Kinetic simulations of magnetic reconnection typically employ periodic boundary conditions that limit the duration in which the results are physically meaningful. To address this issue, a new model is proposed that is open with respect to particles, magnetic flux and electromagnetic radiation. The model is used to examine undriven reconnection in a neutral sheet initialized with a single x-point. While at early times the results are in excellent agreement with previous periodic studies, the evolution over longer intervals is entirely different. In particular, the length of the electron diffusion region is observed to increase with time resulting in the formation of an extended electron current sheet. As a consequence, the electron diffusion region forms a bottleneck and the reconnection rate is substantially reduced. Periodically, the electron layer becomes unstable and produces a secondary island, breaking the diffusion region into two shorter segments. After growing for some period, the island is ejected and the diffusion region again expands until a new island is formed. Fast reconnection may still be possible provided that the generation of secondary islands remains sufficiently robust. These results indicate that reconnection in a neutral sheet may be inherently unsteady and raise serious questions regarding the standard model of Hall mediated reconnection.

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...

Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density σ ≡ B 2 /(4πnmec 2 ) > 1 and when the system size is sufficiently large. In the limit σ 1, the spectral index approaches p = 1 and most of the available energy is converted into non-thermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection.PACS numbers: 52.27. Ny, 52.35.Vd, 98.54.Cm, 98.70.Rz Introduction -Magnetic reconnection is a fundamental plasma process that allows rapid changes of magnetic field topology and the conversion of magnetic energy into plasma kinetic energy. It has been extensively discussed in solar flares, Earth's magnetosphere, and laboratory applications. However, magnetic reconnection remains poorly understood in high-energy astrophysical systems [1]. Magnetic reconnection has been suggested as a mechanism for producing high-energy emissions from pulsar wind nebula, gamma-ray bursts, and jets from active galactic nuclei [2][3][4][5][6]. In those systems, it is often expected that the magnetization parameter σ ≡ B 2 /(4πnmc 2 ) exceeds unity. Most previous kinetic studies focused on the non-relativistic regime σ < 1 and reported several acceleration mechanisms such as acceleration at X-line regions [7][8][9] and Fermi-type acceleration within magnetic islands [8][9][10][11]. More recently, the regime σ = 1-100 has been explored using pressure-balanced current sheets and strong particle acceleration has been found in both diffusion regions [12][13][14][15] and island regions [16,17]. However, this initial condition requires a hot plasma component inside the current sheet to maintain force balance, which may not be justified for high-σ plasmas.

Magnetic reconnection is thought to be the driver for many explosive phenomena in the universe. The energy release and particle acceleration during reconnection have been proposed as a mechanism for producing high-energy emissions and cosmic rays. We carry out two-and three-dimensional kinetic simulations to investigate relativistic magnetic reconnection and the associated particle acceleration. The simulations focus on electron-positron plasmas starting with a magnetically dominated, force-free current sheet (σ ≡ B 2 /(4πn e m e c 2 ) 1). For this limit, we demonstrate that relativistic reconnection is highly efficient at accelerating particles through a first-order Fermi process accomplished by the curvature drift of particles along the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra f ∝ (γ − 1) −p and approaches p = 1 for sufficiently large σ and system size. Eventually most of the available magnetic free energy is converted into nonthermal particle kinetic energy. An analytic model is presented to explain the key results and predict a general condition for the formation of power-law distributions. The development of reconnection in these regimes leads to relativistic inflow and outflow speeds and enhanced reconnection rates relative to non-relativistic regimes. In the three-dimensional simulation, the interplay between secondary kink and tearing instabilities leads to strong magnetic turbulence, but does not significantly change the energy conversion, reconnection rate, or particle acceleration. This study suggests that relativistic reconnection sites are strong sources of nonthermal particles, which may have important implications to a variety of high-energy astrophysical problems.

