Works of D. Tsiklauri, T. Haruki, Phys. of Plasmas, 15, 102902 (2008) and D. Tsiklauri and T. Haruki, Phys. of Plasmas, 14, 112905, (2007) are extended by inclusion of the out-of-plane magnetic (guide) field. In particular, magnetic reconnection during collisionless, stressed $X$-point collapse for varying out-of-plane guide-fields is studied using a kinetic, 2.5D, fully electromagnetic, relativistic particle-in-cell numerical code. Cases for both open and closed boundary conditions are investigated, where magnetic flux and particles are lost and conserved respectively. It is found that reconnection rates and out-of-plane currents in the $X$-point increase more rapidly and peak sooner in the closed boundary case, but higher values are reached in the open boundary case. The normalized reconnection rate is fast: 0.10-0.25. In the open boundary case an increase of guide-field yields later onsets in the reconnection peak rates, while in the closed boundary case initial peak rates occur sooner but are suppressed. The reconnection current increases for low guide-fields but then decreases similarly. In the open boundary case, for guide-fields of the order of the in-plane magnetic field, the generation of electron vortices occurs. Possible causes of the vortex generation, based on the flow of particles in the diffusion region and localized plasma heating, are discussed. Before peak reconnection onset, oscillations in the out-of-plane electric field at the $X$-point are found, ranging in frequency from approximately 1 to 2 $ω_{pe}$ and coinciding with oscillatory reconnection. These oscillations are found to be part of a larger wave pattern. Mapping the out-of-plane electric field over time and applying 2D Fourier transforms reveals that the waves predominantly correspond to the ordinary mode and may correspond to observable radio waves such as solar radio burst fine structure spikes.
A new measure to identify a small-scale dissipation region in collisionless magnetic reconnection is proposed. The energy transfer from the electromagnetic field to plasmas in the electron's rest frame is formulated as a Lorentz-invariant scalar quantity. The measure is tested by two-dimensional particle-in-cell simulations in typical configurations: symmetric and asymmetric reconnection, with and without the guide field. The innermost region surrounding the reconnection site is accurately located in all cases. We further discuss implications for nonideal MHD dissipation.
The out-of-plane magnetic field, generated by fast magnetic reconnection, during collisionless, stressed $X$-point collapse, was studied with a kinetic, 2.5D, fully electromagnetic, relativistic particle-in-cell numerical code, using both closed (flux conserving) and open boundary conditions on a square grid. It was discovered that the well known quadrupolar structure in the out-of-plane magnetic field gains four additional regions of opposite magnetic polarity, emerging near the corners of the simulation box, moving towards the $X$-point. The emerging, outer, magnetic field structure has oppo…
A stationary, two-dimensional, and non-driven antiparallel magnetic field configuration consisting of a central current film, flanked by two non-magnetic domains of electron inertial scale, resembling the Josephson model. Landau-Ginsburg conditions apply at the boundaries to the oppositely directed external magnetic fields, whose sources are located at infinity. On the microscopic level sufficiently large magnetic islands and X points form from exchange of small numbers of elementary magnetic fluxes without reference to any plasma instabilities which on these scales are purely electrostatic. T…
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 two of the widely examined asymmetric reconnection model [Cassak and Shay, Phys. Plasmas 14, 102114, 2007] 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 o…
Although turbulence has been conjectured to be important for magnetic reconnection, still very little is known about its role in collisionless plasmas. Previous attempts to quantify the effect of turbulence on reconnection usually prescribed Alfvénic or other low-frequency fluctuations or investigated collisionless kinetic effects in just two-dimensional configurations and antiparallel magnetic fields. In view of this, we analyzed the kinetic turbulence self-generated by three-dimensional guide-field reconnection through force-free current sheets in frequency and wavenumber spaces, utilizing 3…
System Size Dependence of Collisionless Reconnection Rate
University of Maryland, College Park（马里兰大学帕克分校）；National Aeronautics and Space Administration Goddard Space Flight Center（美国国家航空航天局戈达德太空飞行中心）；Princeton University（普林斯顿大学）
We report a newly found two-stage mechanism of electron acceleration near X-lines of 3D collisionless guide-field magnetic reconnection in the non-relativistic regime typical, e.g., for stellar coronae. We found that after electrons are first pre-accelerated during the linear growth of reconnection, they become additionally accelerated in the course of the nonlinear stage of 3D guide-field magnetic reconnection. This additional acceleration is due to the filamentation of electric and magnetic fields caused by streaming instabilities. In addition to enhanced parallel electric fields, the filame…
