Fast reconnection operating in magnetically dominated plasmas is often invoked in models for magnetar giant flares, for magnetic dissipation in pulsar winds, or to explain the gamma-ray flares observed in the Crab nebula, hence its investigation is of paramount importance in high-energy astrophysics. Here we study, by means of two dimensional numerical simulations, the linear phase and the subsequent nonlinear evolution of the tearing instability within the framework of relativistic resistive magnetohydrodynamics, as appropriate in situations where the Alfven velocity approaches the speed of light. It is found that the linear phase of the instability closely matches the analysis in classical MHD, where the growth rate scales with the Lundquist number S as S^-1/2, with the only exception of an enhanced inertial term due to the thermal and magnetic energy contributions. In addition, when thin current sheets of inverse aspect ratio scaling as S^-1/3 are considered, the so-called "ideal" tearing regime is retrieved, with modes growing independently on S and extremely fast, on only a few light crossing times of the sheet length. The overall growth of fluctuations is seen to solely depend on the value of the background Alfven velocity. In the fully nonlinear stage we observe an inverse cascade towards the fundamental mode, with Petschek-type supersonic jets propagating at the external Alfven speed from the X-point, and a fast reconnection rate at the predicted value R~(ln S)^-1.
We study the magneto-hydrodynamic tearing instability occurring in a double current sheet configuration when a guide field is present. This is investigated by means of resistive relativistic magneto-hydrodynamic (RRMHD) simulations. Following the dynamics of the double tearing mode (DTM), we are able to compute synthetic synchrotron spectra in the explosive reconnection phase. The pulsar striped wind model represents a site where such current sheets are formed, including a guide field. The variability of the Crab nebula/pulsar system, seen as flares, can be therefore naturally explained by the…
Over the last few years it became clear that turbulent magnetic reconnection and magnetized turbulence are inseparable. It was not only shown that reconnection is responsible for violating the frozen-in condition in turbulence, but also that stochastic reconnection in 3D generates turbulence by itself. The actual mechanism responsible for this driving is still unknown. Processes such tearing mode or Kelvin-Helmholtz, among other plasma instabilities, could generate turbulence from irregular current sheets. We address the nature of driving mechanism for this process and consider a relative role…
Magnetic reconnection associated to the double tearing mode (DTM) is investigated by means of resistive relativistic magnetohydrodynamic (RRMHD) simulations. A linearly unstable double current sheet system in two dimensional cartesian geometry is considered. For initial perturbations of large enough longitudinal wavelengths, a fast reconnection event is triggered by a secondary instability that is structurally driven by the nonlinear evolution of the magnetic islands. The latter reconnection phase and time scale appear to weakly depend on the plasma resistivity and magnetization parameter. We …
Magnetic reconnection is believed to be the driver of many explosive phenomena in Astrophysics, from solar to gamma-ray flares in magnetars and in the Crab nebula. However, reconnection rates from classic MHD models are far too slow to explain such observations. Recently, it was realized that when a current sheet gets sufficiently thin, the reconnection rate of the tearing instability becomes "ideal", in the sense that the current sheet destabilizes on the "macroscopic" Alfvénic timescales, regardless of the Lundquist number of the plasma. Here we present 2D compressible MHD simulations in the…
The recent realization that Sweet-Parker current sheets are violently unstable to the secondary tearing (plasmoid) instability implies that such current sheets cannot occur in real systems. This suggests that, in order to understand the onset of magnetic reconnection, one needs to consider the growth of the tearing instability in a current layer as it is being formed. Such an analysis is performed here in the context of nonlinear resistive MHD for a generic time-dependent equilibrium representing a gradually forming current sheet. It is shown that two onset regimes, single-island and multi-isl…
