Magnetic Island Merging Research Articles

Magnetic island merging: Two-dimensional MHD simulation and test-particle modeling

In an idealized system where four current channels interact in a two-dimensional periodic setting, we follow the detailed evolution of current sheets (CSs) forming in between the channels, as a result of a large-scale merging. A central X-point collapses and a gradually extending CS marks the site of continuous magnetic reconnection. Using grid-adaptive, non-relativistic, resistive magnetohydrodynamic (MHD) simulations, we establish that slow, near-steady Sweet-Parker reconnection transits to a chaotic, multi-plasmoid fragmented state, when the Lundquist number exceeds about ten to the fourth power, well in the range of previous studies on plasmoid instability. The extreme resolution employed in the MHD study shows significant magnetic island substructures. With relativistic test-particle simulations, we explore how charged particles can be accelerated in the vicinity of an O-point, either at embedded tiny-islands within larger "monster"-islands or near the centers of monster-islands. While the planar MHD setting artificially causes strong acceleration in the ignored third direction, it also allows for the full analytic study of all aspects leading to the acceleration and the in-plane-projected trapping of particles in the vicinities of O-points. Our analytic approach uses a decomposition of the particle velocity in slow- and fast-changing components, akin to the Reynolds decomposition in turbulence studies. Our analytic description is validated with several representative test-particle simulations. We find that after an initial non-relativistic motion throughout a monster island, particles can experience acceleration in the vicinity of an O-point beyond 0.7c, at which speed the acceleration is at its highest efficiency

The role of guide field in magnetic reconnection driven by island coalescence

A number of studies have considered how the rate of magnetic reconnection scales in large and weakly collisional systems by the modelling of long reconnecting current sheets. However, this set-up neglects both the formation of the current sheet and the coupling between the diffusion region and a larger system that supplies the magnetic flux. Recent studies of magnetic island merging, which naturally include these features, have found that ion kinetic physics is crucial to describe the reconnection rate and global evolution of such systems. In this paper, the effect of a guide field on reconnection during island merging is considered. In contrast to the earlier current sheet studies, we identify a limited range of guide fields for which the reconnection rate, outflow velocity, and pile-up magnetic field increase in magnitude as the guide field increases. The Hall-MHD fluid model is found to reproduce kinetic reconnection rates only for a sufficiently strong guide field, for which ion inertia breaks the frozen-in condition and the outflow becomes Alfvénic in the kinetic system. The merging of large islands occurs on a longer timescale in the zero guide field limit, which may in part be due to a mirror-like instability that occurs upstream of the reconnection region.

DIFFUSIVE SHOCK ACCELERATION AND RECONNECTION ACCELERATION PROCESSES

Shock waves, as shown by simulations and observations, can generate high levels of downstream vortical turbulence, including magnetic islands. We consider a combination of diffusive shock acceleration (DSA) and downstream magnetic-island-reconnection-related processes as an energization mechanism for charged particles. Observations of electron and ion distributions downstream of interplanetary shocks and the heliospheric termination shock (HTS) are frequently inconsistent with the predictions of classical DSA. We utilize a recently developed transport theory for charged particles propagating diffusively in a turbulent region filled with contracting and reconnecting plasmoids and small-scale current sheets. Particle energization associated with the anti-reconnection electric field, a consequence of magnetic island merging, and magnetic island contraction, are considered. For the former only, we find that (i) the spectrum is a hard power law in particle speed, and (ii) the downstream solution is constant. For downstream plasmoid contraction only, (i) the accelerated spectrum is a hard power law in particle speed; (ii) the particle intensity for a given energy peaks downstream of the shock, and the distance to the peak location increases with increasing particle energy, and (iii) the particle intensity amplification for a particular particle energy, f(x,c/c_0)/f(0,c/c_0), is not 1, as predicted by DSA, but increases with increasing particle energy. The general solution combines both the reconnection-induced electric field and plasmoid contraction. The observed energetic particle intensity profile observed by Voyager 2 downstream of the HTS appears to support a particle acceleration mechanism that combines both DSA and magnetic-island-reconnection-related processes.

