Magnetic reconnection in laboratory, space and astrophysical plasmas is often invoked to explain explosive energy release and particle acceleration. However, the timescales involved in classical models within the macroscopic MHD regime are far too slow to match the observations. Here we revisit the tearing instability by performing visco-resistive two-dimensional numerical simulations of the evolution of thin current sheets, for a variety of initial configurations and of values of the Lunquist number $S$, up to $10^7$. Results confirm that when the critical aspect ratio of $S^{1/3}$ is reached in the reconnecting current sheets, the instability proceeds on ideal (Alfvénic) macroscopic timescales, as required to explain observations. Moreover, the same scaling is seen to apply also to the local, secondary reconnection events triggered during the nonlinear phase of the tearing instability, thus accelerating the cascading process to increasingly smaller spatial and temporal scales. The process appears to be robust, as the predicted scaling is measured both in inviscid simulations and when using a Prandtl number $P=1$ in the viscous regime.
We study the effects of the Hall electric field on magnetic island coalescence in the large island limit and find evidence for both a elongated electron current sheet layer with a Sweet-Parker-like reconnection rate and a collapsed, Petschek-like electron sheet with a peak reconnection rate approaching the 0.1 vA B0 Hall MHD rate. The state observed in our simulations appears to depend on grid scale. Furthermore, even at the largest system sizes, we find that flux-pileup effects cause the islands to "bounce" despite the presence of a collapsed current sheet allowing for fast instantaneous reco…
Astrophysical fluids are generally turbulent and this preexisting turbulence must be taken into account for the models of magnetic reconnection which are attepmted to be applied to astrophysical, solar or heliospheric environments. In addition, reconnection itself induces turbulence which provides an important feedback on the reconnection process. In this paper we discuss both theoretical model and numerical evidence that magnetic reconnection gets fast in the approximation of resistive MHD. We consider the relation between the Lazarian & Vishniac turbulent reconnection theory and Lapenta's nu…
Recently, secondary island formation due to the tearing instability of the Sweet-Parker current sheet was identified as a possible mechanism that can lead to fast reconnection (less sensitive dependence on Lundquist number $S$) both in numerical simulations using Particle-in-Cell (PIC) method [Daughton et al. 2009], as well as using resistive magnetohydrodynamics (MHD) [Lapenta 2008; Bhattacharjee et al. 2009]. This instability is thought to appear when $S$ is greater than a certain threshold. These recent results prompt us to perform more resistive MHD simulations of a basic reconnection conf…
Forced magnetic reconnection, a reconnection event triggered by external perturbation, should be ubiquitous in the solar corona. Energy released during such cases can be much greater than that which was introduced by the perturbation. It is unclear how the properties of the external perturbation and the initial current sheet affect the reconnection region properties, and thereby the reconnection dynamics and energy release profile. We investigate the effect of the form of the external perturbation and initial current sheet on the evolution of the reconnection region and the energy release proc…
The spontaneous evolution of magnetic reconnection in generalized situations (with thermodynamic asymmetry regarding the current sheet and magnetic shear) is investigated using two-dimensional magnetohydrodynamic simulation. We focus on the asymptotic state of temporal evolution, i.e., the self-similarly expanding phase (Nitta et al. 2001). 1) A long fast-mode shock is generated in front of the shorter plasmoid as in the shear-less thermodynamically asymmetric case; however, the sheared magnetic component weakens the shock. This fast shock may work as a particle acceleration site. 2) The short…
The current understanding of MHD turbulence envisions turbulent eddies which are anisotropic in all three directions. In the plane perpendicular to the local mean magnetic field, this implies that such eddies become current-sheet-like structures at small scales. We analyze the role of magnetic reconnection in these structures and conclude that reconnection becomes important at a scale $λ\sim L S_L^{-4/7}$, where $S_L$ is the outer-scale ($L$) Lundquist number and $λ$ is the smallest of the field-perpendicular eddy dimensions. This scale is larger than the scale set by the resistive diffusion o…
We present a constructive numerical example of fast magnetic reconnection in a three dimensional periodic box. Reconnection is initiated by a strong, localized perturbation to the field lines. The solution is intrinsically three dimensional, and its gross properties do not depend on the details of the simulations. $\sim 50%$ of the magnetic energy is released in an event which lasts about one Alfven time, but only after a delay during which the field lines evolve into a critical configuration. We present a physical picture of the process. The reconnection regions are dynamical and mutually int…
We study the formation of slow-mode shocks in collisionless magnetic reconnection by using one- and two-dimensional collisionless MHD codes based on the double adiabatic approximation and the Landau closure model. We bridge the gap between the Petschek-type MHD reconnection model accompanied by a pair of slow shocks and the observational evidence of the rare occasion of in-situ slow shock observation. Our results showed that once magnetic reconnection takes place, a firehose-sense pressure anisotropy arises in the downstream region, and the generated slow shocks are quite weak comparing with t…
Princeton University（普林斯顿大学）；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）