We present large scale 3D particle-in-cell (PIC) simulations to examine particle energization in magnetic reconnection of relativistic electron-positron (pair) plasmas. The initial configuration is set up as a relativistic Harris equilibrium without a guide field. These simulations are large enough to accommodate a sufficient number of tearing and kink modes. Contrary to the non-relativistic limit, the linear tearing instability is faster than the linear kink instability, at least in our specific parameters. We find that the magnetic energy dissipation is first facilitated by the tearing insta…
Guide-Field-mediated Multiscale Instabilities in Relativistic Reconnection
KU Leuven（荷语鲁汶大学）；Royal Belgian Institute for Space Aeronomy（比利时皇家空间气科学研究院）；Dartmouth College（达特茅斯学院）；University of Maryland（马里兰大学）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）
The stability of current sheets in collisionless relativistic pair plasma was studied via two-dimensional two-fluid relativistic magnetohydrodynamic simulations with vanishing internal friction between fluids. In particular, we investigated the linear growth of the tearing and drift-kink modes in the current sheets both with and without the guide field and obtained the growth rates which are very similar to what has been found in the corresponding PIC simulations. This suggests that the two-fluid simulations can be useful in studying the large-scale dynamics of astrophysical relativistic plasm…
Revisiting the Growth Rate of the Relativistic Tearing Instability: The Role of the Non-ideal MHD Structure
SIT Research Laboratories, Shibaura Institute of Technology（芝浦工业大学 SIT 研究实验室）；Yukawa Institute for Theoretical Physics (YITP), Kyoto University（京都大学汤川理论物理研究所（YITP））；Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
We present 2D MHD numerical simulations of tearing-unstable current sheets coupled to a population of non-thermal test-particles, in order to address the problem of numerical convergence with respect to grid resolution, numerical method and physical resistivity. Numerical simulations are performed with the PLUTO code for astrophysical fluid dynamics through different combinations of Riemann solvers, reconstruction methods, grid resolutions at various Lundquist numbers. The constrained transport method is employed to control the divergence-free condition of magnetic field. Our results indicate …
In a magnetized, collisionless plasma, the magnetic moment of the constituent particles is an adiabatic invariant. An increase in the magnetic-field strength in such a plasma thus leads to an increase in the thermal pressure perpendicular to the field lines. Above a $β$-dependent threshold (where $β$ is the ratio of thermal to magnetic pressure), this pressure anisotropy drives the mirror instability, producing strong distortions in the field lines on ion-Larmor scales. The impact of this instability on magnetic reconnection is investigated using a simple analytical model for the formation of …
Current-driven reconnection is investigated as a possible mechanism for angular momentum transport in astrophysical disks. A theoretical and computational study of angular momentum transport from current-driven magnetohydrodynamic instabilities is performed. It is found that both a single resistive tearing instability and an ideal instability can transport momentum in the presence of azimuthal Keplerian flow. The structure of the Maxwell stress is examined for a single mode through analytic quasilinear theory and computation. Full nonlinear multiple mode computation shows that a global Maxwell…
2D or not 2D? Exploring 3D relativistic magnetic reconnection dynamics with highly accurate numerical simulations
University of Toronto（多伦多大学）；Columbia University（哥伦比亚大学）；Università degli Studi di Torino（都灵大学）；Institut d’Astrophysique de Paris, UMR 7095, CNRS & Sorbonne Université（巴黎天体物理研究所，UMR 7095，法国国家科学研究中心与索邦大学）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学，巴黎西岱大学，法国原子能和替代能源委员会，法国国家科学研究中心，AIM）；INFN - sezione di Torino（意大利国家核物理研究所都灵分部）；Max-Planck-Institut für Astronomie（马克斯·普朗克天文学研究所）；Università degli Studi di Firenze（佛罗伦萨大学）；INAF - Osservatorio Astrofisico di Arcetri（意大利国家天体物理研究所阿切尔奇天文台）
Basic properties of relativistic magnetic reconnection in electron-positron pair plasmas are investigated by using a particle-in-cell (PIC) simulation. We first revisit a problem by Hesse & Zenitani (2007), who examined the kinetic Ohm's law across the X line. We formulate a relativistic Ohm's law by decomposing the stress-energy tensor. Then, the role of the new term, called the heat-flow inertial term, is examined in the PIC simulation data. We further evaluate the energy balance in the reconnection system. These analyses demonstrate physically transparent ways to diagnose relativistic kinet…
