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In this paper, we performed magnetohydrodynamics numerical experiments to look into the dynamic behaviour of the current sheet (CS) between the coronal mass ejection (CME) and the associated solar flare, especially the CS oscillation and plasmoid motions in coronal conditions. During the evolution, the disrupting magnetic configuration becomes asymmetric first in the buffer region at the bottom of the CME bubble. The Rayleigh−Taylor instability in the buffer region and the deflected motion of the plasma driven by the termination shock at the bottom of the CME bubble cause the buffer region to oscillate around the y-axis. The local oscillation propagates downwards through the CS, prompting an overall CS oscillation. As the buffer region grows, the oscillation period becomes longer, increasing from about 30 s to about 16 min. Meanwhile, there is another separated oscillation with a period between 0.25 and 1.5 min in the cusp region of the flare generated by velocity shearing. The tearing mode instability yields formations of plasmoids inside the CS. The motions of all the plasmoids observed in the experiment accelerate, which implies that the large-scale CME/flare CS itself in the true eruptive event is filled with the diffusion region according the the standard theory of magnetic reconnection.

We attempt to model magnetic reconnection during the two-ribbon flare in the gravitationally stratified solar atmosphere with the Lundquist number of $S=10^6$ using 2D simulations. We found that the tearing mode instability leads to the inhomogeneous turbulence inside the reconnecting current sheet (CS) and invokes the fast phase of reconnection. Fast reconnection brings an extra dissipation of magnetic field which enhances the reconnection rate in an apparent way. The energy spectrum in the CS shows the power-law pattern and the dynamics of plasmoids governs the associated spectral index. We noticed that the energy dissipation occurs at a scale $l_{ko}$ of 100-200~km, and the associated CS thickness ranges from 1500 to 2500~km, which follows the Taylor scale $l_T=l_{ko} S^{1/6}$. The termination shock(TS) appears in the turbulent region above flare loops, which is an important contributor to heating flare loops. Substantial magnetic energy is converted into both kinetic and thermal energies via TS, and the cumulative heating rate is greater than the rate of the kinetic energy transfer. In addition, the turbulence is somehow amplified by TS, of which the amplitude is related to the local geometry of the TS., 22 pages, 10 figures; Accepted for publication in Research in Astronomy and Astrophysics

This paper describes a numerical study of the magnetic reconnection between two magnetic fields of opposite polarity. The magnetic fields are created by an electric current in a coil connected to two metal disks. One of the disks is irradiated by a strong laser beam, whereby large amounts of free electrons flow toward the other disk, constituting a closed circuit for the electric current flowing through the coil. Two parallel coils are arranged to connect the two disks, and irradiation of the laser beam on one disk results in parallel electric currents in the two coils, inducing two magnetic fields of opposite polarity in the region between them. The magnetic reconnection that occurs in this region is three-dimensional. This three-dimensional magnetic reconnection is investigated via magnetohydrodynamic numerical simulations. The characteristics of the Petschek-type magnetic reconnection are observed for the first time in such numerical simulations of magnetic reconnection. Changes in the shape of the magnetic field lines form the boundary of the dissipation region and the outflow region. Moreover, the thermal plasma generated by reconnection is strongly confined to the region where the reconnecting current sheet and the slow-mode shock are located, and no leaks of thermal plasma are observed. Comparisons with existing laboratory experiment results confirm that our numerical simulations reproduce the experimental outcomes and provide reasonable explanations for the results observed in laboratories.

Electric field induced in magnetic reconnection is an efficient mechanism for generating energetic particles, but the detailed role it plays is still an open question in solar flares. In this work, accelerations of particles in an evolving reconnecting current sheet are investigated via the test-particle approach, and the electromagnetic field is taken in a self-consistent fashion from a 2.5D numerical experiment for the magnetic reconnection process in the corona. The plasma instabilities like the tearing mode in the current sheet produce magnetic islands in the sheet, and island merging occurs as well. For the motion of the magnetic island, it yields the occurrence of the opposite electric field at both endpoints of the island; hence, tracking the accelerated particles around magnetic islands suggests that the parallel acceleration does not apparently impact the energy gain of particles, but the perpendicular acceleration does. Furthermore, our results indicate that the impact of the guide field on the trajectory of accelerated particles in a more realistic electromagnetic configuration works only on those particles that are energetic enough. The energy spectra of both species show a single power-law shape. The higher-energy component of the power-law spectrum results from the particles that are trapped in the current sheet, while the escaped and partly trapped particles contribute to the lower-energy component of the spectrum. The evolution of the spectrum shows a soft-hard-soft pattern that has been observed in flares.

