MHD simulations of fast reconnection spontaneously developing in a current sheet

Magnetic reconnection is widely believed to be involved in dynamical phenomena such as solar flares or magnetospheric substorms. The Sweet–Parker model of magnetic reconnection in a Y-type geometry predicts a characteristic time scale proportional to S1/2 (where S is the Lundquist number), which is too slow to account for the observed time scales. The Petschek model, in contrast, predicts a time scale proportional to ln S in an X-point geometry. Numerical magnetohydrodynamic (MHD) simulations in the high-S regime generally validate the Sweet–Parker model, unless the resistivity is enhanced in the diffusion region to large values (such that typically S<103). It is demonstrated in this paper that nonlinear reconnection dynamics in a Harris sheet driven by inward boundary flows occurs on a nonlinear time scale that is proportional to S1/5 and thus has a weaker dependence on resistivity than the Sweet–Parker time scale. The current sheet amplitude at the separatrix (spanning Y points) grows algebraically in the linear regime but is suddenly enhanced after it makes a transition to the nonlinear regime. An analytical calculation is given for both the linear and the nonlinear regimes, and supported by two-dimensional resistive MHD simulations. The features of sudden current sheet enhancement and fast reconnection, controlled by boundary flows, are relevant to the phenomena of substorm onset or the impulsive phase of flares.

Standard magnetohydrodynamic (MHD) theory predicts reconnection rate that is far too slow to account for a wide variety of reconnection events observed in space and laboratory plasmas. Therefore, it was commonly accepted that some non-MHD (kinetic) effects play a crucial role in fast reconnection. A recently renewed interest in simple MHD models is associated with the so-called plasmoid instability of reconnecting current sheets. Although it is now evident that this effect can significantly enhance the rate of reconnection, many details of the underlying multiple-plasmoid process still remain controversial. Here, we report results of a high-resolution computer simulation which demonstrate that fast albeit intermittent magnetic reconnection is sustained by numerous small-scale Petschek-type shocks spontaneously formed in the current sheet due to its plasmoid instability.

Magnetic reconnection and non-thermal particle distributions associated with\ncurrent-driven instabilities are investigated by means of resistive\nmagnetohydrodynamics (MHD) simulations combined with relativistic test particle\nmethods. We propose a system with two parallel, repelling current channels in\nan initially force-free equilibrium, as a simplified representation of flux\nropes in a stellar magnetosphere. The current channels undergo a rotation and\nseparation on Alfv\\'enic timescales, forming secondary islands and (up to\ntearing unstable) current sheets in which non-thermal energy distributions are\nexpected to develop. Using the recently developed particle module of our\nopen-source grid-adaptive MPI-AMRVAC software, we simulate MHD evolution\ncombined with test particle treatments in MHD snapshots. We explore under which\nplasma-$\\beta$ conditions the fastest reconnection occurs in two-and-a-half\ndimensional (2.5D) scenarios and in these settings test particles are evolved.\nWe quantify energy distributions, acceleration mechanisms, relativistic\ncorrections to the particle equations of motion and effects of resistivity in\nmagnetically dominated proton-electron plasmas. Due to large resistive electric\nfields and indefinite acceleration of particles in the infinitely long current\nchannels, hard energy spectra are found in 2.5D configurations. Solutions to\nthese numerical artifacts are proposed for both 2.5D setups and future 3D work.\nWe discuss the magnetohydrodynamics of an additional kink instability in 3D\nsetups and the expected effects on energy distributions. The obtained results\nhold as a proof-of-principle for test particle approaches in MHD simulations,\nrelevant to explore less idealised scenarios like solar flares and more exotic\nastrophysical phenomena, like black hole flares, magnetar magnetospheres and\npulsar wind nebulae.