Particle acceleration by combined diffusive shock acceleration and downstream multiple magnetic island acceleration

As a consequence of the evolutionary conditions [28; 29], shock waves can generate high levels of downstream vortical turbulence. Simulations [32-34] and observations [30; 31] support the idea that downstream magnetic islands (also called plasmoids or flux ropes) result from the interaction of shocks with upstream turbulence. Zank et al. [18] speculated that a combination of diffusive shock acceleration (DSA) and downstream reconnection-related effects associated with the dynamical evolution of a “sea of magnetic islands” would result in the energization of charged particles. Here, we utilize the transport theory [18; 19] for charged particles propagating diffusively in a turbulent region filled with contracting and reconnecting plasmoids and small-scale current sheets to investigate a combined DSA and downstream multiple magnetic island charged particle acceleration mechanism. We consider separately the effects of the anti-reconnection electric field that is a consequence of magnetic island merging [17], and magnetic island contraction [14]. For the merging plasmoid reconnection- induced electric field only, we find i) that the particle spectrum is a power law in particle speed, flatter than that derived from conventional DSA theory, and ii) that the solution is constant downstream of the shock. For downstream plasmoid contraction only, we find that i) the accelerated particle spectrum is a power law in particle speed, flatter than that derived from conventional DSA theory; ii) for a given energy, the particle intensity peaks downstream of the shock, and the peak location occurs further downstream of the shock with increasing particle energy, and iii) the particle intensity amplification for a particular particle energy, f(x, c/c0)/f(0, c/c0), is not 1, as predicted by DSA theory, but increases with increasing particle energy. These predictions can be tested against observations of electrons and ions accelerated at interplanetary shocks and the heliospheric termination shock.

SMALL-SCALE MAGNETIC ISLANDS IN THE SOLAR WIND AND THEIR ROLE IN PARTICLE ACCELERATION. I. DYNAMICS OF MAGNETIC ISLANDS NEAR THE HELIOSPHERIC CURRENT SHEET

Increases of ion fluxes in the keV-MeV range are sometimes observed near the heliospheric current sheet (HCS) during periods when other sources are absent. These resemble solar energetic particle (SEP) events, but the events are weaker and apparently local. Conventional explanations based on either shock acceleration of charged particles or particle acceleration due to magnetic reconnection at interplanetary current sheets are not persuasive. We suggest instead that recurrent magnetic reconnection occurs at the HCS and smaller current sheets in the solar wind (Zharkova & Khabarova 2012), of which a consequence is particle energization by the dynamically evolving secondary current sheets and magnetic islands (Zank et al. 2014; Drake et al. 2006a). The effectiveness of the trapping and acceleration process associated with magnetic islands depends in part on the topology of the HCS. We show that the HCS possesses ripples superimposed on the large-scale flat or wavy structure. We conjecture that the ripples can efficiently confine plasma and provide tokamak-like conditions that are favorable for the appearance of small-scale magnetic islands that merge and/or contract. Particles trapped in the vicinity of merging islands and experiencing multiple small-scale reconnection events are accelerated by the induced electric field, and experience first-order Fermi acceleration in contracting magnetic islands (Zank et al. 2014). We present multi-spacecraft observations of magnetic island merging and particle energization in the absence of other sources, providing support for theory and simulations that show particle energization by reconnection related processes of magnetic island merging and contraction.

PARTICLE ACCELERATION VIA RECONNECTION PROCESSES IN THE SUPERSONIC SOLAR WIND

An emerging paradigm for the dissipation of magnetic turbulence in the supersonic solar wind is via localized small-scale reconnection processes, essentially between quasi-2D interacting magnetic islands. Charged particles trapped in merging magnetic islands can be accelerated by the electric field generated by magnetic island merging and the contraction of magnetic islands. We derive a gyrophase-averaged transport equation for particles experiencing pitch-angle scattering and energization in a super-Alfvenic flowing plasma experiencing multiple small-scale reconnection events. A simpler advection-diffusion transport equation for a nearly isotropic particle distribution is derived. The dominant charged particle energization processes are (1) the electric field induced by quasi-2D magnetic island merging and (2) magnetic island contraction. The magnetic island topology ensures that charged particles are trapped in regions where they experience repeated interactions with the induced electric field or contracting magnetic islands. Steady-state solutions of the isotropic transport equation with only the induced electric field and a fixed source yield a power-law spectrum for the accelerated particles with index α = –(3 + M{sub A} )/2, where M{sub A} is the Alfven Mach number. Considering only magnetic island contraction yields power-law-like solutions with index –3(1 + τ {sub c}/(8τ{sub diff})), where τ {sub c}/τ{sub diff} is themore » ratio of timescales between magnetic island contraction and charged particle diffusion. The general solution is a power-law-like solution with an index that depends on the Alfven Mach number and the timescale ratio τ{sub diff}/τ {sub c}. Observed power-law distributions of energetic particles observed in the quiet supersonic solar wind at 1 AU may be a consequence of particle acceleration associated with dissipative small-scale reconnection processes in a turbulent plasma, including the widely reported c {sup –5} (c particle speed) spectra observed by Fisk and Gloeckler and Mewaldt et al.« less

