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↗
Onset of Plasmoid Reconnection during Magnetorotational Instability
The evolution of current sheets in accretion flows undergoing magnetorotational instability (MRI) is examined through two- and three-dimensional numerical modeling of the resistive MHD equations in global cylindrical geometry. With an initial uniform magnetic field aligned in the vertical (z) direction, MRI produces radially extended toroidal (azimuthal) current sheets. In both 2D and 3D when axisymmetric modes dominate, these current sheets attract each other and merge in the poloidal (rz) plane, driving magnetic reconnection when the Lundquist number S > 3 × 10 2 , making it a possible source of plasmoids (closed magnetic loops) in accretion disks. At high Lundquist numbers in the 2D regime, starting at S = 5 × 10 3 , self-consistent MRI-generated current sheets become thin and subject to plasmoid instability, and therefore spontaneous magnetic reconnection. When nonaxisymmetric 3D modes dominate, turbulence makes the azimuthal current sheets more unstable and stretch vertically. Toroidally extended vertical current sheets in the inner region, as well as larger 3D magnetic islands in the outer regions of the disks are also formed. These findings have strong ramifications for astrophysical disks as potential sources of plasmoids that could cause local heating, particle acceleration, and high energy EM radiation.
79 ASTRONOMY AND ASTROPHYSICS↗
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↗
Plasma Dynamics and Nonthermal Particle Acceleration in 3D Nonrelativistic Magnetic Reconnection
Understanding plasma dynamics and nonthermal particle acceleration in 3D magnetic reconnection has been a long-standing challenge. In this paper, we explore these problems by performing large-scale fully kinetic simulations of multi-X-line plasmoid reconnection with various parameters in both the weak- and strong-guide-field regimes. In each regime, we have identified its unique 3D dynamics that lead to field-line chaos and efficient acceleration, and we have achieved nonthermal acceleration of both electrons and protons into power-law spectra. The spectral indices agree well with a simple Fermi acceleration theory that includes guide-field dependence. In the low-guide-field regime, the flux rope kink instability governs the 3D dynamics for efficient acceleration. The weak dependence of the spectra on the ion-to-electron mass ratio and β ($\ll$1) implies that the particles are sufficiently magnetized for Fermi acceleration in our simulations. While both electrons and protons are injected at reconnection exhausts, protons are primarily injected by perpendicular electric fields through Fermi reflections and electrons are injected by a combination of perpendicular and parallel electric fields. The magnetic power spectra agree with in situ magnetotail observations, and the spectral index may reflect a reconnection-driven size distribution of plasmoids instead of the Goldreich–Sridhar vortex cascade. As the guide field becomes stronger, the oblique flux ropes of large sizes capture the main 3D dynamics for efficient acceleration. Intriguingly, the oblique flux ropes can also experience flux rope kink instability, to drive extra 3D dynamics. This work has broad implications for 3D reconnection dynamics and particle acceleration in heliophysics and astrophysics.
79 ASTRONOMY AND ASTROPHYSICS↗
Generation of Near-Equipartition Magnetic Fields in Turbulent Collisionless Plasmas
The mechanisms that generate “seed” magnetic fields in our Universe and that amplify them throughout cosmic time remain poorly understood. By means of fully kinetic particle-in-cell simulations of turbulent, initially unmagnetized plasmas, here we study the genesis of magnetic fields via the Weibel instability and follow their dynamo growth up to near-equipartition levels. In the kinematic stage of the dynamo, we find that the rms magnetic field strength grows exponentially with rate γ B ≃0.4u rms /L, where L/2π is the driving scale and u rms is the rms turbulent velocity. In the saturated stage, the magnetic field energy reaches about half of the turbulent kinetic energy. Here, magnetic field growth is balanced by dissipation via reconnection, as revealed by the appearance of plasmoid chains. At saturation, the integral-scale wave number of the magnetic spectrum approaches k int ≃12π/L. Our results show that turbulence—induced by, e.g., the gravitational buildup of galaxies and galaxy clusters—can magnetize collisionless plasmas with large-scale near-equipartition fields.
79 ASTRONOMY AND ASTROPHYSICS↗
High-energy synchrotron flares powered by strongly radiative relativistic magnetic reconnection: 2D and 3D PIC simulations
ABSTRACT The time evolution of high-energy synchrotron radiation generated in a relativistic pair plasma energized by reconnection of strong magnetic fields is investigated with 2D and 3D particle-in-cell (PIC) simulations. The simulations in this 2D/3D comparison study are conducted with the radiative PIC code OSIRIS, which self-consistently accounts for the synchrotron radiation reaction on the emitting particles, and enables us to explore the effects of synchrotron cooling. Magnetic reconnection causes compression of the plasma and magnetic field deep inside magnetic islands (plasmoids), leading to an enhancement of the flaring emission, which may help explain some astrophysical gamma-ray flare observations. Although radiative cooling weakens the emission from plasmoid cores, it facilitates additional compression there, further amplifying the magnetic field B and plasma density n, and thus partially mitigating this effect. Novel simulation diagnostics utilizing 2D histograms in the n-B space are developed and used to visualize and quantify the effects of compression. The n-B histograms are observed to be bounded by relatively sharp power-law boundaries marking clear limits on compression. Theoretical explanations for some of these compression limits are developed, rooted in radiative resistivity or 3D kinking instabilities. Systematic parameter-space studies with respect to guide magnetic field, system size, and upstream magnetization are conducted and suggest that stronger compression, brighter high-energy radiation, and perhaps significant quantum electrodynamic effects such as pair production, may occur in environments with larger reconnection-region sizes and higher magnetization, particularly when magnetic field strengths approach the critical (Schwinger) field, as found in magnetar magnetospheres.
Schoeffler, K. M. (ORCID:0000000276447381)↗
Marginally stable current sheets in collisionless magnetic reconnection
Noncollisional current sheets that form during the nonlinear development of spontaneous magnetic reconnection are characterized by a small thickness, of the order of the electron skin depth. They can become unstable to the formation of plasmoids, which allows the magnetic reconnection process to reach high reconnection rates. In this work, we investigate the marginal stability conditions for the development of plasmoids when the forming current sheet is purely collisionless and in the presence of a strong guide field. We analyze the geometry that characterizes the reconnecting current sheet, and what promotes its elongation. Once the reconnecting current sheet is formed, we identify the regimes for which it is plasmoid unstable. Finally, our study shows that plasmoids can be obtained, in this context, from current sheets with an aspect ratio much smaller than in the collisional regime, and that the plasma flow channel of the marginally stable current layers maintains an inverse aspect ratio of 0.1.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