We study the time-dependent formation and evolution of a current sheet (CS) in a magnetized, collisionless, high-beta plasma using hybrid-kinetic particle-in-cell simulations. An initially tearing-stable Harris sheet is frozen into a persistently driven incompressible flow so that its characteristic thickness gradually decreases in time. As the CS thins, the strength of the reconnecting field increases, and adiabatic invariance in the inflowing fluid elements produces a field-biased pressure anisotropy with excess perpendicular pressure. At large plasma beta, this anisotropy excites the mirror…
A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid pha…
3D Kinetic Simulations of Driven Reconnection in Merging Flux Tubes
University of Maryland（马里兰大学）；Canadian Institute for Theoretical Astrophysics（加拿大理论天体物理研究所）；KU Leuven（荷语鲁汶大学）；Royal Belgian Institute for Space Aeronomy（比利时皇家空间气动力学研究所）；Columbia University（哥伦比亚大学）；Flatiron Institute（平顿研究所）
We performed numerical simulations of general relativistic magnetohydrodynamics with uniform resistivity to investigatethe occurrence of magnetic reconnection in a split-monopole magnetic field around a Schwarzschild black hole. We found that magnetic reconnection happens near the black hole at its equatorial plane. The magnetic reconnection has a point-like reconnection region and slow shock waves, as in the Petschek reconnection model. The magnetic reconnection rate decreases as the resistivity becomes smaller. When the global magnetic Reynolds number is $10^4$ or larger, the magnetic reconn…
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…
Magnetic reconnection is a process of magnetic field topology change, which is one of the most fundamental processes in magnetized plasmas. In most astrophysical environments the Reynolds numbers are large and therefore the transition to turbulence is inevitable. This turbulence must be taken into account for any theory of magnetic reconnection, since the initially laminar configurations can transit to the turbulence state, what is demonstrated by 3D high resolution numerical simulations. We discuss ideas of how turbulence can modify reconnection with the focus on the Lazarian & Vishniac (1999…
We demonstrate the dragging of the magnetic field by the super-Alfvenic shear flows out of the reconnection plane can strongly localize the reconnection x-line in collisionless plasmas, reversing the current direction at the x-line. Reconnection with this new morphology, which is impossible in resistive-magnetohydrodynamic (MHD), is enabled by electron inertia. Surprisingly, the quasi-steady reconnection rate remains of order 0.1 even though the aspect ratio of the local x-line geometry is larger than unity. We explain this by examining the transport of the reconnected magnetic flux and the op…
Magnetic reconnection is a fundamental process of magnetic field topology change. We analyze the connection of this process with turbulence which is ubiquitous in astrophysical environments. We show how Lazarian & Vishniac (1999) model of turbulent reconnection is connected to the experimentally proven concept of Richardson diffusion and discuss how turbulence violates the generally accepted notion of magnetic flux freezing. We note that in environments that are laminar initially turbulence can develop as a result of magnetic reconnection and this can result in flares of magnetic reconnection …
We investigate guide-field magnetic reconnection and particle acceleration in relativistic pair plasmas with three-dimensional particle-in-cell (PIC) simulations of a kinetic-scale current sheet in a periodic geometry at low magnetizations. The tearing instability is the dominant mode in the current sheet for all guide field strengths, while the linear kink mode is less important even without guide field. Oblique modes seem to be suppressed entirely. In its nonlinear evolution, the reconnection layer develops a network of interconnected and interacting magnetic flux ropes. As smaller flux rope…
We study a resistive tearing instability developing in a system evolving through the combined effect of Hall drift in the Electron-MHD limit and Ohmic dissipation. We explore first the exponential growth of the instability in the linear case and we find the fastest growing mode, the corresponding eigenvalues and dispersion relation. The instability growth rate scales as $γ\propto B^{2/3} σ^{-1/3}$ where $B$ is the magnetic field and $σ$ the electrical conductivity. We confirm the development of the tearing resistive instability in the fully non-linear case, in a plane parallel configuration wh…
