Plasmoid instability, magnetic field line chaos, and reconnection
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Nuclear Science & Technology↗
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Three-dimensional plasmoid-mediated reconnection and turbulence in Hall magnetohydrodynamics
Plasmoid instability accelerates reconnection in collisional plasmas by transforming a laminar reconnection layer into numerous plasmoids connected by secondary current sheets in two dimensions (2D) and by fostering self-generated turbulent reconnection in three dimensions (3D). In large-scale astrophysical and space systems, plasmoid instability likely initiates in the collisional regime but may transition into the collisionless regime as the fragmentation of the current sheet progresses toward kinetic scales. Hall magnetohydrodynamics (MHD) models are widely regarded as a simplified yet effective representation of the transition from collisional to collisionless reconnection. However, plasmoid instability in 2D Hall MHD simulations often leads to a single-X-line reconnection configuration, which significantly differs from fully kinetic particle-in-cell simulation results. This study shows that single-X-line reconnection is less likely to occur in 3D compared to 2D. Moreover, depending on the Lundquist number and the ratio between the system size and the kinetic scale, Hall MHD can also realize 3D self-generated turbulent reconnection. We analyze the features of the self-generated turbulent state, including the energy power spectra and the scale dependence of turbulent eddy anisotropy.
Physics↗
Magnetic reconnection in the era of exascale computing and multiscale experiments
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 with in situ spacecraft observations or laboratory experiments. However, major challenges remain in understanding magnetic reconnection in large systems, such as the solar corona, where the collisionality is weak and the kinetic scales are vanishingly small in comparison with macroscopic scales. The plasmoid instability or formation of multiple plasmoids in long, reconnecting current sheets is one possible multiscale solution for bridging this vast range of scales, and new laboratory experiments are poised to study these regimes. In conjunction with these efforts, we anticipate that the coming era of exascale computing, together with the next generation of observational capabilities, will enable new progress on a range of challenging problems, including the energy build-up and onset of reconnection, partially ionized regimes, the influence of magnetic turbulence and particle acceleration.
79 ASTRONOMY AND ASTROPHYSICS↗
An adaptive scalable fully implicit algorithm based on stabilized finite element for reduced visco-resistive MHD
The magnetohydrodynamics (MHD) equations are continuum models used in the study of a wide range of plasma physics systems, including the evolution of complex plasma dynamics in tokamak disruptions. However, efficient numerical solution methods for MHD are extremely challenging due to disparate time and length scales, strong hyperbolic phenomena, and nonlinearity. Additionally, therefore the development of scalable, implicit MHD algorithms and high-resolution adaptive mesh refinement strategies is of considerable importance. In this work, we develop a high-order stabilized finite-element algorithm for the reduced visco-resistive MHD equations based on the MFEM finite element library (mfem.org). The scheme is fully implicit, solved with the Jacobian-free Newton-Krylov (JFNK) method with a physics-based preconditioning strategy. Our preconditioning strategy is a generalization of the physics-based preconditioning methods in Chacón et al. (2002) to adaptive, stabilized finite elements. Algebraic multigrid methods are used to invert sub-block operators to achieve scalability. A parallel adaptive mesh refinement scheme with dynamic load-balancing is implemented to efficiently resolve the multi-scale spatial features of the system. Our implementation uses the MFEM framework, which provides arbitrary-order polynomials and flexible adaptive conforming and non-conforming meshes capabilities. Results demonstrate the accuracy, efficiency, and scalability of the implicit scheme in the presence of large scale disparity. The potential of the AMR approach is demonstrated on an island coalescence problem in the high Lundquist-number regime (≥ 10 7 ) with the successful resolution of plasmoid instabilities and thin current sheets.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Collaborative Research: Unveiling the Interplay Between Magnetic Reconnection and Turbulence — Theory and Modeling