Coalescence of Macroscopic Magnetic Islands and Electron Acceleration from STEREO Observation

Spacecraft data on immense solar coronal mass ejection (CME) combined with numerical magnetohydrodynamic simulations reveals for the first time both the merging of magnetic islands in a CME's trailing current sheet and associated electron acceleration.

NUMERICAL EXPERIMENTS ON FINE STRUCTURE WITHIN RECONNECTING CURRENT SHEETS IN SOLAR FLARES

We perform resistive magnetohydrodynamic simulations to study the internal structure of current sheets that form during solar eruptions. The simulations start with a vertical current sheet in mechanical and thermal equilibrium that separates two regions of the magnetic field with opposite polarity which are line-tied at the lower boundary representing the photosphere. Reconnection commences gradually due to an initially imposed perturbation, but becomes faster when plasmoids form and produce small-scale structures inside the current sheet. These structures include magnetic islands or plasma blobs flowing in both directions along the sheet, and X-points between pairs of adjacent islands. Among these X-points, a principal one exists at which the reconnection rate reaches maximum. A fluid stagnation point (S-point) in the sheet appeared where the reconnection outflow bifurcates. The S-point and the principal X-point (PX-point) are not co-located in space though they are very close to one another. Their relative positions alternate as reconnection progresses and determine the direction of motion of individual magnetic islands. Newly formed islands move upward if the S-point is located above the PX-point, and downward if the S-point is below the PX-point. Merging of magnetic islands was observed occasionally between islands moving in the same direction. Reconnected plasma flow was observed to move faster than blobs nearby.

Merging of magnetic islands as an efficient accelerator of electrons

In a thin elongated current sheet, it is likely that more than one X-line forms and thus multiple magnetic islands are produced. The islands are then subject to merging. By simulating such a case with a two-dimensional full-particle code, we show that a merger forming a large island produces the most energetic electron population in the system. By setting the lateral extent of the simulation box to be as large as ∼100 ion inertial lengths, we introduce many (16) small islands in the initial thin current sheet (∼1 ion inertial length thickness). Merging of these islands proceeds to leave only two islands in the system. Then, strong electron acceleration is seen upon the final merger that produces the single island in the large simulation box. The most energetic electrons in the system are accelerated at the merging line. The merging line acceleration dominates because the reverse-reconnection facilitating the final merger is in such a strongly driven manner that the associated electric field is an order of magnitude larger than those available upon normal reconnection. Combining the results from additional runs enables us to obtain a scaling law, which suggests a non-negligible role played by merging lines in the observed electron acceleration phenomena.

A model of solar flares based on arcade field reconnection and merging of magnetic islands

Solar flares are intense, abrupt releases of energy in the solar corona. In the impulsive phase of a flare, the intensity of hard x-ray emission reaches a sharp peak indicating the highest reconnection rate. It is often observed that an x-ray emitting plasma ejecta (plasmoid) is launched before the impulsive phase and accelerated throughout the phase. Thus, the plasmoid ejection may not be an effect of fast magnetic reconnection as conventionally assumed, but a cause of fast reconnection. Based on resistive magnetohydrodynamic simulations, a solar flare model is presented, which can explain these observational characteristics of flares. In the model, merging of a newly generated magnetic island and a preexisting island results in stretching and thinning of a current sheet, in which fast magnetic reconnection is induced. Recurrence of homologous flares naturally arises in this model. Mechanisms of magnetic island formation are also discussed.