Classical MHD reconnection theories, both the stationary Sweet-Parker model and the tearing instability, are known to provide rates which are too slow to explain the observations. However, a recent analysis has shown that there exists a critical threshold on current sheet's thickness, namely a/L~S^(-1/3), beyond which the tearing modes evolve on fast macroscopic Alfvenic timescales, provided the Lunquist number S is high enough, as invariably found in solar and astrophysical plasmas. Therefore, the classical Sweet-Parker scenario, for which the diffusive region scales as a/L~S^(-1/2) and thus …
Magnetic reconnection, a plasma process converting magnetic energy to particle kinetic energy, is often invoked to explain magnetic energy releases powering high-energy flares in astrophysical sources including pulsar wind nebulae and black hole jets. Reconnection is usually seen as the (essentially 2D) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in 3D, we conduct a comprehensive particle-in-cell simulation study comparing 2D and 3D evolution of long, thin current sheets in moderately-magnetized, collisionless, relativistica…
Magnetic energy around compact objects often dominates over plasma rest mass, and its dissipation can power the object luminosity. We describe a dissipation mechanism which works faster than magnetic reconnection. The mechanism involves two strong Alfvén waves with anti-aligned magnetic fields $\boldsymbol{B}_1$ and $\boldsymbol{B}_2$ that propagate in opposite directions along background magnetic field $\boldsymbol{B}_0$ and collide. The collision forms a thin current sheet perpendicular to $\boldsymbol{B}_0$, which absorbs the incoming waves. The current sheet is sustained by electric field …
Magnetic reconnection associated with the tearing instability occurring in double-current sheet systems is investigated within the framework of reduced resistive magnetohydrodynamics (MHD) in a two-dimensional Cartesian geometry. The explosive non linear phase is particularly explored using the adaptive finite-element FINMHD code. The critical aspect ratio, that is defined as the minimum $L/x_s$ ratio (with $L$ and $x_s$ being the periodic system length and half-distance between the two current layers respectively) necessary for non linear destabilization after the linear and early non linear …
Magnetic reconnection, topological change in magnetic fields, is a fundamental process in magnetized plasmas. It is associated with energy release in regions of magnetic field annihilation, but this is only one facet of this process. Astrophysical flows normally have very large Reynolds numbers and are expected to be turbulent, in agreement with observations. In strong turbulence magnetic lines constantly reconnect everywhere at all scales, making magnetic reconnection an intrinsic part of turbulent cascade. We note that this is inconsistent with the usual practice of regarding magnetic lines …
In the context of particle acceleration in high-energy astrophysical environments featuring magnetic reconnection, the importance of the resistive term of the electric field compared to the convective one is still under debate. In this work, we present a quantitative analysis through 2D magnetohydrodynamic numerical simulations of tearing-unstable current sheets coupled to a test-particles approach, performed with the PLUTO code. We find that the resistive field plays a significant role in the early-stage energization of high-energy particles. Indeed, these particles are firstly accelerated du…
Magnetic reconnection and non-thermal particle distributions associated with current-driven instabilities are investigated by means of resistive magnetohydrodynamics (MHD) simulations combined with relativistic test particle methods. We propose a system with two parallel, repelling current channels in an initially force-free equilibrium, as a simplified representation of flux ropes in a stellar magnetosphere. The current channels undergo a rotation and separation on Alfvénic timescales, forming secondary islands and (up to tearing unstable) current sheets in which non-thermal energy distributi…
Magnetic reconnection is a plasma phenomenon where a topological rearrangement of magnetic field lines with opposite polarity results in dissipation of magnetic energy into heat, kinetic energy and particle acceleration. Such a phenomenon is considered as an efficient mechanism for energy release in laboratory and astrophysical plasmas. An important question is how to make the process fast enough to account for observed explosive energy releases. The classical model for steady state magnetic reconnection predicts reconnection times scaling as $S^{1/2}$ (where $S$ is the Lundquist number) and y…
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 ($σ\equiv B^2/(4πn_e m_e c^2) \gg 1$). For this limit, we demonstrate that relativis…