Particle dynamics in the electron current layer in collisionless magnetic reconnection is investigated by using a particle-in-cell simulation. Electron motion and velocity distribution functions are studied by tracking self-consistent trajectories. New classes of electron orbits are discovered: figure-eight-shaped regular orbits inside the electron jet, noncrossing regular orbits on the jet flanks, noncrossing Speiser orbits, and nongyrotropic electrons in the downstream of the jet termination region. Properties of a super-Alfvénic outflow jet are attributed to an ensemble of electrons traveli…
During magnetically dominated relativistic reconnection, inflowing plasma depletes the initial relativistic pressure at the x-line and collisionless plasma heating inside the diffusion region is insufficient to overcome this loss. The resulting pressure drop causes a collapse at the x-line, essentially a localization mechanism of the diffusion region necessary for fast reconnection. The extension of this low-pressure region further explains the bursty nature of anti-parallel reconnection because a once opened outflow exhaust can also collapse, which repeatedly triggers secondary tearing island…
In previous simulations of collisionless 2D magnetic reconnection it was consistently found that the term in the generalised Ohm's law that breaks the frozen-in condition is the divergence of the electron pressure tensor's non-gyrotropic components. A fully relativistic particle-in-cell (PIC) code was used to model $X$-point collapse with a guide-field in two and three spatial dimensions. We show that in a 2D $X$-point collapse with a guide-field close to the strength of the in-plane field, the increased induced shear flows along the diffusion region lead to a new reconnection regime in which …
The spontaneous onset of magnetic reconnection in thin collisionless current sheets is shown to result from a thermal-anisotropy driven magnetic Weibel-mode, generating seed-magnetic field {\sf X}-points in the centre of the current layer.
It was recently proposed that the electron-frame dissipation measure, the energy transfer from the electromagnetic field to plasmas in the electron's rest frame, identifies the dissipation region of collisionless magnetic reconnection [Zenitani et al. Phys. Rev. Lett. 106, 195003 (2011)]. The measure is further applied to the electron-scale structures of antiparallel reconnection, by using two-dimensional particle-in-cell (PIC) simulations. The size of the central dissipation region is controlled by the electron-ion mass ratio, suggesting that electron physics is essential. A narrow electron j…
Simulations of collisionless oblique propagating slow shocks have revealed the existence of a transition associated with a critical temperature anisotropy epsilon=1-mu_0(P_parallel-P_perpendicular)/ B^2 = 0.25 (Liu, Drake and Swisdak (2011)). An explanation for this phenomenon is proposed here based on anisotropic fluid theory, in particular the Anisotropic Derivative Nonlinear-Schrodinger-Burgers equation, with an intuitive model of the energy closure for the downstream counter-streaming ions. The anisotropy value of 0.25 is significant because it is closely related to the degeneracy point of…
Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov-Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The…
The kinetic features of secondary magnetic reconnection in a single flux rope undergoing internal kink instability are studied by means of three-dimensional Particle-in-Cell simulations. Several signatures of secondary magnetic reconnection are identified in the plane perpendicular to the flux rope: a quadrupolar electron and ion density structure and a bipolar Hall magnetic field develop in proximity of the reconnection region. The most intense electric fields form perpendicularly to the local magnetic field, and a reconnection electric field is identified in the plane perpendicular to the fl…
Using fully kinetic simulations, we study the suppression of asymmetric reconnection in the limit where the diamagnetic drift speed >> Alfven speed and the magnetic shear angle is moderate. We demonstrate that the slippage between electrons and the magnetic flux facilitates reconnection, and can even result in fast reconnection that lacks one of the outflow jets. Through comparing a case where the diamagnetic drift is supported by the temperature gradient with a companion case that has a density gradient instead, we identify a robust suppression mechanism. The drift of the x-line is slowed dow…
Results of the first validation of large guide field, $B_g / δB_0 \gg 1$, 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 $β_i B_g / δB_0 \gtrsim 1$ and $B_g / δB_0 \gg 1$. In the regime of convergence, …