We performed 2D magnetohydrodynamical numerical experiments to study the response of the coronal magnetic configuration to the newly emerging magnetic flux. The configuration includes an electric-current-carrying flux rope modeling the prominence floating in the corona and the background magnetic field produced by two separated magnetic dipoles embedded in the photosphere. Parameters for one dipole are fixed in space and time to model the quiet background, and those for another one are time dependent to model the new flux. These numerical experiments duplicate important results of the analytic solution but also reveal new results. Unlike previous works, the configuration here possesses no symmetry, and the flux rope could move in any direction. The non-force-free environment causes the deviation of the flux rope equilibrium in the experiments from that determined in the analytic solution. As the flux rope radius decreases, the equilibrium could be found, and it evolves quasi-statically until the flux rope reaches the critical location at which the catastrophe occurs. As the radius increases, no equilibrium exists at all. During the catastrophe, two current sheets form in different ways. One forms as the surrounding closed magnetic field is stretched by the catastrophe, and another one forms as the flux rope squeezes the magnetic field nearby. Although reconnection happens in both the current sheets, it erases the first one quickly and enhances the second simultaneously. These results indicate the occurrence of the catastrophe in asymmetric and non-force-free environment, and the non-radial motion of the flux rope following the catastrophe.

We review and discuss insights on ideal magnetohydrodynamic (MHD) instabilities that can play a role in destabilizing solar coronal flux rope structures. For single flux ropes, failed or actual eruptions may result from internal or external kink evolutions, or from torus unstable configurations. We highlight recent findings from 3D magnetic field reconstructions and simulations where kink and torus instabilities play a prominent role. For interacting current systems, we critically discuss different routes to coronal dynamics and global eruptions, due to current channel coalescence or to tilt-kink scenarios. These scenarios involve the presence of two nearby current channels and are clearly distinct from the popular kink or torus instability. Since the solar corona is pervaded with myriads of magnetic loops—creating interacting flux ropes typified by parallel or antiparallel current channels as exemplified in various recent observational studies—coalescence or tilt-kink evolutions must be very common for destabilizing adjacent flux rope systems. Since they also evolve on ideal MHD timescales, they may well drive many sympathetic eruptions witnessed in the solar corona. Moreover, they necessarily lead to thin current sheets that are liable to reconnection. We review findings from 2D and 3D MHD simulations for tilt and coalescence evolutions, as well as on particle acceleration aspects derived from computed charged particle motions in tilt-kink disruptions and coalescing flux ropes. The latter were recently studied in two-way coupled kinetic-fluid models, where the complete phase-space information of reconnection is incorporated.

Based on the catastrophe model of the solar eruption, we explore the disturbances caused by solar eruptions via numerical experiments, with special attention given to large-scale waves. In addition to the phenomena shown by previous works, a new structure known as the plasma pile-up is also seen. As the disrupting magnetic structure moves outwards, a fast-mode shock is driven ahead of it. The fast-mode shock expands sideways when propagating forward and evolves to a crescent shape. Eventually the two ends of the crescent touch the bottom boundary and cause various types of disturbance behind the shock, including a shock echo. A plasma pile-up region produced by plasma accumulation behind the echo is associated with this. This is a brand new phenomenon that was not reported previously. Two features of the pile-up region draw our attention: first, its height from the bottom boundary is similar to that of some extreme ultraviolet (EUV) waves and second, its velocity is about one-third of the velocity of the fast-mode shock along the low layer of the atmosphere, which is believed to be the location of the Moreton wavefront. This suggests that the pile-up may be a source of EUV waves as well. According to our numerical results, we also synthesize the 'observed' Solar Dynamics Observatory (SDO) Atmospheric Imaging Assembly (AIA) images in different wavebands. The results demonstrate that the characteristics of the EUV waves 'observed' in different bands are indeed different, which is consistent with the true observational results regarding EUV waves in a certain sense.

Magnetohydrodynamic (MHD) turbulence plays an important role for the fast energy release and wave structures related to coronal mass ejections (CMEs). The CME plasma has been observed to be strongly heated during solar eruptions, but the heating mechanism is not understood. In this paper, we focus on the hot, dense region at the bottom of the CME and the generation of coronal wave trains therein using a high-resolution 2.5D MHD simulation. Our results show that the interaction between the tearing current sheet and the turbulence, including the termination shocks (TSs) at the bottom of the CME, can make a significant contribution to heating the CME, and the heating rate in this region is found to be greater than the kinetic energy transfer rate. Also, the turbulence can be somewhat amplified by the TSs. The compression ratio of the TS under the CME can exceed 4 due to thermal conduction, but such a strong TS is hardly detectable in all Solar Dynamics Observatory/Atmospheric Imaging Assembly bands. And turbulence is an indispensable source for the periodic generation of coronal wave trains around the CME.

