Forced Magnetic Reconnection Research Articles

Unified framework of forced magnetic reconnection and Alfvén resonance

A unified linear theory that includes forced reconnection as a particular case of Alfvén resonance is presented. We consider a generalized Taylor problem in which a sheared magnetic field is subject to a time-dependent boundary perturbation oscillating at frequency ω0. By analyzing the asymptotic time response of the system, the theory demonstrates that the Alfvén resonance is due to the residues at the resonant poles, in the complex frequency plane, introduced by the boundary perturbation. Alfvén resonance transitions towards forced reconnection, described by the constant-psi regime for (normalized) times t≫S1/3, when the forcing frequency of the boundary perturbation is ω0≪S−1/3, allowing the coupling of the Alfvén resonances across the neutral line with the reconnecting mode, as originally suggested in Uberoi and Zweibel, (1999). Additionally, it is shown that even if forced reconnection develops for finite, albeit small, frequencies, the reconnection rate and reconnected flux are strongly reduced for frequencies ω0≫S−3/5.

Nonlinear interaction between double tearing mode and Kelvin–Helmholtz instability with different shear flows

The nonlinear interaction between the double tearing mode (DTM) and Kelvin–Helmholtz (KH) instabilities with different shear flow profiles has been numerically investigated via the use of a compressible magnetohydrodynamics (MHD) model. We focus on KH instabilities in weak and reversed magnetic shear plasmas with strong stabilizing effect of field line bending. Results show that KH instabilities coupled with DTMs occur in these plasmas and the KH mode dominates the instability dynamics, suggesting the crucial role of weak magnetic shear in the formation of high-mode harmonics. For symmetric flows, an asymmetric forced magnetic reconnection configuration is maintained during the growth phase, leading to interlocking of the modes. Additionally, this investigation of the DTM-KH instability interaction contributes to our understanding of the nonlinear reconnection mechanism in the regime of weak and reversed magnetic shear plasmas, which is relevant for astrophysical and fusion studies.

The Prominence Driven Forced Reconnection in the Solar Corona and Associated Plasma Dynamics

Abstract Using the multitemperature observations from SDO/AIA on 2019 December 30, we provide a signature of prominence driven forced magnetic reconnection in the corona and associated plasma dynamics from 09:20 UT to 10:38 UT. A hot prominence segment erupts with a speed of ≈21 km s−1 and destabilizes the entire prominence system. Thereafter, it rises upward in the north from 09:28 UT to 09:48 UT with a speed of 24 km s−1 . The eruptive prominence stretches overlying field lines upward with the speed of 27–28 km s−1, which further undergo the forced reconnection. The coronal plasma also flows southward with a speed of 7 km s−1, and both of these inflows trigger the reconnection at ≈09:48 UT. Thereafter, the eastward and westward magnetic channels are developed and separated. The east–west reorganization of the magnetic fields starts creating bidirectional plasma outflows toward the limb with their respective speeds of 28 and 37 km s−1. Their upper ends are diffused in the overlying corona, transporting another set of upflows with the speeds of ≈22 km and 19 km s−1. The multitemperature plasma (log T e = 6.0–7.2 K) evolves and elongates to a length of ≈105 km on the reorganized fields. The hot plasma and remaining prominence threads move from the reconnection region toward another segment of a prominence in the eastward direction. The prominence–prominence/loop interaction and associated reconnection generate jet-like eruptions with a speed of 178–183 km s−1. After the formation of the jet, the overlying magnetic channel disappears in the corona.

Quasi-linear theory of forced magnetic reconnection for the transition from the linear to the Rutherford regime

Using the in-viscid two-field reduced magneto-hydrodynamic (MHD) model, a new analytical theory is developed to unify the Hahm–Kulsrud–Taylor (HKT) linear solution and the Rutherford quasi-linear regime. Adopting a quasi-linear approach, we obtain a closed system of equations for plasma response in the Taylor problem. An integral form of an analytical solution is obtained for the forced magnetic reconnection, uniformly valid throughout the entire regimes from the HKT linear solution to the Rutherford quasi-linear solution. In particular, the quasi-linear effect can be described by a single coefficient , where and ψ c are the Lundquist number and amplitude of external magnetic perturbation, respectively. The HKT linear solution for the response can be recovered when the index K s → 0. On the other hand, the quasi-linear effect plays a key role in the island growth when K s ∼ 1. Our new analytical solution has also been compared with reduced MHD simulations with agreement.