The conversion of magnetic energy into other forms during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucial role in these conversion processes. To achieve the rapid energy release required in solar flares, an anomalous resistivity, orders of magnitude higher than the Spitzer resistivity, is often used in MHD simulations of reconnection. Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle ac…
Properties of plasmoid-dominated turbulent reconnection in a low-$β$ background plasma are investigated by resistive magnetohydrodynamic (MHD) simulations. In the $β_{\rm in} < 1$ regime, where $β_{\rm in}$ is plasma $β$ in the inflow region, the reconnection site is dominated by shocks and shock-related structures and plasma compression is significant. The effective reconnection rate increases from $0.01$ to $0.02$ as $β_{\rm in}$ decreases. We hypothesize that plasma compression allows faster reconnection rate, and then we estimate a speed-up factor, based on a compressible MHD theory. We va…
Factors Controlling the Statistics of Magnetic Reconnection in MHD Turbulence
University of Delaware（特拉华大学）；University of Waikato（怀卡托大学）；University of Hawaii at Manoa（夏威夷大学马诺阿分校）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；Princeton University（普林斯顿大学）
The paper examines the prospects of using laser plasmas for studying novel regimes of the magnetic field line reconnection and charged particle acceleration. Basic features of plasma dynamics in the three-dimensional configurations relevant to the formation of current sheets in a plasma are addressed by analyzing exact self-similar solutions of the magneto-hydrodynamics and electron magneto-hydrodynamics equations. Then the magnetic field annihilation in the ultrarelativistic limit is considered, when the opposite polarity magnetic field is generated in collisionless plasma by multiple laser p…
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…
Classical Sweet-Parker models of reconnection predict that reconnection rates depend inversely on the resistivity, usually parameterized using the dimensionless Lundquist number ($\Lund$). We describe magnetohydrodynamic (MHD) simulations using a static, nested grid that show the development of a three-dimensional instability in the plane of a current sheet between reversing field lines without a guide field. The instability leads to rapid reconnection of magnetic field lines at a rate independent of $\Lund$ over at least the range $3.2\times 10^3 \lesssim \Lund \lesssim 3.2 \times 10^5$ resol…
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 …
A new computational model is presented suitable for exploring the self-consistent production of energetic electrons during magnetic reconnection in macroscale systems. The equations are based on the recent discovery that parallel electric fields are ineffective drivers of energetic particles during reconnection so that the kinetic scales which control the development of such fields can be ordered out of the equations. The resulting equations consist of a magnetohydrodynamic (MHD) backbone with the energetic component represented by macro-particles described by the guiding center equations. Cru…
We present results of Reynolds-averaged turbulence model simulation on the problem of magnetic reconnection. In the model, in addition to the mean density, momentum, magnetic field, and energy equations, the evolution equations of the turbulent cross-helicity $W$, turbulent energy $K$ and its dissipation rate $\varepsilon$ are simultaneously solved to calculate the rate of magnetic reconnection for a Harris-type current sheet. In contrast to previous works based on algebraic modeling, the turbulence timescale is self-determined by the nonlinear evolutions of $K$ and $\varepsilon$, their ratio …
In this paper, we develop a lattice Boltzmann model for relativistic magnetohydrodynamics (MHD). Even though the model is derived for resistive MHD, it is shown that it is numerically robust even in the high conductivity (ideal MHD) limit. In order to validate the numerical method, test simulations are carried out for both ideal and resistive limits, namely the propagation of Alfvén waves in the ideal MHD and the evolution of current sheets in the resistive regime, where very good agreement is observed comparing to the analytical results. Additionally, two-dimensional magnetic reconnection dri…
Numerical MHD simulations of 3D reconnection events in the solar corona have improved enormously over the last few years, not only in resolution, but also in their complexity, enabling more and more realistic modeling. Various ways to obtain the initial magnetic field, different forms of solar atmospheric models as well as diverse driving speeds and patterns have been employed. This study considers differences between simulations with stratified and non-stratified solar atmospheres, addresses the influence of the driving speed on the plasma flow and energetics, and provides quantitative formul…
This paper discusses the transition to fast growth of the tearing instability in thin current sheets in the collisionless limit where electron inertia drives the reconnection process. It has been previously suggested that in resistive MHD there is a natural maximum aspect ratio (ratio of sheet length and breadth to thickness) which may be reached for current sheets with a macroscopic length L, the limit being provided by the fact that the tearing mode growth time becomes of the same order as the Alfvèn time calculated on the macroscopic scale (Pucci and Velli (2014)). For current sheets with a…
We present a two-fluid magnetohydrodynamics (MHD) model of quasi-stationary, two-dimensional magnetic reconnection in an incompressible plasma composed of electrons and ions. We find two distinct regimes of slow and fast reconnection. The presence of these two regimes can provide a possible explanation for the initial slow build up and subsequent rapid release of magnetic energy frequently observed in cosmic and laboratory plasmas.
