In laboratory and natural plasmas of practical interest, the spatial scale $Δ_d$ at which magnetic field lines lose distinguishability differs enormously from the scale $a$ of magnetic reconnection across the field lines. In the solar corona, plasma resistivity gives $a/Δ_d\sim10^{12}$, which is the magnetic Reynold number $R_m$. The traditional resolution of the paradox of disparate scales is for the current density $j$ associated with the reconnecting field $B_{rec}$ to be concentrated by a factor of $R_m$ by the ideal evolution, so $ j\sim B_{rec}/μ_0Δ_d$. A second resolution is for the ideal evolution to increase the ratio of the maximum to minimum separation between pairs of arbitrarily chosen magnetic field lines, $Δ_{max}/Δ_{min}$, when calculated at various points in time. Reconnection becomes inevitable where $Δ_{max}/Δ_{min}\sim R_m$. A simple model of the solar corona will be used for a numerical illustration that the natural rate of increase in time is linear for the current density but exponential for $Δ_{max}/Δ_{min}$. Reconnection occurs on a time scale and with a current density enhanced by only $\ln(a/Δ_d)$ from the ideal evolution time and from the current density $B_{rec}/μ_0a$. In both resolutions, once a sufficiently wide region, $Δ_r$, has undergone reconnection, the magnetic field loses static force balance and evolves on an Alfvénic time scale. The Alfvénic evolution is intrinsically ideal but expands the region in which $Δ_{max}/Δ_{min}$ is large.
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…
We report simulation results for turbulent magnetic reconnection obtained using a newly developed Reynolds-averaged magnetohydrodynamics model. We find that the initial Harris current sheet develops in three ways, depending on the strength of turbulence: laminar reconnection, turbulent reconnection, and turbulent diffusion. The turbulent reconnection explosively converts the magnetic field energy into both kinetic and thermal energy of plasmas, and generates open fast reconnection jets. This fast turbulent reconnection is achieved by the localization of turbulent diffusion. Additionally, local…
Within a MHD approach we find magnetic reconnection to progress in two entirely different ways. The first is well-known: the laminar Sweet-Parker process. But a second, completely different and chaotic reconnection process is possible. This regime has properties of immediate practical relevance: i) it is much faster, developing on scales of the order of the Alfvén time, and ii) the areas of reconnection become distributed chaotically over a macroscopic region. The onset of the faster process is the formation of closed circulation patterns where the jets going out of the reconnection regions tu…
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…
The process of magnetic reconnection when studied in Nature or when modeled in 3D simulations differs in one key way from the standard 2D paradigmatic cartoon: it is accompanied by much fluctuations in the electromagnetic fields and plasma properties. We developed a new diagnostics, the topographical fluctuations analysis (TFA) to study the spectrum of fluctuations in the various regions around a reconnection site. We find that fluctuations belong to two very different regimes. The first regime is better known, it develops in the reconnection outflows and is characterized by a strong link betw…
Earth's magnetotail is an excellent laboratory to study the interplay of reconnection and turbulence in determining electron energization. The process of formation of a power law tail during turbulent reconnection is a documented fact still in need of a comprehensive explanation. We conduct a massively parallel particle in cell 3D simulation and use enhanced statistical resolution of the high energy range of the particle velocities to study how reconnection creates the conditions for the tail to be formed. The process is not direct acceleration by the coherent, laminar, reconnection-generated …
Models for collisionless magnetic reconnection in near-Earth space are distinctly characterized as 2D or 3D. In 2D kinetic models, the frozen-in law for the electron fluid is usually broken by laminar dynamics involving structures set by the electron orbit size, while in 3D models the width of the electron diffusion region is broadened by turbulent effects. We present an analysis of in situ spacecraft observations from the Earth's magnetotail of a fortuitous encounter with an active reconnection region, mapping the observations onto a 2D spatial domain. While the event likely was perturbed by …
Our understanding of magnetic reconnection in resistive magnetohydrodynamics has gone through a fundamental change in recent years. The conventional wisdom is that magnetic reconnection mediated by resistivity is slow in laminar high Lundquist ($S$) plasmas, constrained by the scaling of the reconnection rate predicted by Sweet-Parker theory. However, recent studies have shown that when $S$ exceeds a critical value $\sim10^{4}$, the Sweet-Parker current sheet is unstable to a super-Alfvénic plasmoid instability, with a linear growth rate that scales as $S^{1/4}$. In the fully developed statist…
Realistic models of magnetic reconnection in the solar chromosphere must take into account that the plasma is partially ionized and that plasma conditions within any two magnetic flux bundles undergoing reconnection may not be the same. Asymmetric reconnection in the chromosphere may occur when newly emerged flux interacts with pre-existing, overlying flux. We present 2.5D simulations of asymmetric reconnection in weakly ionized, reacting plasmas where the magnetic field strengths, ion and neutral densities, and temperatures are different in each upstream region. The plasma and neutral compone…