On the Observations of Rapid Forced Reconnection in the Solar Corona

Abstract Using multiwavelength imaging observations from the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory on 2012 May 3, we present a novel physical scenario for the formation of a temporary X-point in the solar corona, where plasma dynamics are forced externally by a moving prominence. Natural diffusion was not predominant; however, a prominence driven inflow occurred first, forming a thin current sheet, thereafter enabling a forced magnetic reconnection at a considerably high rate. Observations in relation to the numerical model reveal that forced reconnection may rapidly and efficiently occur at higher rates in the solar corona. This physical process may also heat the corona locally even without establishing a significant and self-consistent diffusion region. Using a parametric numerical study, we demonstrate that the implementation of the external driver increases the rate of the reconnection even when the resistivity required for creating normal diffusion region decreases at the X-point. We conjecture that the appropriate external forcing can bring the oppositely directed field lines into the temporarily created diffusion region first via the plasma inflows as seen in the observations. The reconnection and related plasma outflows may occur thereafter at considerably larger rates.

Mode penetration induced by transient magnetic perturbations

Three dimensional magnetic fields in tokamaks can induce forced magnetic reconnection (FMR) and produce magnetic islands on resonant surfaces. Conventional analytic solutions to FMR focus on describing the time asymptotic state given a steady-state field error. The focus of this work is to understand the nonlinear dynamics of mode penetration, an evolution from a high-slip, flow-screened metastable equilibrium into a low-slip, field-penetrated metastable equilibrium. In this work, we extend previous work by incorporating a temporally varying external magnetic field as a simple model for a magnetohydrodynamic (MHD) event that produces resonant magnetic perturbations. Proof-of-principle, extended-MHD, NIMROD computations vary parameterizations of the transient external perturbation to probe the threshold for mode penetration. We test these computational results against analytical theory that captures the temporal evolution properties of the electromagnetic and viscous forces during and after a transient. We find qualitative agreement between computational and analytical results. However, computational tools are necessary to accurately capture the threshold conditions for mode penetration induced by an MHD transient.

Erratum: “Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD” [Phys. Plasmas 24, 052508 (2017)

Erratum: “Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD” [Phys. Plasmas <b>24</b>, 052508 (2017)

Particle acceleration in relativistic magnetic flux-merging events

Using analytical and numerical methods (fluid and particle-in-cell simulations) we study a number of model problems involving merger of magnetic flux tubes in relativistic magnetically dominated plasma. Mergers of current-carrying flux tubes (exemplified by the two-dimensional ‘ABC’ structures) and zero-total-current magnetic flux tubes are considered. In all cases regimes of spontaneous and driven evolution are investigated. We identify two stages of particle acceleration during flux mergers: (i) fast explosive prompt X-point collapse and (ii) ensuing island merger. The fastest acceleration occurs during the initial catastrophic X-point collapse, with the reconnection electric field of the order of the magnetic field. During the X-point collapse, particles are accelerated by charge-starved electric fields, which can reach (and even exceed) values of the local magnetic field. The explosive stage of reconnection produces non-thermal power-law tails with slopes that depend on the average magnetization $\unicode[STIX]{x1D70E}$. For plasma magnetization $\unicode[STIX]{x1D70E}\leqslant 10^{2}$ the spectrum power-law index is $p&gt;2$; in this case the maximal energy depends linearly on the size of the reconnecting islands. For higher magnetization, $\unicode[STIX]{x1D70E}\geqslant 10^{2}$, the spectra are hard, $p&lt;2$, yet the maximal energy $\unicode[STIX]{x1D6FE}_{\text{max}}$ can still exceed the average magnetic energy per particle, ${\sim}\unicode[STIX]{x1D70E}$, by orders of magnitude (if $p$ is not too close to unity). The X-point collapse stage is followed by magnetic island merger that dissipates a large fraction of the initial magnetic energy in a regime of forced magnetic reconnection, further accelerating the particles, but proceeds at a slower reconnection rate.

Forced magnetic reconnection

This is a tutorial-style selective review explaining basic concepts of forced magnetic reconnection. It is based on a celebrated model of forced reconnection suggested by J. B. Taylor. The standard magnetohydrodynamic (MHD) theory of this process has been pioneered by Hahm &amp; Kulsrud (Phys. Fluids, vol. 28, 1985, p. 2412). Here we also discuss several more recent developments related to this problem. These include energetics of forced reconnection, its Hall-mediated regime, and nonlinear effects with the associated onset of the secondary tearing (plasmoid) instability.