We investigate a role of the Hall-effect in the current sheet evolution and onset of the secondary tearing (plasmoid) instability in the framework of the incompressible resistive Hall-magnetohydrodynamics (MHD). The model under consideration is a force-free modification of the Taylor's problem. Thus, the first part of the paper is devoted to a detailed analytical study of the Hall-MHD forced magnetic reconnection in a tearing stable force-free magnetic configuration. Then, in the second part, these results are used to investigate when and how the plasmoid instability can develop in the course …
Here we detail the dynamic evolution of localised reconnection regions about three-dimensional (3D) magnetic null points by using numerical simulation. We demonstrate for the first time that reconnection triggered by the localised collapse of a 3D null point due to an external MHD wave involves a self-generated oscillation, whereby the current sheet and outflow jets undergo a reconnection reversal process during which back-pressure formation at the jet heads acts to prise open the collapsed field before overshooting the equilibrium into an opposite-polarity configuration. The discovery that re…
Fast magnetic reconnection plays a fundamental role in driving explosive dynamics and heating in the solar chromosphere. The reconnection time scale of traditional models is shortened at the onset of the coalescence instability, which forms a turbulent reconnecting current sheet through plasmoid interaction. In this work we aim to investigate the role of partial ionisation on the development of fast reconnection through the study of the coalescence instability of plasmoids. Unlike the processes occurring in fully ionised coronal plasmas, relatively little is known about how fast reconnection d…
As modeling of collisionless magnetic reconnection in most space plasmas with realistic parameters is beyond the capability of today's simulations, due to the separation between global and kinetic length scales, it is important to establish scaling relations in model problems so as to extrapolate to realistic scales. Recently, large scale particle-in-cell (PIC) simulations of island coalescence have shown that the time averaged reconnection rate decreases with system size, while fluid systems at such large scales in the Hall regime have not been studied. Here we perform the complementary resis…
Plasma flows with an MHD-like turbulent inertial range, such as the solar wind, require a generalization of General Magnetic Reconnection (GMR) theory. We introduce the slip-velocity source vector, which gives the rate of development of slip velocity per unit arc length of field line. The slip source vector is the ratio of the curl of the non ideal electric field in the Generalized Ohm's Law and the magnetic field strength. It diverges at magnetic nulls, unifying GMR with magnetic null-point reconnection. Only under restrictive assumptions is the slip velocity related to the gradient of the qu…
We investigate the nonlinear evolution of the $m = 1$ resistive internal kink mode in a two-dimensional (2D) configuration containing a central region of negative current density, also known as the "current hole" setup. The finite-element code FINMHD is used to solve a reduced set of incompressible Magnetohydrodynamic (MHD) equations with a current-vorticity formulation. First, the kink instability linearly develops in agreement with the general theory of resistive internal kink mode, and it subsequently leads to the formation of a current sheet. At relatively low Lundquist number $S$, a magne…
Magnetic reconnection provides the primary source for explosive energy release, plasma heating and particle acceleration in many astrophysical environments. The last years witnessed a revival of interest in the MHD tearing instability as a driver for efficient reconnection. It has been established that, provided the current sheet aspect ratio becomes small enough ($a/L \sim S^{-1/3}$ for a given Lundquist number $S\gg 1$), reconnection occurs on ideal Alfvén timescales and becomes independent on $S$. Here we investigate, by means of two-dimensional simulations, the \emph{ideal} tearing instabi…
A set of reduced Hall magnetohydrodynamic (MHD) equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands). Reconnection is driven by resistivity in this analysis, which occurs at the resistive skin depth $d_η\equiv S_L^{-1/2} \sqrt{L v_A/γ}$, where $S_L$ is the Lundquist number, $L$ the length of the current sheet, $v_A$ the Alfvén speed, and $γ$ the growth rate. Modifications to a recent resistive MHD analysis [N.\ F.\ Loureiro, A.\ A.\ Schekochihin, and S.\ C. Cowley, Phys.\ Plasmas {\bf 14}, 100703 (2007)] arise when …
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 …
We investigate the properties of plasma turbulence by means of two-dimensional Hall-magnetohydrodynamic (HMHD) and hybrid particle-in-cell (HPIC) numerical simulations. We find that HMHD simulations exhibit spectral properties that are in most cases in agreement with the results of the HPIC simulations and with solar wind observations. The energy spectra of magnetic fluctuations exhibit a double power-law with spectral index $-5/3$ at MHD scales and $-3$ at kinetic scales, while for velocity fluctuations the spectral index is $-3/2$ at MHD scales. The break between the MHD and the kinetic scal…