[1] Kinetic simulations of magnetic reconnection indicate that the electron diffusion region (EDR) can elongate into a highly stretched current layer with a width on the electron scale and a length that exceeds tens of ion inertial lengths. The resulting structure has no fluid analogue and consists of two regions in the exhaust direction. The inner region is characterized by the locale where electrons reach a peak outflow speed near the electron Alfvén velocity. Ions also approach $80% of their peak velocity in this inner region but remain sub-Alfvénic. There exists a large electrostatic potential that can temporarily trap electrons within this inner region. The electron frozen-in condition is violated over a wider outer region characterized by highly collimated electron jets that are gradually decelerated and thermalized. Reconnection proceeds continuously but the rate is modulated in time as the EDR elongates into an extended layer. The elongation of the EDR is controlled by the competition between the outward convection of magnetic flux and the non-ideal term involving the divergence of the electron pressure tensor. The occasional balance between these two terms leads to periods of quasi-steady reconnection. However, over longer time scales, a natural feature of the reconnection process appears to be frequent formation of plasmoids due to the instability of the elongated EDR which leads to larger variations in the reconnection rate. These new findings provide testable predictions and indicate the need to reconsider the diagnostics for identification of the diffusion region and interpretation of observational data.

The linear and nonlinear properties of the lower-hybrid drift instability are examined in a thin current sheet with thickness comparable to a thermal ion gyroradius ρi∼L. The linear Vlasov stability is calculated using a formally exact technique in which the orbit integrals are treated numerically and the eigenvalue problem for the resulting system of integrodifferential equations is solved using a finite element representation of the eigenfunction. For the fastest growing lower-hybrid modes with wavelength on the electron gyroscale (kyρe∼1), the resulting mode structure is localized on the edge of the current sheet. However, for modes with wavelengths intermediate between the electron and ion gyroscale kyρiρe∼1, the lower-hybrid instability has a significant electromagnetic component to the mode structure which is localized in the central region of the sheet. The addition of a weak guide field complicates the mode structure and gives rise to fluctuations in all three components of the magnetic field. These new predictions from linear Vlasov theory are confirmed using fully kinetic particle-in-cell simulations which indicate the modes saturate at large amplitude in the central region of the sheet. These results suggest the possibility that the electromagnetic fluctuations may potentially influence the development of magnetic reconnection.

An unsolved problem in plasma turbulence is how energy is dissipated at small scales. Particle collisions are too infrequent in hot plasmas to provide the necessary dissipation. Simulations either treat the fluid scales and impose an ad hoc form of dissipation (e.g., resistivity) or consider dissipation arising from resonant damping of small amplitude disturbances where damping rates are found to be comparable to that predicted from linear theory. Here, we report kinetic simulations that span the macroscopic fluid scales down to the motion of electrons. We find that turbulent cascade leads to generation of coherent structures in the form of current sheets that steepen to electron scales, triggering strong localized heating of the plasma. The dominant heating mechanism is due to parallel electric fields associated with the current sheets, leading to anisotropic electron and ion distributions which can be measured with NASA's upcoming Magnetospheric Multiscale mission. The motion of coherent structures also generates waves that are emitted into the ambient plasma in form of highly oblique compressional and shear Alfven modes. In 3D, modes propagating at other angles can also be generated. This indicates that intermittent plasma turbulence will in general consist of both coherent structures and waves. However, the current sheet heating is found to be locally several orders of magnitude more efficient than wave damping and is sufficient to explain the observed heating rates in the solar wind.

Global hybrid (electron fluid, kinetic ions) and fully kinetic simulations of the magnetosphere have been used to show surprising interconnection between shocks, turbulence, and magnetic reconnection. In particular, collisionless shocks with their reflected ions that can get upstream before retransmission can generate previously unforeseen phenomena in the post shocked flows: (i) formation of reconnecting current sheets and magnetic islands with sizes up to tens of ion inertial length. (ii) Generation of large scale low frequency electromagnetic waves that are compressed and amplified as they cross the shock. These "wavefronts" maintain their integrity for tens of ion cyclotron times but eventually disrupt and dissipate their energy. (iii) Rippling of the shock front, which can in turn lead to formation of fast collimated jets extending to hundreds of ion inertial lengths downstream of the shock. The jets, which have high dynamical pressure, "stir" the downstream region, creating large scale disturbances such as vortices, sunward flows, and can trigger flux ropes along the magnetopause. This phenomenology closes the loop between shocks, turbulence, and magnetic reconnection in ways previously unrealized. These interconnections appear generic for the collisionless plasmas typical of space and are expected even at planar shocks, although they will also occur at curved shocks as occur at planets or around ejecta. V C 2014 AIP Publishing LLC. [http://dx.