Laboratory simulation of energy release in solar flares

A laboratory simulation method is proposed for energy release processes occurring in a fragment of the flare current sheet on the Sun. The method relies on the assumption that the spatial scale of such processes is represented by the current sheet's thickness whose values can be close for both the solar and laboratory conditions. It is shown that in an extended current sheet, current dissipation on anomalous resistivity that ensures the specific power of energy release close to that observed in a flare, is the main energy release mechanism. A rapid compression of the sheet by external magnetic fields can provide the condition for switching on a powerful energy release. The tearing instability developing in a homogeneous neutral sheet, leads to the formation of magnetic islands in which the energy release is localized.     

Numerical Solutions of Three-Dimensional Pressure-Bounded Magnetohydrostatic Flux Tubes

We present a three-dimensional technique for the solution of the magnetohydrostatic equations when we are modeling structures bounded by a current sheet that is free to move to satisfy pressure balance. The magnetic field is expressed in terms of Euler potentials and the equations are transformed to flux coordinates, greatly simplifying the problem of locating the free boundary. Multi-grid techniques are used to rapidly solve the resulting nonlinear elliptic partial differential equations. The method is tested against Low's (1982) exact solution of a bipolar plasma loop. It is shown that fast, accurate solutions can be found.     

A circuit model for filament eruptions and two-ribbon flares

We derive a circuit model for solar filament eruptions and two-ribbon flares which reproduces the slow energy build up and eruption of the filament, and the energy dissipation in a current sheet at the top of post-flare loops during the two-ribbon flare. In our model the free magnetic energy is concentrated in a current through the filament, another current through an underlying current sheet, and surface return currents. The magnetic field configuration, generated by these currents and a general photospheric background field, has a topology similar to the field topology derived from observations.We consider two circuits, that of the filament and its return current, and that of the current sheet and its return current. These circuits are inductively coupled and free energy stored in the filament in the pre-flare phase is found to be transferred to the sheet during the impulsive phase, and rapidly dissipated there. A comparable amount of magnetic energy is converted into kinetic energy of the ejected filament. The basic equations of the model are the momentum equations for the filament and the current sheet, and the induction equations for the filament and sheet circuits. The derivation of the equations is an extension of previous models by Kuperus and Raadu, Van Tend and Kuperus, Syrovatskii, and Kaastra. The set of equations is closed in the sense that only the initial conditions and a number of parameters, all related to pre-flare observables, are needed to calculate the evolution of the system. The pre-flare observations we need to determine these parameters, are: (1) a magnetogram, (2) an picture, (3) a measurement of the coronal density in the region, and (4) estimates of the photospheric velocity fields in the region.In the solutions for the evolution of the filament current sheet system we distinghuish 4 phases: (1) a slow energy build up, lasting for almost two days, during which the filament evolves quasi-statically, (2) a metastable state, lasting for about three hours, during which the filament is susceptible to flare triggers, and during which a current sheet emerges, (3) the eruptive phase, with strong acceleration of the filament, during which a large current is induced and dissipated in the current sheet, and energy is injected in the post-flare loops, and finally (4) a post-flare phase, in which the filament acceleration declines and the current sheet vanishes.From further numerical work we derive the following conclusions: (1) The magnetic flux input into the filament circuit has to surpass a certain threshold for an eruption to occur. Below that threshold we find solutions representing quiescent filaments. (2)Flare triggers are neither necessary nor sufficient for an eruption, but may set off the eruption during the metastable state. (3) The model reproduces the increase in shear in the filament prior to the eruption, through adecline of the filament current, in contrast to most models for filament eruptions. (4) The ratio of energy lost as kinetic energy of ejecta to the energy radiated away in the post-flare loops is sensitively dependent on the resistance of the current sheet. (5) Flare prediction is possible with this model, but the potential for triggering during the metastable state complicates the prediction of the exact moment of eruption.Former NAS/NRC Resident Research Associate.ST Systems Corporation.     