It has recently been proposed (Loureiro & Boldyrev 2017; Mallet et al. 2017) that the inertial interval in magnetohydrodynamic (MHD) turbulence is terminated at small scales not by a Kolmogorov-like dissipation region, but rather by a new sub-inertial interval mediated by tearing instability. However, many astrophysical plasmas are nearly collisionless so that the MHD approximation is not applicable to turbulence at small scales. In this Letter, we propose the extension of the theory of reconnection-mediated turbulence to plasmas which are so weakly collisional that the reconnection occurring …
Magnetic reconnection in strongly magnetized (low-beta), weakly collisional plasmas is investigated using a novel fluid-kinetic model [Zocco & Schekochihin, Phys. Plasmas 18, 102309 (2011)] which retains non-isothermal electron kinetics. It is shown that electron heating via Landau damping (linear phase mixing) is the dominant dissipation mechanism. In time, electron heating occurs after the peak of the reconnection rate; in space, it is concentrated along the separatrices of the magnetic island. For sufficiently large systems, the peak reconnection rate is $cE_{max}\approx 0.2v_AB_{y,0}$, whe…
Magnetic reconnection requires the violation of the frozen-in condition which ties gyrating charged particles to the magnetic field inhibiting diffusion. Ongoing reconnection has been identified in near-Earth space as being responsible for the excitation of substorms, magnetic storms, generation of field aligned currents and their consequences, the wealth of auroral phenomena. Its theoretical understanding is now on the verge of being completed. Reconnection takes place in thin current sheets. Analytical concepts proceeded gradually down to the microscopic scale, the scale of the electron skin…
A 2-D Riemann problem is designed to study the development and dynamics of the slow shocks that are thought to form at the boundaries of reconnection exhausts. Simulations are carried out for varying ratios of normal magnetic field to the transverse upstream magnetic field (i.e., propagation angle with respect to the upstream magnetic field). When the angle is sufficiently oblique, the simulations reveal a large firehose-sense (P_parallel>P_perpendicular) temperature anisotropy in the downstream region, accompanied by a transition from a coplanar slow shock to a non-coplanar rotational mode. I…
The first detailed comparison between gyrokinetic and gyrofluid simulations of collisionless magnetic reconnection has been carried out. Both the linear and nonlinear evolution of the collisionless tearing mode have been analyzed. In the linear regime, we have found a good agreement between the two approaches over the whole spectrum of linearly unstable wave numbers, both in the drift kinetic limit and for finite ion temperature. Nonlinearly, focusing on the small-$Δ'$ regime, with $Δ'$ indicating the standard tearing stability parameter, we have compared relevant observables such as the evolu…
Modeling collisionless magnetic reconnection rate is an outstanding challenge in basic plasma physics research. While the seemingly universal rate of an order $\mathcal{O}(0.1)$ is often reported in the low-$β$ regime, it is not clear how reconnection rate scales with a higher plasma $β$. Due to the complexity of the pressure tensor, the available reconnection rate model is limited to the low plasma-$β$ regime, where the thermal pressure is arguably negligible. However, the thermal pressure effect becomes important when $β\gtrsim \mathcal{O}(1)$. Using first-principle kinetic simulations, we s…
We calculate the disruption scale $λ_{\rm D}$ at which sheet-like structures in dynamically aligned Alfvénic turbulence are destroyed by the onset of magnetic reconnection in a low-$β$ collisionless plasma. The scaling of $λ_{\rm D}$ depends on the order of the statistics being considered, with more intense structures being disrupted at larger scales. The disruption scale for the structures that dominate the energy spectrum is $λ_{\rm D}\sim L_\perp^{1/9}(d_eρ_s)^{4/9}$, where $d_e$ is the electron inertial scale, $ρ_s$ is the ion sound scale, and $L_\perp$ is the outer scale of the turbulence…
The debate surrounding fast magnetic energy dissipation by magnetic reconnection has remained a fundamental topic in the plasma universe, not only in the Earth's magnetosphere but in astrophysical objects such as pulsar magnetospheres and magnetars, for more than half a century. Recently, nonthermal particle acceleration and plasma heating during reconnection have been extensively studied, and it has been argued that rapid energy dissipation can occur for a collisionless "thin" current sheet, the thickness of which is of the order of the particle gyro-radius. However, it is an intriguing enigm…
The concept of diffusion in collisionless space plasmas like those near the magnetopause and in the geomagnetic tail is reexamined from a fundamental statistical point of view making use of the division of particle orbits into waiting orbits and break-out into ballistic motion lying at the bottom, for instance, of Lévy flights and the celebrated $κ$-distribution. A stringent derivation yields an anomalous diffusion coefficient increasing with time, thus describing superdiffusion. Contrary to wide belief, superdiffusion, though faster than classical, is a weak process. Absolute values of the co…