Local magnetic reversals are an inseparable part of magnetohydrodynamic (MHD) turbulence whose collective outcome on an arbitrary scale in the inertial range may lead to a global stochastic reconnection event with a rate independent of small scale physics. We show that this picture is intimately related to the nanoflare theory of the solar corona. First, we argue that due to stochastic flux freezing, a generalized version of flux freezing in turbulence, the magnetic field follows the turbulent flow in a statistical sense. Bending and stretching an initially smooth field, therefore, the turbule…
Magnetic reconnection is a fundamental physical process in various astrophysical, space, and laboratory environments. Many pieces of evidence for magnetic reconnection have been uncovered. However, its specific processes that could be fragmented and turbulent have been short of direct observational evidence. Here, we present observations of a super-hot current sheet during SOL2017-09-10T X8.2-class solar flare that display the fragmented and turbulent nature of magnetic reconnection. As bilateral plasmas converge toward the current sheet, significant plasma heating and non-thermal motions are …
Blazar emission models based on magnetic reconnection succeed in reproducing many observed spectral and temporal features, including the short-duration luminous flaring events. Plasmoids, a self-consistent by-product of the tearing instability in the reconnection layer, can be the main source of blazar emission. Kinetic simulations of relativistic reconnection have demonstrated that plasmoids are characterized by rough energy equipartition between their radiating particles and magnetic fields. This is the main reason behind the apparent shortcoming of plasmoid-dominated emission models to expl…
Collisionless magnetic reconnection is a prime candidate to account for flare-like or steady emission, outflow launching, or plasma heating, in a variety of high-energy astrophysical objects, including ones with relativistic ion-electron plasmas. But the fate of the initial magnetic energy in a reconnection event remains poorly known: what is the amount given to kinetic energy, the ion/electron repartition, and the hardness of the particle distributions? We explore these questions with 2D particle-in-cell simulations of ion-electron plasmas. We find that 45 to 75% of the total initial magnetic…
We apply the general relativistic resistive magnetohydrodynamics code {\tt BHAC} to perform a 2D study of the formation and evolution of a reconnection layer in between two merging magnetic flux tubes in Minkowski spacetime. Small-scale effects in the regime of low resistivity most relevant for dilute astrophysical plasmas are resolved with very high accuracy due to the extreme resolutions obtained with adaptive mesh refinement. Numerical convergence in the highly nonlinear plasmoid-dominated regime is confirmed for a sweep of resolutions. We employ both uniform resistivity and non-uniform res…
Axisymmetric current-carrying plasmoids are formed in the presence of nonaxisymmetric fluctuations during nonlinear three-dimensional resistive MHD simulations in a global toroidal geometry. We utilize the helicity injection technique to form an initial poloidal flux in the presence of a toroidal guide field. As helicity is injected, two types of current sheets are formed from 1) the oppositely directed field lines in the injector region (primary reconnecting current sheet), and 2) the poloidal flux compression near the plasma edge (edge current sheet). We first find that nonaxisymmetic fluctu…
In this paper, we investigate the evolution of the plasmoid-chain in a Poynting-dominated plasma. We model the relativistic current sheet with cold background plasma using the relativistic resistive magnetohydrodynamic approximation, and solve its temporal evolution numerically. We perform various calculations using different magnetization parameters of the background plasma and different Lundquist numbers. Numerical results show that the initially induced plasmoid triggers a secondary tearing instability, which gradually fills the current sheet with plasmoids, as has also been observed in the…
The scaling of plasmoid instability maximum linear growth rate with respect to Lundquist number $S$ in a Sweet-Parker current sheet, $γ_{max}\sim S^{1/4}$, indicates that at high $S$, the current sheet will break apart before it approaches the Sweet-Parker width. Therefore, a proper description for the onset of the plasmoid instability must incorporate the evolving process of the current sheet. We carry out a series of two-dimensional simulations and develop diagnostics to separate fluctuations from an evolving background. It is found that the fluctuation amplitude starts to grow only when the…