Thermal trigger for solar flares and coronal loops formation

A longitudinal stability is considered for the quasi-steady current sheet which is uniform along the current. In the MHD approximation, the stability problem is solved for the plane neutral sheet and small disturbances propagating along the current. The current sheet is shown to break-up into the system of cooler and more dense filaments due to radiative cooling. The filaments are parallel to magnetic field lines. This process corresponds to the condensation mode of a thermal instability and can play a trigger role for a solar flare. Moreover, at the nonlinear stage of development, it can lead to the formation of very dense cold filaments surrounded by high-temperature low-density plasma inside the current sheet. Flowing into the filaments, hot plasma is cooled by radiation and compressed. Then the cold dense plasma flows out from the current sheet along the filaments. We think that the process under consideration is responsible for the often observed picture of an arcade of cold loops in the solar corona.The text of this paper was written by B. V. Somov after the death of Prof. S. I. Syrovatskii.     

Magnetically-regulated fragmentation induced by nonlinear flows and ambipolar diffusion

We present a parameter study of simulations of fragmentation regulated by gravity, magnetic fields, ambipolar diffusion, and nonlinear flows. The thin-sheet approximation is employed with periodic lateral boundary conditions, and the nonlinear flow field (“turbulence”) is allowed to freely decay. In agreement with previous results in the literature, our results show that the onset of runaway collapse (formation of the first star) in subcritical clouds is significantly accelerated by nonlinear flows in which a large-scale wave mode dominates the power spectrum. In addition, we find that a power spectrum with equal energy on all scales also accelerates collapse, but by a lesser amount. For a highly super-Alfvénic initial velocity field with most power on the largest scales, the collapse occurs promptly during the initial compression wave. However, for trans-Alfvénic perturbations, a subcritical magnetic field causes a rebound from the initial compression, and the system undergoes several oscillations before runaway collapse occurs. Models that undergo prompt collapse have highly supersonic infall motions at the core boundaries. Cores in magnetically subcritical models with trans-Alfvénic initial perturbations also pick up significant systematic speeds by inheriting motions associated with magnetically-driven oscillations. Core mass distributions are much broader than in models with small-amplitude initial perturbations, although the disturbed structure of cores that form due to nonlinear flows does not guarantee subsequent monolithic collapse. Our simulations also demonstrate that significant power (if present initially) can be maintained with negligible dissipation in large-scale compressive modes of a magnetic thin sheet, in the limit of perfect flux freezing.     

Double current sheet and coronal transients

A double current sheet forms when an opposite magnetic flux emerges into a background magnetic field which has a zero field-line in the corona. It consists of an upper sheet, resulting from the squeezing of field lines near the original zero field region and a lower sheet formed in the region between the new and old fields. We use a pair of linear dipoles to model the background and a pair of line charges to model the emerging field and discuss the formation and evolution of the double current sheet. Matter will condense onto the sheets during their formation. The matter in the lower sheet comes mainly from the transition region and the photosphere; it is further cooled by radiation, giving rise to a low-temperature prominence loop. The matter in the upper sheet comes from the corona and forms a high-temperature coronal loop.This scenario seems to be realized in the coronal transient of 1984 April 14.     

A numerical simulation of magnetic reconnection and radiative cooling in line-tied current sheets

We have used the radiative MHD equations for an optically thin plasma to carry out a numerical experiment related to the formation of post-flare loops. The numerical experiment starts with a current sheet that is in mechanical and thermal equilibrium, but which is unstable to both tearing-mode and thermal-condensation instabilities. The current sheet is line-tied at one end to a photospheric-like boundary and evolves asymmetrically. The effects of thermal conduction, resistivity variation, and gravity are ignored. In general, we find that reconnection in the nonlinear stage of the tearing-mode instability can strongly affect the onset of condensations unless the radiative cooling time scale is much smaller than the tearing-mode time scale. When the ambient plasma is less than 0.2, the reconnection enters a regime where the outflow from the reconnection region is supermagnetosonic with respect to the fast-mode wave speed. In the supermagnetosonic regime the most rapidly condensing regions occur downstream of a fast-mode shock that forms where the outflow impinges on closed loops attached to the photospheric-like boundary. A similar shock-induced condensation might occur during the formation of post-flare loops.     