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…
MHD turbulence has long been proposed as a mechanism for the heating of coronal loops in the framework of the Parker scenario for coronal heating. So far most of the studies have focused on its dynamical properties without considering its thermodynamical and radiative features, because of the very demanding computational requirements. In this paper we extend this previous research to the compressible regime, including an energy equation, by using HYPERION, a new parallelized, viscoresistive, three-dimensional compressible MHD code. HYPERION employs a Fourier collocation -- finite difference sp…
Magnetic reconnection requires, at least locally, a non-ideal plasma response. In collisionless space and astrophysical plasmas, turbulence could permit this instead of the too rare binary collisions. We investigated the influence of turbulence on the reconnection rate in the framework of a single fluid compressible MHD approach. The goal is to find out, whether unresolved, sub-grid for MHD simulations, turbulence can enhance the reconnection process in high Reynolds number astrophysical plasma. We solve, simultaneously with the grid-scale MHD equations, evolution equations for the sub-grid tu…
Magnetic field-lines in astrophysical plasmas are expected to be frozen-in at scales larger than the ion gyroradius. The rapid reconnection of magnetic flux structures with dimensions vastly larger than the gyroradius requires a breakdown in the standard Alfvén flux-freezing law. We attribute this breakdown to ubiquitous MHD plasma turbulence with power-law scaling ranges of velocity and magnetic energy spectra. Lagrangian particle trajectories in such environments become "spontaneously stochastic", so that infinitely-many magnetic field-lines are advected to each point and must be averaged to…
Magnetic reconnection is thought to be the dynamical mechanism underlying many explosive phenomena observed both in space and in the laboratory, though the question of how fast magnetic reconnection is triggered in such high Lundquist ($S$) number plasmas has remained elusive. It has been well established that reconnection can develop over timescales faster than those predicted traditionally once kinetic scales are reached. It has also been shown that, within the framework of resistive Magnetohydrodynamics (MHD), fast reconnection is achieved for thin enough sheets via the onset of the so-call…
This paper presents Sweet-Parker type scaling arguments in the context of hyper-resistive Hall magnetohyrdodynamics (MHD). The predicted steady state scalings are consistent with those found by Chacón et al. [PRL 99, 235001 (2007)], though as with that study, no prediction of electron dissipation region \emph{length} is made. Numerical experiments confirm that both cusp-like and modestly more extended geometries are realizable. However, importantly, the length of the electron dissipation region, which is taken as a parameter by several recent studies, is found to depend explicitly on the level…
We describe a method for coupling an embedded domain in a magnetohydrodynamic (MHD) simulation with a particle-in-cell (PIC) method. In this two-way coupling we follow the work of Daldorff et al. in which the PIC domain receives its initial and boundary conditions from MHD variables (MHD to PIC coupling) while the MHD simulation is updated based on the PIC variables (PIC to MHD coupling). This method can be useful for simulating large plasma systems, where kinetic effects captured by particle-in-cell simulations are localized but affect global dynamics. We describe the numerical implementation…
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…
The role of a super-Alfvénic plasmoid instability in the onset of fast reconnection is studied by means of the largest Hall magnetohydrodynamics simulations to date, with system sizes up to $10^{4}$ ion skin depths ($d_{i}$). It is demonstrated that the plasmoid instability can facilitate the onset of rapid Hall reconnection, in a regime where the onset would otherwise be inaccessible because the Sweet-Parker width is significantly above $d_{i}$. However, the topology of Hall reconnection is not inevitably a single stable X-point. There exists an intermediate regime where the single X-point to…
We study, by means of MHD simulations, the onset and evolution of fast reconnection via the "ideal" tearing mode within a collapsing current sheet at high Lundquist numbers ($S\gg10^4$). We first confirm that as the collapse proceeds, fast reconnection is triggered well before a Sweet-Parker type configuration can form: during the linear stage plasmoids rapidly grow in a few Alfvén times when the predicted "ideal" tearing threshold $S^{-1/3}$ is approached from above; after the linear phase of the initial instability, X-points collapse and reform nonlinearly. We show that these give rise to a …
We perform direct numerical simulations of magnetohydrodynamic (MHD) turbulence with kinetic energy and cross helicity injections at large scales. We observe that the cross helicity changes sign as we go from large and intermediate scales to small scales. In addition, the magnetic reconnections are strongest at the regions where the cross helicity changes sign and becomes smallest in magnitude. Thus, our simulations provide an important window to explore the regions of magnetic reconnections in nonlinear MHD.