This is the final technical report for the project "Collaborative Research: Unveiling the Interplay Between Magnetic Reconnection and Turbulence — Theory and Modeling." This project investigated the interplay between two fundamental plasma processes — turbulence and magnetic reconnection — and the associated heating and particle acceleration. In particular, we focused on a new regime where the plasmoid instability mediates the turbulent energy cascade. In this new regime, reconnecting current sheets are disrupted by the growth of plasmoids/flux ropes on time scales shorter than the typical turnover times of eddies, speeding up the energy cascade and steepening the turbulence energy spectrum. This project addressed the following outstanding open questions: (1) What are the fundamental differences between plasmoid‐mediated turbulence cascade in three dimensions (3D) and two dimensions (2D)? (2) What are the essential features of plasmoid‐mediated turbulence in weakly collisional or collisionless regimes beyond resistive MHD? (3) How does the interplay of turbulence and reconnection regulate the energy release and dissipation in space and astrophysical plasmas? To address these questions, we have carried out three investigations: (1) Three-dimensional plasmoid-mediated turbulence energy cascade; (2) plasmoid-mediated reconnection and turbulence in three-dimensional Hall MHD; (3) reconnection and heating in coronal loops. This technical report summarizes the key findings of these investigations.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Simulations of radiatively cooled magnetic reconnection driven by pulsed power
Magnetic reconnection is an important process in astrophysical environments, as it reconfigures magnetic field topology and converts magnetic energy into thermal and kinetic energy. In extreme astrophysical systems, such as black hole coronae and pulsar magnetospheres, radiative cooling modifies the energy partition by radiating away internal energy, which can lead to the radiative collapse of the reconnection layer. In this paper, we perform two- and three-dimensional simulations to model the MARZ (Magnetic Reconnection on Z) experiments, which are designed to access cooling rates in the laboratory necessary to investigate reconnection in a previously unexplored radiatively cooled regime. These simulations are performed in GORGON, an Eulerian two-temperature resistive magnetohydrodynamic code, which models the experimental geometry comprising two exploding wire arrays driven by 20 MA of current on the Z machine (Sandia National Laboratories). Radiative losses are implemented using non-local thermodynamic equilibrium tables computed using the atomic code Spk, and we probe the effects of radiation transport by implementing both a local radiation loss model and P 1/3 multi-group radiation transport. The load produces highly collisional, super-Alfvénic (Alfvén Mach number M A ≈ 1.5), supersonic (Sonic Mach number M S ≈ 4–5) strongly driven plasma flows which generate an elongated reconnection layer (Aspect Ratio L/δ≈100 , Lundquist number S L ≈ 400). The reconnection layer undergoes radiative collapse when the radiative losses exceed the rates of ohmic and compressional heating (cooling rate/hydrodynamic transit rate = τ$^{–1}_{cool}$/τ$^{–1}_{H}$ ≈100); this generates a cold strongly compressed current sheet, leading to an accelerated reconnection rate, consistent with theoretical predictions. Lastly, the current sheet is also unstable to the plasmoid instability, but the magnetic islands are extinguished by strong radiative cooling before ejection from the layer.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
MMS Examination of FTEs at the Earth's Subsolar Magnetopause
Determining the magnetic field structure, electric currents, and plasma distributions within flux transfer event (FTE)-type flux ropes is critical to the understanding of their origin, evolution, and dynamics. Here the Magnetospheric Multiscale mission's high-resolution magnetic field and plasma measurements are used to identify FTEs in the vicinity of the subsolar magnetopause. The constant-alpha flux rope model is used to identify quasi-force free flux ropes and to infer the size, the core magnetic field strength, the magnetic flux content, and the spacecraft trajectories through these structures. Our statistical analysis determines a mean diameter of 1,700 ± 400 km (~30 ± 9 d(sub i)) and an average magnetic flux content of 100 ± 30 kWb for the quasi-force free FTEs at the Earth's subsolar magnetopause which are smaller than values reported by Cluster at high latitudes. These observed nonlinear size and magnetic flux content distributions of FTEs appear consistent with the plasmoid instability theory, which relies on the merging of neighboring, small-scale FTEs to generate larger structures. The ratio of the perpendicular to parallel components of current density, R(sub J), indicates that our FTEs are magnetically force-free, defined as R(sub J) < 1, in their core regions (<0.6 R(sub flux rope)). Plasma density is shown to be larger in smaller, newly formed FTEs and dropping with increasing FTE size. It is also shown that parallel ion velocity dominates inside FTEs with largest plasma density. Field-aligned flow facilitates the evacuation of plasma inside newly formed FTEs, while their core magnetic field strengthens with increasing FTE size.