Modulational instability of fast magnetosonic waves emitted from a pinching current sheet

We investigate how fast magnetosonic waves can be produced from a pinching current sheet, by using 3-D MHD code. We show that after magnetic pinch of the current sheet due to pressure imbalance, the current sheet begins to expand by an excess of plasma pressure at the center of the current sheet. During the expansion phase, strong fast magnetosonic waves can be created at the steep region of the density gradient and propagate away from the current sheet. It is shown that the fast magnetosonic waves become unstable against modulational instability, as found by Sakai (1983). After the emission of the fast magnetosonic waves, the current sheet will relax to a new equilibrium state, where the current sheet can be heated by adiabatic compression. The emission processes of the fast magnetosonic waves from the current sheet, as well as the modulational instability of these waves that can lead to effective plasma heating through the Landau damping of the slow waves, are important for an understanding of coronal heating and coronal transient brightening.     

Non-linear tearing structures in equilibrium current sheet

A family of exact analytic solutions of the time-independent Vlasov-Maxwell equations is presented. The solutions describe two-dimensional equilibrium current sheet with magnetic field structures resembling that produced by the tearing instability. In particular, the solutions presented here do not restrict the field in the magnetic island to small magnitude. It is shown that as the scale length of the magnetic island increases, the thickness of the current sheet increases while the average current and the average magnetic energy decrease. The tearing structures described by the solutions may exist in the magnetotail current sheet, the magnetopause current layer and the field-aligned auroral sheet current.     

A numerical experiment relevant to line-tied reconnection in two-ribbon flares

The nonlinear evolution of a reconnecting magnetic field configuration similar to that occurring just before the onset of ‘post’-flare loops in two-ribbon flares is determined. The evolution, which is obtained by numerically solving the resistive MHD equations, shows two new features that have not yet been incorporated into contemporary models of ‘post’-flare loops. The first of these new features is the formation of a nearly stationary fast-mode shock above the region corresponding to the top of the loops. This fast-mode shock occurs just below the magnetic neutral line and between the slow-mode shocks associated with fast magnetic reconnection at the neutral line. The second new feature is the creation and annihilation of large-scale magnetic islands in the current sheet above the loops. The annihilation of the islands occurs very rapidly and appears to be a manifestation of the coalescence instability. The creation and annihilation of magnetic islands could be important in understanding the energetics of ‘post’-flare loops since the coalescence instability can produce an intermittent energy release more than an order of magnitude faster than that predicted by steady-state reconnection theories.     

The study of magnetic reconnection in solar spicules

This work is devoted to study the magnetic reconnection instability under solar spicule conditions. Numerical study of the resistive tearing instability in a current sheet is presented by considering the magnetohydrodynamic (MHD) framework. To investigate the effect of this instability in a stratified atmosphere of solar spicules, we solve linear and non-ideal MHD equations in the x?z plane. In the linear analysis it is assumed that resistivity is only important within the current sheet, and the exponential growth of energies takes place faster as plasma resistivity increases. We are interested to see the occurrence of magnetic reconnection during the lifetime of a typical solar spicule.     