J. Graf von der Pahlen and D. Tsiklauri, Phys. Plas. 21, 060705 (2014), established that the generation of octupolar out-of-plane magnetic field structure in a stressed $X$-point collapse is due to ion currents. The field has a central region, comprising of the well-known qaudrupolar field (quadrupolar components), as well as four additional poles of reversed polarity closer to the corners of the domain (octupolar components). In this extended work, the dependence of the octupolar structure on domain size and ion mass variation is investigated. Simulations show that the strength and spatial st…
The spreading of the X-line out of the reconnection plane under a strong guide field is investigated using large-scale three-dimensional (3D) particle-in-cell (PIC) simulations in asymmetric magnetic reconnection. A simulation with a thick, ion-scale equilibrium current sheet (CS) reveals that the X-line spreads at the ambient ion/electron drift speeds, significantly slower than the Alfvén speed based on the guide field $V_{Ag}$. Additional simulations with a thinner, sub-ion-scale CS show that the X-line spreads at $V_{Ag}$ (Alfvénic spreading), much higher than the ambient species drifts. An…
It is well known that collisionless systems are dissipation free from the perspective of particle collision and thus conserve entropy. On the other hand, processes such as magnetic reconnection and turbulence appear to convert large-scale magnetic energy into heat. In this paper, we investigate the energization and heating of collisionless plasma. The dissipation process is discussed in terms of fluid entropy in both isotropic and gyrotropic forms. Evolution equations for the entropy are derived and they reveal mechanisms that lead to changes in fluid entropy. These equations are verified by a…
Solar flares are accessible to a broad variety of observational methods to see and investigate the {\em magnetic reconnection} phenomenon in high-temperature strongly-magnetized plasma of the solar corona. An analysis of the topological peculiarities of magnetic field in active regions shows that the {\em topological trigger} effect is necessary to allow for in order to construct models for large eruptive flares. The topological trigger is not a resistive instability which leads to a change of the topology of the field configuration from pre- to post reconnection state. On the contrary, the to…
A minimal model for magnetic reconnection and, generally, low-frequency dynamics in low-beta plasmas is proposed. The model combines analytical and computational simplicity with physical realizability: it is a rigorous limit of gyrokinetics for plasma beta of order the electron-ion mass ratio. The model contains collisions and can be used both in the collisional and collisionless reconnection regimes. It includes gyrokinetic ions (not assumed cold) and allows for the topological rearrangement of the magnetic field lines by either resistivity or electron inertia, whichever predominates. The two…
We develop a first-principles scaling theory of the spreading of three-dimensional (3D) magnetic reconnection of finite extent in the out of plane direction. This theory addresses systems with or without an out of plane (guide) magnetic field, and with or without Hall physics. The theory reproduces known spreading speeds and directions with and without guide fields, unifying previous knowledge in a single theory. New results include: (1) Reconnection spreads in a particular direction if an x-line is induced at the interface between reconnecting and non-reconnecting regions, which is controlled…
The magnetic reconnection process is studied in relativistic pair plasmas when the thermal and inertial properties of the magnetohydrodynamical fluid are included. We find that in both Sweet-Parker and Petschek relativistic scenarios there is an increase of the reconnection rate owing to the thermal-inertial effects, both satisfying causality. To characterize the new effects we define a thermal-inertial number which is independent of the relativistic Lundquist number, implying that reconnection can be achieved even for vanishing resistivity as a result of only thermal-inertial effects. The cur…
A conceptual model of resistive magnetic reconnection via a stochastic plasmoid chain is proposed. The global reconnection rate is shown to be independent of the Lundquist number. The distribution of fluxes in the plasmoids is shown to be an inverse square law. It is argued that there is a finite probability of emergence of abnormally large plasmoids, which can disrupt the chain (and may be responsible for observable large abrupt events in solar flares and sawtooth crashes). A criterion for the transition from magnetohydrodynamic to collisionless regime is provided.