Taylor problem and onset of plasmoid instability in the Hall-magnetohydrodynamics

A well-known Taylor problem in the theory of forced magnetic reconnection is investigated in the framework of the Hall-Magnetohydrodynamics. In the first part of the paper, we deal with the linear theory of the Hall-mediated forced reconnection. Then, in the second part, these results are used for demonstrating how the secondary tearing (plasmoid) instability can develop in the course of this process.

Nonlinear modeling of forced magnetic reconnection in slab geometry with NIMROD

The nonlinear, extended-magnetohydrodynamic (MHD) code NIMROD is benchmarked with the theory of time-dependent forced magnetic reconnection induced by small resonant fields in slab geometry in the context of visco-resistive MHD modeling. Linear computations agree with time-asymptotic, linear theory of flow screening of externally applied fields. The inclusion of flow in nonlinear computations can result in mode penetration due to the balance between electromagnetic and viscous forces in the time-asymptotic state, which produces bifurcations from a high-slip state to a low-slip state as the external field is slowly increased. We reproduce mode penetration and unlocking transitions by employing time-dependent externally applied magnetic fields. Mode penetration and unlocking exhibit hysteresis and occur at different magnitudes of applied field. We also establish how nonlinearly determined flow screening of the resonant field is affected by the square of the magnitude of the externally applied field. These results emphasize that the inclusion of nonlinear physics is essential for accurate prediction of the reconnected field in a flowing plasma.

Hyper-resistive forced magnetic reconnection

We study Taylor's model of forced magnetic reconnection mediated by plasma hyper-resistivity. This includes both linear and nonlinear regimes of the process. It is shown how the onset of plasmoid instability occurs in the strongly nonlinear regime of forced reconnection.

Nonlinear regimes of forced magnetic reconnection

This letter presents a self-consistent description of nonlinear forced magnetic reconnection in Taylor's model of this process. If external boundary perturbation is strong enough, nonlinearity in the current sheet evolution becomes important before resistive effects come into play. This terminates the current sheet shrinking that takes place at the linear stage and brings about its nonlinear equilibrium with a finite thickness. Then, in theory, this equilibrium is destroyed by a finite plasma resistivity during the skin-time, and further reconnection proceeds in the Rutherford regime. However, realization of such a scenario is unlikely because of the plasmoid instability, which is fast enough to develop before the transition to the Rutherford phase occurs. The suggested analytical theory is entirely different from all previous studies and provides proper interpretation of the presently available numerical simulations of nonlinear forced magnetic reconnection.

Phase diagrams of forced magnetic reconnection in Taylor’s model

Recent progress in the understanding of how externally driven magnetic reconnection evolves is organized in terms of parameter space diagrams. These diagrams are constructed using four pivotal dimensionless parameters: the Lundquist number $S$, the magnetic Prandtl number $P_{m}$, the amplitude of the boundary perturbation $\hat{{\it\Psi}}_{0}$, and the perturbation wave number $\hat{k}$. This new representation highlights the parameter regions of a given system in which the magnetic reconnection process is expected to be distinguished by a specific evolution. Contrary to previously proposed phase diagrams, the diagrams introduced here take into account the dynamical evolution of the reconnection process and are able to predict slow or fast reconnection regimes for the same values of $S$ and $P_{m}$, depending on the parameters that characterize the external drive, which have not been considered until now. These features are crucial to understanding the onset and evolution of magnetic reconnection in diverse physical systems.

Long-lived impurity-ion snakes in the EAST ELM-free H-mode Sawtoothing plasma

Two types of long-lived impurity-ion snakes (LLSs) including the ideal-like kink mode which damps before the large sawtooth crash, termed sawtooth-free LLSs (SF-LLSs) and complex LLSs (C-LLSs), which coexist with compound sawtooth and final damping after sawtooth crash were observed in EAST ELM-free H-mode sawtoothing plasma. These LLSs have an m = 1 structure, accompanied by several harmonic modes (m = 2, m = 3...). There is a slight frequency-chirping behavior of the LLS. Similar with the typical sawtooth crash phase, a large crescent-shaped helical island-like structure in the core region of the C-LLSs was visible after the major crash of the coexisting compound sawtooth. The strong coupling of the C-LLSs and the 2/1 tearing mode (TM) can trigger a neo-classical tearing mode (NTM) due to a forced magnetic reconnection.

