Magnetic reconnection in a high-temperature plasma of solar flares

In the frame of a simple self-consistent model for high-temperature turbulent current sheet (HTCS) /1/, three effects are considered. (i) Gradient instabilities create anamalous plasma diffusion across magnetic field and increase the power of energy release in HTCS. (ii) Penetration of a small transverse component of magnetic field into HTCS also can significantly increase an energy output of HTCS. (iii) There appears electric current circulating around a current sheet at a compression of longitudinal magnetic field. This current induces a Joule heat; however, a total flux of the longitudinal field remains constant.     

Study of three dimensional structure of the fast convection flow in the plasma sheet by MHD simulations on the basis of spontaneous fast reconnection model

Three dimensional structure of the fast convection flow in the plasma sheet is examined using magnetohydrodynamic (MHD) simulations on the basis of spontaneous fast reconnection model. The fast flow observed in the near-Earth magnetotail is one of the key phenomena in order to understand the causal relationship between magnetic substorm and magnetic reconnection. In this paper, we focus on this earthward fast flow in the near-Earth magnetotail. Our previous studies have shown that the fast reconnection produces the Alfvénic fast reconnection outflow and drastic magnetic field dipolarization in the finite extent. In this paper, the results of our simulations are compared with those of the in-situ observations in the geomagnetotail. They have consistent temporal profiles of the plasma quantities. It is suggested that the fast convection flows are caused by spontaneous fast reconnection.     

Driven reconnection in the near-Earth plasma sheet

In some recent MHD simulations of the near-Earth plasma sheet we studied onset and evolution of reconnection due to non-linear resistive instabilities. In our present contribution we show that these non-linear instabilities can be amplified significantly by inflow through the plasma sheet boundary and we discuss the consequences of that driving mechanism on the global dynamics of the instabilities. For high magnetic Reynolds numbers we find thin current sheets developing.     

Dynamical magnetic reconnection in Parker''s coronal heating model

The excitation (flares, ejections, heating, …) of the corona can be understood in terms of the dynamics of the confectively driven magnetized plasma. In particular, anomalous ohmic heating may be a consequence of the formation and rapid dissipation of small-scale magnetic fields in the corona. We have performed numerical simulations of the loop heating model proposed by Parker (1972, 1994), and have studied its dynamics and global power balance in order to assess its viability as a coronal heating candidate, with promising results. Our results suggest the following view of the small-scale dynamics of coronal loops. First of all, photospheric granular motions quasi-statically twist the magnetic field of the corona in a random-walk fashion. In topologically closed structures, the perpendicular magnetic energy increases, causing magnetic shear to build up at the quasi-separatrices of the resulting close-packed magnetic flux tubes. At some point, the boundary driving causes this stressed configuration to cross the threshold of an ideal time-scale MHD instability (possibly magnetic coalescence or resistive tearing) or a point of nonequilibrium and the field lines pinch toward a small-scale sheared configuration. It then becomes energetically favorable for dynamic reconnection to occur, producing narrow current sheets and an Ohmic heating rate sufficient to balance the input Poynting flux.     

Kink-like mode of a double gradient instability in a compressible plasma current sheet

A linear MHD instability of the electric current sheet, characterized by a small normal magnetic field component, varying along the sheet, is investigated. The tangential magnetic field component is modeled by a hyperbolic function, describing Harris-like variations of the field across the sheet. For this problem, which is formulated in a 3D domain, the conventional compressible ideal MHD equations are applied. By assuming Fourier harmonics along the electric current, the linearized 3D equations are reduced to 2D ones. A finite difference numerical scheme is applied to examine the time evolution of small initial perturbations of the plasma parameters. This work is an extended numerical study of the so called “double gradient instability”, – a possible candidate for the explanation of flapping oscillations in the magnetotail current sheet, which has been analyzed previously in the framework of a simplified analytical approach for an incompressible plasma. The dispersion curve is obtained for the kink-like mode of the instability. It is shown that this curve demonstrates a quantitative agreement with the previous analytical result. The development of the instability is investigated also for various enhanced values of the normal magnetic field component. It is found that the characteristic values of the growth rate of the instability shows a linear dependence on the square root of the parameter, which scales uniformly the normal component of the magnetic field in the current sheet.     

