted by nonlocal Vlasov theory is examined as a function of guide field. In the limit of a neutral sheet, the quadrupole structure has a characteristic scale near the electron meandering width and shows significant differences with the predictions of linear Hall MHD. The addition of a guide field strongly distorts the quadrupole structure and compresses the spatial extent. In the strong guide field limit, the width of the out-of-plane magnetic field perturbation is reduced to the electron gyroscale in the guide field. During the onset phase, these structures represent a distinct signature of the collisionless tearing mode that is significantly different than the typical ion-scale quadrupole pattern from fast reconnection. Finally, we note that the tearing mode maintains a significant growth rate over a large range of guide field so that component merging cannot be ruled out based on linear theory.

We present the first hybrid simulations with kinetic ions and recently developed equations of state for the electron fluid appropriate for reconnection with a guide field. The equations of state account for the main anisotropy of the electron pressure tensor. Magnetic reconnection is studied in two systems, an initially force-free current sheet and a Harris sheet. The hybrid model with the equations of state is compared to two other models, hybrid simulations with isothermal electrons and fully kinetic simulations. Including the anisotropic equations of state in the hybrid model provides a better match to the fully kinetic model. In agreement with fully kinetic results, the main feature captured is the formation of an electron current sheet that extends several ion inertial lengths. This electron current sheet modifies the Hall magnetic field structure near the X-line, and it is not observed in the standard hybrid model with isotropic electrons. The saturated reconnection rate in this regime nevertheless remains similar in all three models. Implications for global modeling are discussed.

This paper outlines the rather narrow conditions on a radiatively decoupled plasma where a Maxwell-Boltzmann (MB) distribution can be assumed with confidence. The complementary non-thermal distribution with nonperturbative kurtosis is argued to have a much broader purview than has previously been accepted. These conditions are expressed in terms of the electron Knudsen number, K e , the ratio of the electron mean free path to the scale length of electron pressure. Rather generally, f (v < v 2 (K e)) will be Gaussian, so that MB atomic or wave particle effects controlled by speeds v < v 2 ≡ w(15/8K e) 1/4 will remain defensible, where w is the most probable speed. The sufficient condition for Spitzer-Braginskii plasma fluid closure at the energy equation requires globally K e (s) 0.01; this global condition pertains to the maximum value of K e along the arc length s of the magnetic field (to its extremities) provided that contiguous plasma remains uncoupled from the radiation field. The non-thermal regime K e > 0.01 is common in all main-sequence stellar atmospheres above approximately 0.05 stellar radii from the surface. The entire solar corona and wind are included in this regime where non-thermal distributions with kurtosis are shown to be ubiquitous, heat flux is not well modeled by Spitzer-Braginskii closure, and fluid modeling is qualitative at best.