Context. Ellerman bombs (EBs) with significant Hα wing emissions and ultraviolet bursts (UV bursts) with strong Si IV emissions are two kinds of small transient brightening events that occur in the low solar atmosphere. The statistical observational results indicate that about 20% of the UV bursts connect with EBs. While some promising models exist for the formation mechanism of colder EBs in conjunction with UV bursts, the topic remains an area of ongoing research and investigation. Aim. We numerically investigated the magnetic reconnection process between the emerging arch magnetic field and the lower atmospheric background magnetic field. We aim to find out if the hot UV emissions and much colder Hα wing emissions can both appear in the same reconnection process and how they are located in the reconnection region. Methods. The open-source code NIRVANA was applied to perform the 2.5D magnetohydrodynamic (MHD) simulation. We developed the related sub-codes to include the more realistic radiative cooling process for the photosphere and chromosphere and the time-dependent ionization degree of hydrogen. The initial background magnetic field is 600 G, and the emerged magnetic field in the solar atmosphere is of the same magnitude, meaning that it results in a low- β magnetic reconnection environment. We also used the radiative transfer code RH1.5D to synthesize the Si IV and Hα spectral line profiles based on the MHD simulation results. Results. Magnetic reconnection between emerged and background magnetic fields creates a thin, curved current sheet, which then leads to the formation of plasmoid instability and the nonuniform density distributions. Initially, the temperature is below 8000 K. As the current sheet becomes more vertical, denser plasmas are drained by gravity, and hotter plasmas above 20 000 K appear in regions with lower plasma density. The mix of hot tenuous and much cooler dense plasmas in the turbulent reconnection region can appear at about the same height, or even in the same plasmoid. Through the reconnection region, the synthesized Si IV emission intensity can reach above 106 erg s−1 sr−1 cm−2 Å−1 and the spectral line profile can be wider than 100 km s−1, the synthesized Hα line profile also show the similar characteristics of a typical EB. The turbulent current sheet is always in a dense plasma environment with an optical depth larger than 6.5 × 10−5 due to the emerged magnetic field pushing high-density plasmas upward. Conclusions. Our simulation results indicate that the cold EB and hot UV burst can both appear in the same reconnection process in the low chromosphere, the EB can either appear several minutes earlier than the UV burst, or they can simultaneously appear at the similar altitude in a turbulent reconnection region below the middle chromosphere.

Strong thermal X-ray emission, called Galactic Ridge X-ray Emission, is observed along the Galactic plane (Koyama et al. 1986). The origin of hot (7 keV) component of GRXE is not known, while cool (0.8 keV) one is associated with supernovae (Kaneda et al. 1997, Sugizaki et al. 2001). We propose a possible mechanism to explain the origin; locally strong magnetic fields of heat interstellar gas to 7 keV via magnetic reconnection (Tanuma et al. 1999). There will be the small-scale ( by integration of Faraday Rotation Measure, if it is localized by a volume filling factor of f 0.1. In order to examine this model, we solved three-dimensional (3D) resistive magnetohydrodynamic (MHD) equations numerically to examine the magnetic reconnect ion triggered by a supernova shock (fig.l). We assume that the magnetic field is Bx = 30tanh(y/20pc) G, By = Bz = 0, and the temperature is uniform, at the initial condition. We put a supernova explosion outside the current sheet. The supernova-shock, as a result, triggers the magnetic reconnect ion, and the gas is heatd to > 7 keV. The magnetic reconnect ion heats the interstellar gas to 7 keV in the Galactic plane, if it occurs in the locally strong magnetic fields of . The heated plasma is confined by the magnetic field for . The required interval of the magnetic reconnect ions (triggered by anything) is 1 - 10 yr. The magnetic reconnect ion will explain the origin of X-rays from the Galactic ridge, furthermore the Galactic halo, and clusters of galaxies.