Anisotropic thermal conduction plays an important role in determining the structure of the hot plasma in the solar corona. When hot plasma appears, the conductivity rises with temperature and becomes highly nonlinear. Explicit solvers for parabolic problems often lead to much smaller time-steps limited by a Courant–Friedrichs–Lewy (CFL) condition in comparison with hyperbolic Magnetohydrodynamics (MHD) equations. In this work, we present a pseudo-linear, directionally-split, semi-implicit method allowing for large time-steps as well as the optimized parallelization algorithm, integrated with the MHD solver. Our scheme can perfectly preserve the monotonicity and the geometry of shocks and discontinuities in complex MHD problems. Two sets of numerical tests show that an increase in time step of ∼ 600 can be easily achieved with an acceptable error by our scheme compared to explicit methods, and the use of large time-steps can still follow fast dynamic processes reliably. In addition, the extendibility studies have proven that the associated parallel efficiency is comparably high. This method is also useful for any kind of time-dependent conductivity problems for the solar applications in the future.

Magnetic reconnection plays a critical role in energy conversion during solar eruptions. This paper presents a set of magnetohydrodynamic experiments for the magnetic reconnection process in a current sheet (CS) formed in the wake of the rising flux rope. The eruption results from the loss of equilibrium in a magnetic configuration that includes a current-carrying flux rope, representing a pre-existing filament. In order to study the fine structure and micro processes inside the CS, mesh refinement is used to reduce the numerical diffusion. We start with a uniform, explicitly defined resistivity which results in a Lundquist number S = 10(4) in the vicinity of CS. The use of mesh refinement allows the simulation to capture high-resolution features such as plasmoids from the tearing mode and plasmoid instability regions of turbulence and slow-mode shocks. Inside the CS, magnetic reconnection goes through the Sweet-Parker and the fractal stages, and eventually displays a time-dependent Petschek pattern. Our results support the concept of fractal reconnection suggested by Shibata et al. and Shibata & Tanuma, and also suggest that the CS evolves through Sweet-Parker reconnection prior to the fast reconnection stage. For the first time, the detailed features and/or fine structures inside the coronal mass ejection/flare CS in the eruption were investigated in this work.

Despite extensive research on various global waves in solar eruptions, debate continues on the intrinsic nature of them. In this work, we performed numerical experiments of the coronal mass ejection with emphases on the associated large-scale MHD waves. A fast-mode shock forms in front of the flux rope during the eruption with a dimming region following it, and the development of a three-component structure of the ejecta is observed. At the flank of the flux rope, the slow-mode shock and the velocity vortices are also invoked. The dependence of the eruption energetics on the strength of the background field and the coronal plasma density distribution is apparent: the stronger the background field is, and/or the lower the coronal plasma density is, the more energetic the eruption is. In the lower Alfv,n speed environment, the slow mode shock and the large scale velocity vortices may be the source of the EIT wave. In the high Alfv,n speed environment, on the other hand, the echo due to the reflection of the fast shock on the bottom boundary could be so strong that its interaction with the slow mode shock and the velocity vortices produces the second echo propagating downward and causing the secondary disturbance to the boundary surface. We suggest that this second echo, together with the slow shock and the velocity vortices, could constitute a possible candidate of the source for the EIT wave.

In this paper, we study the energy conversion and spectra in a corona current sheet by 2.5-dimensional MHD numerical simulations. Numerical results show that many Petschek-like fine structures with slow-mode shocks mediated by plasmoid instabilities develop during the magnetic reconnection process. The termination shocks can also be formed above the primary magnetic island and at the head of secondary islands. These shocks play important roles in generating thermal energy in a corona current sheet. For a numerical simulation with initial conditions close to the solar corona environment, the ratio of the generated thermal energy to the total dissipated magnetic energy is around $1/5$ before secondary islands appear. After secondary islands appear, the generated thermal energy starts to increase sharply and this ratio can reach a value about $3/5$. In an environment with a relatively lower plasma density and plasma $\beta$, the plasma can be heated to a much higher temperature. After secondary islands appear, the one dimensional energy spectra along the current sheet do not behave as a simple power law and the spectrum index increases with the wave number. The average spectrum index for the magnetic energy spectrum along the current sheet is about $1.8$. The two dimensional spectra intuitively show that part of the high energy is cascaded to large $kx$ and $ky$ space after secondary islands appear. The plasmoid distribution function calculated from numerical simulations behaves as a power law closer to $f(\psi) \sim \psi^{-1}$ in the intermediate $\psi$ regime. By using $\eta_{eff} = v_{inflow}\cdot L$, the effective magnetic diffusivity is estimated about $10^{11}\sim10^{12}$~m$^2$\,s$^{-1}$., Comment: arXiv admin note: text overlap with arXiv:1011.4035 by other authors