Extended theory of the Taylor problem in the plasmoid-unstable regime

A fundamental problem of forced magnetic reconnection has been solved taking into account the plasmoid instability of thin reconnecting current sheets. In this problem, the reconnection is driven by a small amplitude boundary perturbation in a tearing-stable slab plasma equilibrium. It is shown that the evolution of the magnetic reconnection process depends on the external source perturbation and the microscopic plasma parameters. Small perturbations lead to a slow nonlinear Rutherford evolution, whereas larger perturbations can lead to either a stable Sweet-Parker-like phase or a plasmoid phase. An expression for the threshold perturbation amplitude required to trigger the plasmoid phase is derived, as well as an analytical expression for the reconnection rate in the plasmoid-dominated regime. Visco-resistive magnetohydrodynamic simulations complement the analytical calculations. The plasmoid formation plays a crucial role in allowing fast reconnection in a magnetohydrodynamical plasma, and the presented results suggest that it may occur and have profound consequences even if the plasma is tearing-stable.

On transition from Alfvén resonance to forced magnetic reconnection

We revisit the transition from Alfvén resonance to forced magnetic reconnection with a focus on the property of their singularities. As the driven frequency tends to zero, the logarithmic singularity of Alfvén resonance shifts to the power-law singularity of forced reconnection, due to merging of the two resonance layers. The transition criterion depends on either kinetic effects or dissipations that resolve the singularity. As an example, a small but finite resistivity η is introduced to investigate the transition process. The transition threshold is then obtained as the driven frequency reaches a level of ∼O((η/k)1/3).

Physics of forced magnetic reconnection in coaxial helicity injection experiments in National Spherical Torus Experiment

We numerically examine the physics of fast flux closure in transient coaxial helicity injection (CHI) experiments in National Spherical Torus Experiment (NSTX). By performing resistive Magnetohydrodynamics (MHD) simulations with poloidal injector coil currents held constant in time, we find that closed flux surfaces are formed through forced magnetic reconnection. Through a local Sweet-Parker type reconnection with an elongated current sheet in the injector region, closed flux surfaces expand in the NSTX global domain. Simulations demonstrate outflows approaching poloidally Alfvénic flows and reconnection times consistent with the Sweet-Parker model. Critical requirements for magnetic reconnection and flux closure are studied in detail. These primary effects, which are magnetic diffusivity, injector flux, injector flux footprint width, and rate of injector voltage reduction, are simulated for transient CHI experiments. The relevant time scales for effective reconnection are τV&amp;lt;τrec≈τAS(1+Pm)1/4&amp;lt;τR, where τV is the time for the injector voltage reduction, τA is the poloidal Alfvén transit time, τR is the global resistive diffusion time, and Pm and S are Prandtl and Lundquist numbers.

Seed island formation by forced magnetic reconnection

Neoclassical tearing modes observed in experiments often grow from seed magnetic islands induced by triggers like sawteeth. The formation of seed islands is studied in this paper using both the reduced MHD and two-fluid equations, with the trigger being modelled by externally applied resonant magnetic perturbations. In the linear phase the growth rate of the driven mode is found to be the same as that of the trigger. A slowly growing trigger drives a tearing mode, while a fast one drives a kink-like mode, which becomes a tearing mode later when the trigger's growth slows down. A finite ion sound Larmor radius (ion Larmor radius by using electron temperature) and electron inertia are found to lead to a larger seed island for a given external perturbation. The electron diamagnetic drift and plasma rotation, if increasing the relative rotation between the trigger and the driven mode, decrease the seed island width.

MICROFLARE ACTIVITY DRIVEN BY FORCED MAGNETIC RECONNECTION

High cadence, multiwavelength, optical observations of a solar active region are presented, obtained with the Swedish Solar Telescope. Two magnetic bright points are seen to separate in opposite directions at a constant velocity of 2.8km/s. After a separation distance of approximately 4400km is reached, multiple Ellerman bombs are observed in both H-alpha and Ca-K images. As a result of the Ellerman bombs, periodic velocity perturbations in the vicinity of the magnetic neutral line, derived from simultaneous MDI data, are generated with amplitude +/- 6km/s and wavelength 1000km. The velocity oscillations are followed by an impulsive brightening visible in H-alpha and Ca-K, with a peak intensity enhancement of 63%. We interpret these velocity perturbations as the magnetic field deformation necessary to trigger forced reconnection. A time delay of approximately 3min between the H-alpha wing and Ca-K observations indicate that the observed magnetic reconnection occurs at a height of 200km above the solar surface. These observations are consistent with theoretical predictions and provide the first observational evidence of microflare activity driven by forced magnetic reconnection.