Akhavan-Tafti, M.↗
Magnetic reconnection during magnetospheric substorms
The near earth reconnection model of substorms represents an attempt to place a broad range of observations into a consistent framework. The roles and requirements of reconnection are discussed. High speed plasma sheet flows, thin current sheet instability, substorm triggering, plasmoids and flux ropes in the distant tail, and magnetohydrodynamic simulations are discussed. Substorms are global, coherent sequences of processes involving solar wind/magnetosphere/ionosphere interaction. Magnetic reconnection is required to explain different dayside and polar cap phenomena, which required nightside reconnection. The modification and expansion of the standard near earth neutral line (NENL) model can integrate breakup arcs, current disruption, current wedge features, and localized plasma flows into the magnetic reconnection framework.
Baker, Daniel N.↗
Magnetotail instability
The stability of the geomagnetic tail is investigated on the basis of three dimensional resistive magnetohydrodynamic simulations, using different dynamic constraints and different initial equilibria. Different forms of the energy equation for isotropic pressure are found to have no significant effect on the dynamic growth of a resistive tearing instability, which is responsible for near Earth reconnection, plasmoid formation and ejection, and the generation of fast plasma flows. The constraints of a modified double adiabatic approach, however, can quench the tearing instability through the development of large, mirror type, anisotropies in the boundary regions of the plasma sheet, unless isotropization occurs on fast, nearly Alfvenic, time scales. The presence of a net cross tail magnetic field component B(sub yN) can reduce the growth of the instability without complete stabilization. An increase of B(sub z) from midnight toward the tail flanks, however, by more than a factor of about 3, apparently completely stabilizes the tearing mode. Stabilization and destabilization thus may depend on properties and constraints (and their release) in regions other than the neutral sheet where reconnection is initiated.
Birn, Joachim↗
Fast plasmoid formation in double arcades
The evolution of two neighboring nonsymmetric arcades with footpoint shearing profiles which can change in time is simulated in order to investigate the quasi-static evolution of a double arcade system. It is found that rapid forced reconnection can take place repeatedly, forming a series of plasmoids. A two-arcade system laterally confined by surrounding fluxes can develop instability with nonsymmetric footpoint shear, but the instability is significantly lower in comparison with the case in which the system is confined by a 'hard box' or periodic boundary conditions. The fast plasmoid formation process due to asymmetry switching is not due to the presence of simulation walls. The behavior of double arcades with asymmetry switching is described using equilibrium bifurcation diagrams with footpoint shear and degree of asymmetry, as two independent control parameters.
Finn, J. M.↗
Evidence of a Plasmoid-Looptop Interaction and Magnetic Inflows During a Solar Flare/Coronal Mass Ejection Eruptive Event
Observational evidence is presented for the merging of a downward-propagating plasmoid with a looptop kernel during an occulted limb event on 2007 January 25. RHESSI light curves in the 9-18 keV energy range, as well as that of the 245 MHz channel of the Learmonth Solar Observatory, show enhanced nonthermal emission in the corona at the time of the merging suggesting that additional particle acceleration took place. This was attributed to a secondary episode of reconnection in the current sheet that formed between the two merging sources. RHESSI images were used to establish a mean downward velocity of the plasmoid of 12 km/s. Complementary observations from the SECCHI suite of instruments on board STEREO-B showed that this process occurred during the acceleration phase of the associated coronal mass ejection (CME). From wavelet-enhanced EUV Imager, image evidence of inflowing magnetic field lines prior to the CME eruption is also presented. The derived inflow velocity was found to be 1.5 km/s. This combination of observations supports a recent numerical simulation of plasmoid formation, propagation, and subsequent particle acceleration due to the tearing mode instability during current sheet formation.