The electron inertia and the off‐diagonal electron pressure terms are well‐known for the frozen‐in condition breakdown in collisionless magnetic reconnection, which are naturally kinetic and difficult to employ in magnetohydrodynamic (MHD) simulations. Considering the limitations of MHD and Hall MHD in neglecting the important electron dynamics such as the inertia and the nongyrotropic pressure, the kinetic characteristics of electrons and ions in the diffusion region are studied and an effective resistivity model involving dynamics of charged particles is proposed (Ma et al. 2018, https://doi.org/10.1038/s41598‐018‐28851‐7 Sci. Rep. 8 10521), where the guide field is omitted to simplify the model by primarily considering the out‐of‐plane velocity of charged particles and the in‐plane reconnecting field. The amplitude of the effective resistivity is mainly determined by electrons in most realistic situations with large ion‐electron mass ratios. In this work, the effective resistivity model for collisionless magnetic reconnection is successfully applied in the 2.5D MHD and Hall MHD simulations, which remarkably improves the simulation results compared with traditional MHD models. For the MHD case, the effective resistivity significantly increases the reconnection rate to a reasonable value of . For the Hall MHD case with effective resistivity, the peak reconnection rate is , and the major structures of the reconnecting field and the current sheet agree well with the particle‐in‐cell (PIC) simulations. Meanwhile, a more general effective resistivity model incorporating guide field corrections for MHD simulations is under development.

Classical models of magnetic reconnection consist of a small diffusion region bounded by two symmetric slow shocks, across which the plasma is accelerated. Asymmetries often present in space plasmas are sheared plasma flow and dissimilar plasma densities on the two sides of current sheets. In this paper, we investigate magnetic reconnection in the presence of a shear flow and an asymmetric density across the current sheet using two‐dimensional magnetohydrodynamic (MHD) simulations. The results demonstrate that magnetic reconnection can occur only for a plasma flow velocity (in the frame of the X line) which is below the Alfvén speed in each inflow region. This limits the velocity of the X line to a certain range for a given flow shear and provides an upper limit to the total velocity shear at which reconnection ceases to operate. Depending on the direction of the flow in the adjacent inflow region, the effects from the sheared flow and from the density asymmetry will compete with or enhance each other in respect to the magnitude and location of the currents which bound the outflow regions. The results are applied to the dayside and flank regions of the magnetosphere. For the dayside region where the magnetosheath flow is slow, the magnetic field transition region is thin and the accelerated flow is earthward of the sharp current layer (magnetopause). At the flanks tailward of the X line, shear flow and density asymmetry effects compete making the magnetic field transition layer broad with the high‐speed flow contained within the transition region which explains corresponding observations. At the flanks sunward of the X line, shear flow and density asymmetry effects enhance each other and lead to a strong current sheet on the magnetosheath side of the accelerated flow. The total volume affected by magnetic reconnection is much larger than the steady state region. A large bulge region precedes the steady state region. Qualitatively, the bulge and the steady state region have similar signatures and both can explain observations. We provide criteria in order to distinguish between the bulge and the steady state region in observations.

Dissipation processes responsible for fast magnetic reconnection in collisionless plasmas are investigated using 3D electromagnetic particle-in-cell simulations. The present study revisits the two simulation runs performed in the previous study (Fujimoto, Phys. Plasmas 16, 042103 (2009)); one with small system size in the current density direction, and the other with larger system size. In the case with small system size, the reconnection processes are almost the same as those in 2D reconnection, while in the other case a kink mode evolves along the current density and deforms the current sheet structure drastically. Although fast reconnection is achieved in both the cases, the dissipation mechanism is very different between them. In the case without kink mode, the electrons transit the electron diffusion region without thermalization, so that the magnetic dissipation is supported by the inertia resistivity alone. On the other hand, in the kinked current sheet, the electrons are not only accelerated in bulk, but they are also partly scattered and thermalized by the kink mode, which results in the anomalous resistivity in addition to the inertia resistivity. It is demonstrated that in 3D reconnection the thickness of the electron current sheet becomes larger than the local electron inertia length, consistent with the theoretical prediction in Fujimoto and Sydora (Phys. Plasmas 16, 112309 (2009)).