A 2.5-dimensional magnetohydrodynamics simulation analysis of the energy release for three different reconnection regimes is presented. The system under investigation consists in a current-sheet located in a medium with a strong density variation along the current layer: such system is modeled as it were located in the high chromosphere/low solar corona as in the case of pre- flare and coronal mass ejection (CME) configurations or in the aftermath of such explosive phenomena. By triggering different magnetic-reconnection dynamics, that is from a laminar slow evolution to a spontaneous non-stea…
Although magnetic reconnection takes place in three-dimensional space, reconnection theory has focused on two-dimensional models for more than sixty years. Well-posed three-dimensional mathematics associated with the theory of fluid mixing provides a predictive and compelling explanation for why fast magnetic reconnection is prevalent---exponentially large variations in the separations between magnetic field lines. The proofs have been simplified to remove any rational reason to maintain a focus on two dimensional models, which fail to represent the mathematical properties of three-dimensional…
The orientation and stability of the reconnection x-line in asymmetric geometry is studied using three-dimensional (3D) particle-in-cell simulations. We initiate reconnection at the center of a large simulation domain to minimize the boundary effect. The resulting x-line has sufficient freedom to develop along an optimal orientation, and it remains laminar. Companion 2D simulations indicate that this x-line orientation maximizes the reconnection rate. The divergence of the non-gyrotropic pressure tensor breaks the frozen-in condition, consistent with its 2D counterpart. We then design 3D simul…
Energy dissipation in collisionless plasmas is a longstanding fundamental physics problem. Although it is well known that magnetic reconnection and turbulence are coupled and transport energy from system-size scales to sub-proton scales, the details of the energy distribution and energy dissipation channels remain poorly understood. Especially, the energy transfer and transport associated with three dimensional (3D) small-scale reconnection that occurs as a consequence of a turbulent cascade is unknown. We use an explicit fully kinetic particle-in-cell code to simulate 3D small scale magnetic …
Regardless of how small non-ideal effects may be, phenomena associated with changes in magnetic field line connections are frequently observed to occur on an Alfvénic time scale. Since it is mathematically impossible for magnetic field line connections to change when non-ideal effects are identically zero, an ideal evolution must naturally lead to states of unbounded sensitivity to non-ideal effects. That such an evolution is natural is demonstrated using Lagrangian coordinates based on the flow velocity of the magnetic field lines. The Lagrangian representation of an evolving magnetic field i…
The process of magnetic reconnection when studied in Nature or when modeled in 3D simulations differs in one key way from the standard 2D paradigmatic cartoon: it is accompanied by much fluctuations in the electromagnetic fields and plasma properties. We developed a diagnostics to study the spectrum of fluctuations in the various regions around a reconnection site. We define the regions in terms of the local value of the flux function that determines the distance form the reconnection site, with positive values in the outflow and negative values in the inflow. We find that fluctuations belong …
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…
Over the past decade, Boozer has argued that three-dimensional (3D) magnetic reconnection fundamentally differs from two-dimensional (2D) reconnection due to the fact that the separation between any pair of neighboring field lines almost always increases exponentially over distance in a 3D magnetic field. According to Boozer, this feature makes 3D field-line mapping chaotic and exponentially sensitive to small non-ideal effects; consequently, 3D reconnection can occur without intense current sheets. We test Boozer's theory via ideal and resistive reduced magnetohydrodynamic simulations of the …
Two- and three-dimensional particle-in-cell simulations of a recent encounter of the Magnetospheric Multiscale Mission (MMS) with an electron diffusion region at the magnetopause are presented. While the two-dimensional simulation is laminar, turbulence develops at both the x-line and along the magnetic separatrices in the three-dimensional simulation. The turbulence is strong enough to make the magnetic field around the reconnection island chaotic and produces both anomalous resistivity and anomalous viscosity. Each contribute significantly to breaking the frozen-in condition in the electron …
We review the basic concepts of magnetic reconnection and propose a general framework for the astrophysical reconnection at large scales. Magnetic reconnection is the rearrangement of magnetic field topology. The conventional Sweet-Parker scheme and some of its extensions presume a non-turbulent medium and generally produce very slow reconnection or an unstable configuration. However, the assumption of laminar flow is unrealistic in astrophysics since, even in an initially quiet environment, magnetic reconnection by itself can drive turbulence. The resulting turbulence has the potential to enh…
The role of turbulence in low-$β$, guide-field reconnection exhausts is explored in 2D reconnection and 2D and 3D Riemann simulations. The structure of the exhaust and associated turbulence is controlled by a pair of rotational discontinuities (RDs) at the exhaust boundary and a pair of slow shocks (SSs) that are generated by counterstreaming ions beams. In 2D the exhaust develops large-amplitude striations at the ion Larmor radius scale that are produced by electron-beam-driven ion cyclotron waves. The electron beams driving the instability are injected into the exhaust from one of the RDs. H…