Milligan, Ryan O.↗
MHD aspects of magnetotail dynamics
The equations of ideal MHD represent the conservation of mass, momentum, and energy; thus, MHD must, in some broad sense, provide a correct description of large-scale structure of the earth's magnetosphere. However, steady-state, ideal MHD (the simplest description) allows only a static interaction between the solar wind and the magnetosphere. Hence an MHD theory of magnetospheric dynamics must involve unsteady flow turbulence, such as might be generated by Kelvin-Helmholtz turbulence at the magnetopause, and dissipative transport, such as reconnection, which violates ideal MHD. This brief review summarizes recent theoretical efforts to explore and extend the early MHD magnetospheric models of Axford and Petschek. Analytic calculations show that steady convection in the magnetotail is nearly impossible. Global magnetospheric simulations exhibit substorm reconnection phenomena for southward IMF and predict a novel convection pattern for northward IMF. Reconnection simulations show plasmoid formation and field-aligned current flows in the tail. The Kelvin-Helmholtz instability can provide a strong anomalous viscosity which can drive the viscous convection system.
Coroniti, F. V.↗
MHD modeling of magnetotail instability for localized resistivity
We present results of a three-dimensional magnetohydrodynamic (MHD) simulation of magnetotail evolution initiated by a sudden occurrence or increase of spatially localized resistivity as the major expected concequence of some localized microinstability. Because of the absence of a quantitative model, possible variations of resistivity levels with current density, or the reduction thereof, are not incorporated in the present investigation. The emphasis of the study is on an investigation of the changes to the overall evolution brought about by this localization, in particular, on the disruption and diversion of the cross-tail current and the nonlinear evolution of the magnetotail instability. The immediate consequences of the occurrence of the localized resistance and the resulting electric field are a reduction and diversion of the electric current around the region of high resistivity, associated with an increase of B(sub z) ('dipolarization') at the earthward edge and a decrease of B(sub z) at the tailward edge of this region. These effects, however, are localized and do not involve a reduction of the total cross-tail current and hence do not lead to the global development of a 'substorm current wedge,' which includes not only the reduction of the cross-tail current but also the buildup of a global field-aligned current system of 'regional 1' type (toward the Earth on the dawnside and away on the duskside of the tail). Such signatures develop at a later time, as consequences of a three-dimensional tearing instability, which is triggered by the occurrence of the resistivity. These features are found in combination with plasmoid formation and ejection, quite similar to results of earlier simulations with uniform resistivity. Differences are found in the timescale of the evolution, which tends to be shorter for localized resistivity, and in the propagation of the dipolarization effects in the equatorial plane. Whereas for uniform resistivity the temporal increase in B(sub z) tends to propagate tailward, apparently due to a pileup effect in the near-Earth region, an earthward propagation is found for the localized resistivity. This propagation results from an earthward convection of the gradient in B(sub z), which is set up by the reconnection process further tailward.
Hesse, Michael↗
The Mechanisms for the Onset and Explosive Eruption of Coronal Mass Ejections and Eruptive Flares
We have investigated the onset and acceleration of coronal mass ejections (CMEs) and eruptive flares. To isolate the eruption physics, our study uses the breakout model, which is insensitive to the energy buildup process leading to the eruption. We performed 2.5D simulations with adaptive mesh refinement that achieved the highest overall spatial resolution to date in a CME/eruptive flare simulation. The ultra-high resolution allows us to separate clearly the timing of the various phases of the eruption. Using new computational tools, we have determined the number and evolution of all X- and O-type nulls in the system, thereby tracking both the progress and the products of reconnection throughout the computational domain. Our results show definitively that CME onset is due to the start of fast reconnection at the breakout current sheet. Once this reconnection begins, eruption is inevitable; if this is the only reconnection in the system, however, the eruption will be slow. The explosive CME acceleration is triggered by fast reconnection at the flare current sheet. Our results indicate that the explosive eruption is caused by a resistive instability, not an ideal process. Moreover, both breakout and flare reconnections begin first as a form of weak tearing characterized by a slowly evolving plasmoids, but eventually transition to a fast form with well-defined Alfvenic reconnection jets and rapid flux transfer. This transition to fast reconnection is required for both CME onset and explosive acceleration. We discuss the key implications of our results for CME/flare observations and for theories of magnetic reconnection.