Fast magnetic reconnection plays a fundamental role in driving explosive\ndynamics and heating in the solar chromosphere. The reconnection time scale of\ntraditional models is shortened at the onset of the coalescence instability,\nwhich forms a turbulent reconnecting current sheet through plasmoid\ninteraction. In this work we aim to investigate the role of partial ionisation\non the development of fast reconnection through the study of the coalescence\ninstability of plasmoids. Unlike the processes occurring in fully ionised\ncoronal plasmas, relatively little is known about how fast reconnection\ndevelops in partially ionised plasmas of the chromosphere. We present 2.5D\nnumerical simulations of coalescing plasmoids in a single fluid\nmagnetohydrodynamic (MHD) model, and a two-fluid model of a partially ionised\nplasma (PIP). We find that in the PIP model, which has the same total density\nas the MHD model but an initial plasma density two orders of magnitude smaller,\nplasmoid coalescence is faster than the MHD case, following the faster thinning\nof the current sheet and secondary plasmoid dynamics. Secondary plasmoids form\nin the PIP model where the effective Lundquist number $S = 7.8 \\cdot 10^3$, but\nare absent from the MHD case where $S = 9.7 \\cdot 10^3$: these are responsible\nfor a more violent reconnection. Secondary plasmoids also form in linearly\nstable conditions as a consequence of the non-linear dynamics of the neutrals\nin the inflow. In the light of these results we can affirm that two-fluid\neffects play a major role on the processes occurring in the solar chromosphere.\n

\n Context. The paper is concerned with heating of the solar corona by nanoflares: a superposition of\nsmall transient events in which stored magnetic energy is dissipated by magnetic reconnection.\nIt is proposed that heating occurs in the nonlinear phase of an ideal kink instability, where\nmagnetic reconnection leads to relaxation to a state of minimum magnetic energy.\n Aims. The aim is to investigate the nonlinear aspects of magnetic relaxation on a current loop with zero net axial current.\nThe dynamical processes leading to the establishment of a relaxed state are explored. The efficiency of\nloop heating is investigated. \n Methods. A 3D magnetohydrodynamic numerical code is used to simulate the evolution of coronal\nloops which are initially in ideally unstable equilibrium. The initial states have zero net current.\nThe results are interpreted by comparison both with linear stability analysis\nand with helicity-conserving relaxation theory.\n Results. The disturbance due to the unstable mode is strongly radially confined when the loop carries\nzero net current. Strong current sheets are still formed in the nonlinear phase with dissipation of\nmagnetic energy by fast reconnection. The nonlinear development consists first of\nreconnection in a large scale current sheet, which forms near the quasi-resonant surface of the equilibrium field.\nSubsequently, the current sheet extends and then fragments, leading to multiple\nreconnections and effective relaxation to a constant α field.\n Conclusions. Magnetic reconnection is triggered in the nonlinear phase of kink instability in loops with zero net current.\nInitially, reconnection occurs in a single current sheet, which then fragments into multiple\nreconnection sites, allowing almost full relaxation to the minimum energy state.\nThe loop is heated to high temperatures throughout its volume.\n

It is generally believed that the magnetic free energy accumulated in the corona serves as a main energy source for solar explosions such as coronal mass ejections (CMEs). In the framework of the flux rope catastrophe model for CMEs, the energy may be abruptly released either by an ideal magnetohydrodynamic (MHD) catastrophe, which belongs to a global magnetic topological instability of the system, or by a fast magnetic reconnection across preexisting or rapidly developing electric current sheets. Both means of magnetic energy release are thought to be important to CME dynamics. To disentangle their contributions, we construct a flux rope catastrophe model in the corona and solar wind and compare different cases in which we either prohibit or allow magnetic reconnection to take place across rapidly growing current sheets during the eruption. It has been demonstrated that CMEs, even fast ones, can be produced taking the ideal MHD catastrophe as the only process of magnetic energy release. Nevertheless, the eruptive speed can be significantly enhanced after magnetic reconnection sets in. In addition, a smooth transition from slow to fast eruptions is observed when increasing the strength of the background magnetic field, simply because in a stronger field there is more free magnetic energy at the catastrophic point available to be released during an eruption. This suggests that fast and slow CMEs may have an identical driving mechanism.