A new path for the generation of a sub-ion scale cascade in collisionless plasma turbulence, triggered by magnetic reconnection, is uncovered by means of high-resolution two-dimensional hybrid-kinetic simulations employing two complementary approaches, Lagrangian and Eulerian, and different driving mechanisms. The simulation results provide clear numerical evidences that the development of power-law energy spectra below the so-called ion break occurs as soon as the first magnetic reconnection events take place, regardless of the actual state of the turbulent cascade at MHD scales. In both simu…
Numerical simulations have consistently shown that the reconnection rate in certain collisionless regimes can be fast, on the order of $0.1 v_A B_u$, where $v_A$ and $B_u$ are the Alfvén speed and the reconnecting magnetic field upstream of the ion diffusion region. This particular value has been reported in myriad numerical simulations under disparate conditions. However, despite decades of research, the reasons underpinning this specific value remain mysterious. Here, we present an overview of this problem and discuss the conditions under which the "0.1 value" is attained. Furthermore, we ex…
A widely accepted scenario of magnetic reconnection in collisionless space plasmas is the breakage of magnetic field lines in X-points. In laboratory, reconnection is commonly studied in pinches, current channels embedded into twisted magnetic fields. No model of magnetic reconnection in space plasmas considers both null-points and pinches as peers. We have performed a particle-in-cell simulation of magnetic reconnection in a three-dimensional configuration where null-points are present initially, and Z-pinches are formed during the simulation along the lines of spiral null-points. The non-spi…
We numerically study magnetic reconnection on different spatial scales and at different heights in the weakly ionized plasma of the low solar atmosphere (around $300-800$~km above the solar surface) within a reactive 2.5 D multi-fluid plasma-neutral model. We consider a strongly magnetized plasma ($β\sim 6\% $) evolving from a force-free magnetic configuration and perturbed to initialize formation of a reconnection current sheet. On large scales, the resulting current sheets are observed to undergo a secondary 'plasmoid' instability. A series of simulations at different scales demonstrate a ca…
Hybrid-Vlasov-Maxwell simulations of magnetized plasma turbulence including non-linear electron-inertia effects in a generalized Ohm's law are presented. When fluctuation energy is injected on scales sufficiently close to ion-kinetic scales, the ions efficiently become de-magnetized and electron-scale current sheets largely dominate the distribution of the emerging current structures, in contrast to the usual picture, where a full hierarchy of structure sizes is generally observed. These current sheets are shown to be the sites of electron-only reconnection (e-rec), in which the usual electron…
We consider quasi-stationary two-dimensional magnetic reconnection in a partially ionized incompressible plasma. We find that when the plasma is weakly ionized and the collisions between the ions and the neutral particles are significant, the transition to fast collisionless reconnection due to the Hall effect in the generalized Ohm's law is expected to occur at much lower values of the Lundquist number, as compared to a fully ionized plasma case. We estimate that these conditions for fast reconnection are satisfied in molecular clouds and in protostellar disks.
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 perform a scaling analysis of 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 non-relativistic electron-proton reconnectio…
Whether turbulence induced anomalous resistivity (AR) can facilitate a fast magnetic reconnection in collisionless plasma is a subject of active debate for decades. Recent space observations suggest that the reconnection rate can be higher than the Hall-reconnection rate and turbulent dissipation is required. In this paper, using particle-in-cell simulations, we present a case study of how AR produced by Buneman instability accelerates magnetic reconnection. We first show that the AR/drag produced by Buneman instability in a thin electron current layer 1) can dissipate magnetic energy stored i…
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 first-principles theory for the reconnection rate in non-relativistic electron-io…
Detailed comparisons are reported between laboratory observations of electron-scale dissipation layers near a reconnecting X-line and direct two-dimensional full-particle simulations. Many experimental features of the electron layers, such as insensitivity to the ion mass, are reproduced by the simulations; the layer thickness, however, is about 3-5 times larger than the predictions. Consequently, the leading candidate 2D mechanism based on collisionless electron nongyrotropic pressure is insufficient to explain the observed reconnection rates. These results suggest that, in addition to the re…
Fast magnetic reconnection is defined by the topology of the magnetic field lines changing on a timescale that is approximately an order of magnitude longer than the topology-conserving ideal-evolution timescale. Fast reconnection is an intrinsic property of Faraday's law when the evolving magnetic field depends non-trivially on all three spatial coordinates and is commonly observed -- even when the effects that allow topology breaking are arbitrarily small. The associated current density need only be enhanced by a factor of approximately ten and flows in thin but broad ribbons along the magne…
Astrophysical plasmas have the remarkable ability to preserve magnetic topology, which inevitably gives rise to the accumulation of magnetic energy within stressed regions including current sheets. This stored energy is often released explosively through the process of magnetic reconnection, which produces a reconfiguration of the magnetic field, along with high-speed flows, thermal heating, and nonthermal particle acceleration. Either collisional or kinetic dissipation mechanisms are required to overcome the topological constraints, both of which have been predicted by theory and validated wi…
Recent years have been marked by substantial changes in our understanding of magnetic turbulence and magnetic reconnection, which, in its turn induced better understanding of cosmic ray diffusion and acceleration. Current models of magnetized turbulence are no more ad hoc constructions, but numerically tested theories. In this very short review we summarize topics presented in two talks given at the conference and provide a brief sketch of the vast and rapidly developing field. We discuss how turbulence decreases the efficient mean free path of the particles in the collisionless plasmas in gal…