双重电流片和日冕瞬变

当背景磁场在日冕中存在零磁场线时,反向新磁通量的喷发将会产生双重电流片,包括零场区附近的磁场受到挤压而形成的横向电流片和新喷发场、原背景场之间形成的拱形电流片、本文用一对线偶极子来模拟背景场,用一对线磁荷来模拟反向喷发场,讨论了上述双重电流片的形成和演变过程。在电流片形成过程中,物质将向电流片集中。拱形电流片物质主要来自过渡层和光球层,并通过辐射损失进一步冷却,形成低温日珥环;横向电流片的物质则全部来自日冕,从而形成高温日冕环。以上结果可用来解释1984年4月14日观测到的日冕瞬变。     

Alfvén-magnetosonic waves interaction in the solar corona

The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the fast wave itself is governed by Burgers type equations possessing both expansion and compression shock solutions. Numerical simulations show that both parallely and perpendicularly propagating fast waves can steepen into shocks if their amplitudes are in excess of some sizeable fraction of the Alfvén velocity. However, if the magnetic field changes linearly in the perpendicular direction, then formation of perpendicular shocks can be hindered. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves whose propagation is described by linearized Boussinesq type equations with ponderomotive terms due to the Alfvén wave. The limits of the slow and fast waves are investigated.     

Interaction between sheared flow and resistive tearing mode

We investigate the nonlinear evolution of resistive tearing mode in a current sheet with a sheared flow in a long, thin cylinder. The results show that a hyperbolic secant (sech) flow field will lead to instability of the resistive tearing mode, formation of magnetic islands and rapid release of magnetic energy. The coupling between sheared flow and the tearing mode and interaction between suprathermal instabilities change the degree of shear in the magnetic field (the electric current gradient) and drive the development of the instability. This process may be one of the mechanisms of solar flares.     

Modelling heliospheric current sheet drift in stochastic cosmic ray transport models

Drifts are one of the major cosmic ray modulation mechanisms in the heliosphere. Three types of drifts occur in the background heliospheric magnetic field, namely curvature, gradient and current sheet drifts. The last component occurs because of the switch in magnetic field polarity across the heliospheric current sheet and is the main topic of study. We discuss and implement a new approach to model drifts in a numerical modulation model. The model employs stochastic differential equations to solve the relevant transport equation in five (three spatial, energy and time) dimensions. What is of interest is the fact that the model can handle current sheet tilt angles up to the theoretical maximum of α=90° and still remain numerically stable. We use the additional insights gained from the numerical model to investigate the effectiveness of drifts along the current sheet by examining the relationship between the current sheet path length and the cosmic ray propagation time. It is found that diffusion can disrupt the drift process very effectively, leading to diffusive short circuiting of the current sheet by the cosmic rays.     

Stability of Current Sheets in the Solar Corona

This work aims at investigating unstable modes of oscillation of quasi-vertical two-dimensional current sheets with sheared magnetic fields under physical conditions typical for the solar corona. We use linear magnetohydrodynamic equations to obtain sets of unstable modes related to the longitudinal inhomogeneity of the current sheet. It is shown that these modes of current sheet oscillations can modulate the current sheet thickness along the polarity inversion line. Based on the obtained results, we propose a scenario which can naturally explain both the quasi-periodic pulsations of hard X-ray emission and the parallel movement of their double footpoint-like sources along the polarity inversion line observed in some eruptive two-ribbon solar flares.     

Non-evolutionarity of a reconnecting current sheet as a cause of its splitting into MHD shocks

Numerical simulations of the magnetic reconnection process in a current sheet show that, in some cases, MHD shocks appear to be attached to edges of the sheet. The appearance of the shocks may be considered to be a result of splitting of the sheet. In the present paper we suppose that this splitting takes place in consequence of non-evolutionarity of the reconnecting current sheet as a discontinuity. The problem of time evolution of small perturbations does not have a unique solution for a non-evolutionary discontinuity, and it splits into other (evolutionary) discontinuities. Such an approach allows us to determine conditions under which the splitting of the-sheet occurs. The main difficulty of this approach is that a current sheet is not reduced to a classified 1D discontinuity, because inhomogeneity of flow velocity inside the sheet is two-dimensional. To formulate the non-evolutionarity problem, we solve the linear MHD equations inside and outside the sheet and deduce linearized 1D boundary conditions at its surface. We show that for large enough conductivity, small perturbations exist which interact with the sheet as with a discontinuity. Then we obtain a non-evolutionarity criterion, with respect to these perturbations, in the form of a restriction on the flow velocity across the surface of the sheet.     