Karpen, Judith T.↗
Impact of 3D Structure on Magnetic Reconnection
Results from 2.5D and 3D studies of the onset and development of the tearing instability are presented, using high fidelity resistive MHD simulations. A limited parameter study of the strength of the reconnecting field (or shear angle) was performed. An initially simple 1D equilibrium was used, consisting of a modified force-free current sheet, with periodic boundary conditions in all directions. In all cases, the linear and nonlinear evolution led to a primary current sheet between two large flux ropes. The global reconnection rate during this later stage was analyzed in all simulations. It was found that in 2.5D the primary current sheet fragmented owing to plasmoids, and as expected, the global reconnection rate, calculated using multiple methods, increases with the strength of the reconnecting field owing to a stronger Alfvén speed. In 3D, the presence of interacting oblique modes of the tearing instability complicates the simple 2.5D picture, entangling the magnetic field of the inflow and introducing a negative effect on the reconnection rate. The two competing effects of stronger Alfvén speed and entangling, which both increase with the strength of the reconnecting field, resulted in a decrease in the reconnection rate with increasing reconnecting field. For all simulations, the 3D rates were less than in 2.5D but suggest that as one goes to weak reconnecting field (or strong guide field) the system becomes more 2.5D-like and the 2.5D and 3D rates converge. These results have relevance to situations like nanoflare heating and flare current sheets in the corona.
Lars K S Daldorff↗
Reconnection and particle acceleration in 3D current sheet evolution in moderately-magnetized astrophysical pair plasma
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, relativistically-hot electron- positron plasma, and find dramatic differences. We first systematically characterize this process in 2D, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths, and system sizes. We then show that 3D simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3D current-sheet evolution is not always fundamentally classical reconnection with perturbing 3D effects, but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details, and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in 2D. Intriguingly, nonthermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in 2D and 3D. Though the variety of underlying current-sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.
Gregory R. Werner↗
Reconnection and particle acceleration in three-dimensional current sheet evolution in moderately magnetized astrophysical pair plasma
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 two-dimensional) nonlinear evolution of the tearing instability disrupting a thin current sheet. To test how this process operates in three dimensions, we conduct a comprehensive particle-in-cell simulation study comparing two- and three-dimensional evolution of long, thin current sheets in moderately magnetized, collisionless, relativistically hot electron–positron plasma, and find dramatic differences. We first systematically characterize this process in two dimensions, where classic, hierarchical plasmoid-chain reconnection determines energy release, and explore a wide range of initial configurations, guide magnetic field strengths and system sizes. We then show that three-dimensional (3-D) simulations of similar configurations exhibit a diversity of behaviours, including some where energy release is determined by the nonlinear relativistic drift-kink instability. Thus, 3-D current sheet evolution is not always fundamentally classical reconnection with perturbing 3-D effects but, rather, a complex interplay of multiple linear and nonlinear instabilities whose relative importance depends sensitively on the ambient plasma, minor configuration details and even stochastic events. It often yields slower but longer-lasting and ultimately greater magnetic energy release than in two dimensions. Intriguingly, non-thermal particle acceleration is astonishingly robust, depending on the upstream magnetization and guide field, but otherwise yielding similar particle energy spectra in two and three dimensions. Although the variety of underlying current sheet behaviours is interesting, the similarities in overall energy release and particle spectra may be more remarkable.
Physics↗
Plasmoid-mediated reconnection during nonlinear peeling–ballooning edge-localized modes
Abstract Plasmoid-mediated reconnection is investigated for nonlinear peeling–ballooning edge-localized modes (P-B ELMs). The formation of current sheets and the transition to 3D current sheet instability is demonstrated through fully nonlinear resistive MHD simulations of P-B ELMs in DIII-D discharges. Large-scale axisymmetric current sheets, as well as small-scale poloidally extended current sheets, are formed as the coherent P-B ELM filaments nonlinearly evolve. It is observed that, at high Lundquist numbers, these current sheets break during a reconnection burst, i.e. a secondary exponential growth of intermediate modes followed by relaxation due to the suppression of P-B drive.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