In this letter, we present a spectacular eruptive flare (X8.2) associated with a coronal mass ejection (CME) on 2017 September 10 at the west limb of the Sun. A flux rope eruption is followed by the inflow, the formation of a current sheet and a cusp structure, which were simultaneously observed during the occurrence of this flare. The hierarchical layers of the cusp-shaped structure are well observed in 131 \AA\ observation. The scenario that can be created from these observations is very consistent with the predictions of some eruptive models. Except for the characteristics mentioned above in the process of the flare predicted by classical eruption models, the current sheet separating into several small current sheets is also observed at the final stage of the flux rope eruption. The quantitative calculation of the velocities and accelerations of the inflow, hot cusp structure, and post-flare loops is presented. The width of the current sheet is estimated to be about 3 $\times$ $10^{3}$ km. These observations are very useful to understand the process of solar eruptions., Comment: 16 pages, 5 figures, accepted for publication in ApJL

The flare-related, persistent and abrupt changes in the photospheric magnetic field have been reported by many authors during recent years. These bewildering observational results pose a challenge to the current flare theories in which the photospheric magnetic field usually remains unchanged in the eruption. In this paper, changes in the photosphere magnetic field during the solar eruption are investigated based on the catastrophe model. The results indicate that the projection effect is an important source that yields the change in the observed photospheric magnetic field in the line-of-sight. Furthermore one may observe the change in the normal component of magnetic field if the spectrum line used to measure the photospheric magnetic field does not exactly come from the photospheric surface. Our results also show that the significance of selecting the correct spectral lines to study the photospheric field becomes more apparent for the magnetic configurations with complex boundary condition (or background field). (c) 2008 Elsevier B.V. All rights reserved.

The effects of the initial upstream plasma beta on the plasmoid instability are studied via two-dimensional resistive magnetohydrodynamic simulations. For cases with nonuniform beta dependent initial plasma mass density and uniform temperature, our numerical results indicate that the critical Lundquist number for onset of the plasmoid instability depends on the initial plasma beta. The critical Lundquist number is approximately 2000 - 3000 for beta = 50 and is 8000 - 10000 for beta = 0.2. The higher the beta, the smaller the critical Lundquist number is. Similar to previous studies of high-beta systems, the average reconnection rate in low beta systems is found to become weakly dependent on the Lundquist number in the plasmoid-unstable regime. However, the average reconnection rate, normalized to the asymptotic value of upstream BVA, is lower in a low beta system than that in a high beta system. The magnetic energy spectral index, which characterizes fragmentation of the reconnection layer, is approximately two and is insensitive to beta in the high-Lunquist number regime. It is also found that the magnetic reconnection rate becomes similar for different beta cases, if the initial force-balance is provided by temperature gradient instead of density gradient. Therefore, it is concluded that the beta-dependence mentioned above may be largely attributed to the density variation.

We present a 3D magnetohydrodynamic numerical experiment of an eruptive magnetic flux rope (MFR) and the various types of disturbances it creates, and employ forward modelling of extreme ultraviolet (EUV) observables to directly compare numerical results and observations. In the beginning, the MFR erupts and a fast shock appears as an expanding 3D dome. Under the MFR, a current sheet grows, in which magnetic field lines reconnect to form closed field lines, which become the outermost part of an expanding coronal mass ejection (CME) bubble. In our synthetic SDO/AIA images, we can observe the bright fast shock dome and the hot MFR in the early stages. Between the MFR and the fast shock, a dimming region appears. Later, the MFR expands so its brightness decays and it becomes difficult to identify the boundary of the CME bubble and distinguish it from the bright MFR in synthetic images. Our synthetic images for EUV disturbances observed at the limb support the bimodality interpretation for coronal disturbances. However, images for disturbances propagating on-disc do not support this interpretation because the morphology of the bright MFR does not lead to circular features in the EUV disturbances. At the flanks of the CME bubble, slow shocks, velocity vortices and shock echoes can also be recognized in the velocity distribution. The slow shocks at the flanks of the bubble are associated with a 3D velocity separatrix. These features are found in our high-resolution simulation, but may be hard to observe as shown in the synthetic images.