Formation of neutral current sheet and loop coronal transients

An eruption of opposite magnetic flux into a bipolar background field is likely to lead to the formation of a natural current sheet between the new emerging field and the background. A numerical study is made on this process, based on the ideal MMD equations, taking into account the interaction between the magnetic field and the coronal plasma. The result shows that a subsonic eruption will give rise to a four region structure; 1) a cool and dense prominence made of the erupting material in the innermost region; 2) a cool and tenuous region further out; 3) a hot and dense loop formed by the concentration of both the erupting material and the coronal material in the neutral current sheet; and 4) a forerunner region outside the loop with density slightly above the background, due to fast magneto-acoustic waves. This structure agrees with the observed features of typical loop coronal transients. Therefore the eruption of opposite magnetic flux into a bipolar background is probably an important mechanism for triggering off such transients.     

Titan's highly dynamic magnetic environment: A systematic survey of Cassini magnetometer observations from flybys TA-T62

We analyze the variability of the ambient magnetic field near Titan during Cassini encounters TA-T62 (October 2004-October 2009). Cassini magnetometer (MAG) data show that the moon's magnetic environment is strongly affected by its proximity to Saturn's warped and highly dynamic magnetodisk. In the nightside sector of Saturn's magnetosphere, the magnetic field near Titan is controlled by intense vertical flapping motions of the magnetodisk current sheet, alternately exposing the moon to radially stretched lobe-type fields and to more dipolar, but highly distorted current sheet fields. In southern summer, when most of the Cassini encounters took place, the magnetodisk current sheet was on average located above Titan's orbital plane. However, around equinox in August 2009, the distortions of Titan's magnetic environment due to the rapidly moving current sheet reached a maximum, thus suggesting that the equilibrium position of the sheet at that time was significantly closer to the moon's orbital plane. In the dayside magnetosphere, the formation of the magnetodisk lobes is partially suppressed due to the proximity of the magnetopause. Therefore, during most encounters that took place near noon, Titan was embedded in highly distorted current sheet fields. Within the framework of this study, we not only provide a systematic classification of all Titan flybys between October 2004 and October 2009 as lobe-type or current sheet scenarios, but we also calculate the magnetospheric background field near Titan's orbit whenever possible. Our results show that so far, there is not a single Cassini flyby that matches the frequently applied picture of Titan's plasma interaction from the pre-Cassini era (background field homogeneous, stationary and perpendicular to the moon's orbital plane). The time scales upon which the ambient magnetospheric field close to Titan undergoes significant changes range between only a few minutes and up to several hours. The implications for the development of numerical models for Titan's local plasma interaction are discussed as well.     

MAGNETIC RECONNECTION IN MULTIPLE HELIOSPHERIC CURRENT SHEETS

Satellite observations of the heliospheric current sheet indicate that the internal structure of sector boundaries is a very complex structure with many directional discontinuities in the magnetic field. This implies that the heliospheric current sheet is not a single surface but a constantly changing layer with a varying number of current sheets. In this paper, we investigate magnetic reconnection caused by the resistive tearing mode instability in non-periodic multiple current sheets by using two-dimensional magnetohydrodynamic simulation. The results show that it is complex unsteady magnetic reconnection. Accompanying the nonlinear development of the tearing mode, the width of each magnetic island in multiple current sheets increases with time, and this leads to new magnetic reconnection. At the same time, the width of each current sheet increases, and the current intensity decreases gradually. Finally, the reverse current disappears, and a big magnetic island is formed in the central region. This process is faster when the separation between the current sheets is smaller. We suggest that the occurrence of multiple directional discontinuities observed at sector boundary crossings in the heliosphere may be associated with the magnetic islands and plasmoids caused by magnetic reconnection in multiple current sheets.