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…
Mathematics demonstrates that an ideally evolving magnetic field has an exponentially increasing sensitivity to non-ideal effects for all but truly exceptional evolutions. On a time scale that depends only logarithmically on the magnitude of non-ideality, an evolving magnetic field will generally reach a state of fast magnetic reconnection. The effects of fast magnetic reconnection proceed at a rate determined by Alfvénic, not resistive, physics. The best known of these effects are associated with the transfer of magnetic field energy to the plasma and the conservation of magnetic helicity, wh…
Kinetic Riemann simulations have been completed to explore particle heating during guide field reconnection in the low-$β$ environment of the inner heliosphere and the solar corona. The reconnection exhaust is bounded by two rotational discontinuities (RD) and two slow shocks (SS) form within the exhaust as in magnetohydrodynamic (MHD) models. At the RDs, ions are accelerated by the magnetic field tension to drive the reconnection outflow as well as flows in the out-of-plane direction. The out-of-plane flows stream toward the midplane and meet to drive the SSs. The SSs differ greatly from thos…
Reconnection is the process by which magnetic fields in a conducting fluid change their topology. This process is essential for understanding a wide variety of astrophysical processes, including stellar and galactic dynamos and astrophysical turbulence. To account for solar flares, solar cycles and the structure of the galactic magnetic field reconnection must be fast, propagating with a speed close to the Alfven speed. We show that the presence of a random magnetic field component substantially enhances the reconnection rate and enables fast reconnection, i.e. reconnection that does not depen…
The magnetic Reynolds number R_M, is defined as the product of a characteristic scale and associated flow speed divided by the microphysical magnetic diffusivity. For laminar flows, R_M also approximates the ratio of advective to dissipative terms in the total magnetic energy equation, but for turbulent flows this latter ratio depends on the energy spectra and approaches unity in a steady state. To generalize for flows of arbitrary spectra we define an effective magnetic dissipation number, R_{M,e}, as the ratio of the advection to microphysical dissipation terms in the total magnetic energy e…
The no-hair theorem of general relativity states that isolated black holes are characterized by three parameters: mass, spin, and charge. In this Letter we consider Kerr black holes endowed with highly magnetized plasma-filled magnetospheres. Using general relativistic kinetic plasma and resistive magnetohydrodynamics simulations, we show that a dipole magnetic field on the event horizon opens into a split-monopole and reconnects in a plasmoid-unstable current-sheet. The no-hair theorem is satisfied, in the sense that all components of the stress-energy tensor decay exponentially in time. We m…
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）
Magnetic fields without a direction of continuous symmetry have the generic feature that neighboring field lines exponentiate away from each other and become stochastic, hence the ideal constraint of preserving magnetic field line connectivity becomes exponentially sensitive to small deviations from ideal Ohm's law. The idea of breaking field line connectivity by stochasticity as a mechanism for fast reconnection is tested with numerical simulations based on reduced magnetohydrodynamics equations with a strong guide field line-tied to two perfectly conducting end plates. Starting from an ideal…
One of the greatest challenges in solar physics is understanding the heating of the Sun's corona. Most theories for coronal heating postulate that free energy in the form of magnetic twist/stress is injected by the photosphere into the corona where the free energy is converted into heat either through reconnection or wave dissipation. The magnetic helicity associated with the twist/stress, however, is expected to be conserved and appear in the corona. In previous work we showed that helicity associated with the small-scale twists undergoes an inverse cascade via stochastic reconnection in the …
We develop a quantitative relationship between magnetic diffusion and the level of randomness, or stochasticity, of the diffusing magnetic field in a magnetized medium. A general mathematical formulation of magnetic stochasticity in turbulence has been developed in previous work in terms of the ${\cal L}_p$-norm $S_p(t)={1\over 2}|| 1-\hat{\bf B}_l.\hat{\bf B}_L||_p$, $p$th order magnetic stochasticity of the stochastic field ${\bf B}({\bf x}, t)$, based on the coarse-grained fields, ${\bf B}_l$ and ${\bf B}_L$, at different scales, $l\neq L$. For laminar flows, stochasticity level becomes the…
Spectral Properties and Energy Injection in Mercury's Magnetotail Current Sheet
Boston University（波士顿大学）；Laboratoire de Physique des Plasmas (LPP), CNRS, Observatoire de Paris, Sorbonne Université, Université Paris Saclay, Ecole polytechnique, Institut Polytechnique de Paris（等离子体物理实验室，法国国家科学研究中心，巴黎天文台，索邦大学，巴黎萨克雷大学，巴黎综合理工学院，巴黎理工学院）；Department of Climate and Space Sciences and Engineering, University of Michigan（密歇根大学气候与空间科学与工程系）；INAF-Institute for Astrophysics and Space Planetology（意大利国家天体物理学研究所空间与行星物理学研究所）
Study of low-frequency core-edge coupling in a tokamak: III. Core-localized MHD continuum pulsations \& distant forced reconnection
National Institutes for Quantum Science and Technology (QST)（量子科学和技术研究院）；KAIST（韩国科学技术院）；Research Organization for Information Science and Technology (RIST)（信息技术科学研究机构）
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…