We conduct forward-modeling analysis based on our 2.5 dimensional magnetohydrodynamics (MHD) simulation of magnetic flux rope (MFR) formation and eruption driven by photospheric converging motion. The current sheet (CS) evolution during the MFR formation and eruption process in our MHD simulation can be divided into four stages. The first stage shows the CS forming and gradually lengthening. Resistive instabilities that disrupt the CS mark the beginning of the second stage. Magnetic islands disappear in the third stage and reappear in the fourth stage. Synthetic images and light curves of the seven Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) channels, i.e., 94 Å, 131 Å, 171 Å, 193 Å, 211 Å, 304 Å, and 335 Å, and the 3–25 keV thermal X-ray are obtained with forward-modeling analysis. The loop-top source and the coronal sources of the soft X-ray are reproduced in forward modeling. The light curves of the seven SDO/AIA channels start to rise once resistive instabilities develop. The light curve of the 3–25 keV thermal X-ray starts to go up when the reconnection rate reaches one of its peaks. Quasiperiodic pulsations (QPPs) appear twice in the SDO/AIA 171 Å, 211 Å, and 304 Å channels, corresponding to the period of chaotic (re)appearance and CS-guided displacements of the magnetic islands. QPPs appear once in the SDO/AIA 94 Å and 335 Å channels after the disruption of the CS by resistive instabilities and in the 193 Å channel when the chaotic motion of the magnetic islands reappears.

The solar X-ray satellite, Yohkoh, has found extensive evidence for magnetic reconnection in solar corona. Here we extend the magnetic reconnection model of solar flares to hard X-ray flares observed in star forming regions. A new ingredient is a protostellar disk which can inject helicity into the magnetosphere if the disk is threaded by the dip ole magnetic field of the protostar. We carried out 2.5-dimensional magnetohydrodynamic (MHD) simulations of the disk-star interaction. The closed magnetic loops connecting the central star and the disk are twisted by the rotation of the disk. In the presence of resistivity, magnetic reconnection takes place in the current sheet formed inside the expanding loops. A hot, outgoing plasmoid and hot post flare loops are formed as a result of the reconnection. Numerical results are consistent with the observed plasma temperature (107 – 108K), the length of the flaring loop (1011 – 1012cm), and the velocity of optical jets (200 – 400km/s). We showed by high-resolution numerical simulations using parallel computers that multiple magnetic islands are created in the current sheet due to the growth of the tearing mode instability. The magnetic islands are ejected quasi-periodically. Intermittent flaring activity continues as long as the disk matter twists the dipole magnetic field.

Magnetic reconnection

Solar eruptions are explosive disruption of coronal magnetic fields, and often launch coronal mass ejections into the interplanetary space. Intriguingly, many solar eruptions fail to escape from the Sun, and the prevailing theory for such failed eruption is based on ideal magnetohydrodynamic (MHD) instabilities of magnetic flux rope (MFR); that is, an MFR runs into kink instability and erupts but cannot reach the height for torus instability. Here, based on numerical MHD simulation, we present a new model of failed eruption in which magnetic reconnection plays a leading role in the initiation and failure of the eruption. Initially, a core bipolar potential field is embedded in a background bipolar field, and by applying shearing and converging motions to the core field, a current sheet is formed within the core field. Then, tether-cutting reconnection is triggered at the current sheet, first slow for a while and becoming fast, driving an erupting MFR. Eventually, the rise of MFR is halted by the downward magnetic tension force of the overlying field, although the MFR apex has well exceeded the critical height of torus instability. More importantly, during the rise of the MFR, it experiences a significant rotation around the vertical axis (with a direction contrary to that predicted by kink instability), rendering the field direction at the rope apex almost inverse to the overlying field. As a result, a strong current sheet is formed between the MFR and the overlying flux, and reconnection occurring in this current sheet ruins completely the MFR.