Theoretical model of steady-state magnetic reconnection in collisionless incompressible plasma based on the Grad–Shafranov equation solution

The problem of steady-state magnetic reconnection in an infinite current layer in collisionless, incompressible, nonresistive plasma, except of the electron diffusion region, is examined analytically using the electron Hall magnetohydrodynamics approach. It is found that this approach allows reducing the problem to the magnetic field potential finding, while last one has to satisfy the Grad–Shafranov equation. The obtained solution demonstrates all essential Hall reconnection features, namely proton acceleration up to Alfvén velocities, the forming of Hall current systems and the magnetic field structure expected. It turns out that the necessary condition of steady-state reconnection to exist is an electric field potential jump across the electron diffusion region and the separatrices. Besides, the powerful mechanism of electron acceleration in X-line direction is required. It must accelerate electrons up to the electron Alfvén velocity inside the diffusion region and on the separatrixes. This is a necessary condition for steady-state reconnection as well.     

Numerical simulation of three-dimensional reconnection due to the instability of collisionless current sheets

Based on analytical calculations we have currently argued that spontaneous reconnection through thin collisionless current sheets is an essentially three-dimensional (3 D) process (Büchner, 1996 a, b). Since 3 D kinetic PIC codes have become available, the three dimensional nature of the collisionless current sheet decay are now illustrated by numerical simulations (Büchner and Kuska, 1996; Pritchett and Coroniti, 1996; Zhu and Winglee, 1996). While the latter two claim a coupling to a longer wavelength kink mode as a main factor, destabilizing thin current sheets in 3 D, our simulations have revealed that even shorter scale perturbations in the current direction suffice to destabilize thin sheets very quickly. Since past simulation runs, however, were limited to mass ratios near unity, the influence of the electrons was not treated adequately. We have now investigated the stability of thin collisionless current sheets including 64 times lighter negatively charged particles. We can now show that while the two-dimensional tearing instability slows down for M = M_p/m_e = 64, the three-dimensional current sheet decay is a much faster process — practically as fast as the mass ratio M = 1 3 D sheet decay, even without kinking the sheet. We further conclude that, unlike the two-dimensional tearing instability, the three-dimensional decay of thin current sheets is not controlled by the electrons. For a sheet width comparable with the ion inertial length, we also recovered signatures of the Hall effect as predicted by Vasyliunas (1975) in the mass ratio M = 64 case. The ion inertial length seems to be the critical scale at which the sheet starts to decay.     

Large-scale reconnection in a large flare

Some specific features of the large-scale magnetic reconnection in large solar flares are briefly reviewed. In particular, the large-scale structure and dynamics of the 3B/X5.7 flare on 14 July 2000 are interpreted in terms of the topological model. The role of the betatron effect in collapsing magnetic traps, that are created by reconnection in the solar corona, is considered. We discuss some possibilities to observe the collapsing trap acceleration in solar flares.     

Generation mechanism of the whistler-mode waves in the plasma sheet prior to magnetic reconnection

The whistler-mode waves and electron temperature anisotropy play a key role prior to and during magnetic reconnection. On August 21, 2002, the Cluster spacecrafts encountered a quasi-collisionless magnetic reconnection event when they crossed the plasma sheet. Prior to the southward turning of magnetospheric magnetic field and high speed ion flow, the whistler-mode waves and positive electron temperature anisotropy are simultaneously observed. Theoretic analysis shows that the electrons with positive temperature anisotropy can excite the whistler-mode waves via cyclotron resonances. Using the data of particles and magnetic field, we estimated the whistler-mode wave growth rate and the ratio of whistler-mode growth rate to wave frequency. They are 0.0016f_ce (Electron cyclotron frequency) and 0.0086f_ce, respectively. Therefore the whistler-mode waves can grow quickly in the current sheet. The combined observations of energetic electron beams and waves show that after the southward turning of magnetic field, energetic electrons in the reconnection process are accelerated by the whistler-mode waves.     

Magnetic reconnection and energy release in a long-duration stellar flare

A dynamical model of magnetic reconnection in solar two-ribbon flares is applied to EXOSAT observations of a long-decay flare from the star EQ Peg. We show that the model is able of reproducing correctly the energy release rate and temporal evolution of the decay phase of the observed flare. We conclude that the flare was the stellar counterpart of solar two-ribbon flares and we derive the physical parameters of the emitting region.     

Numerical model of time-dependent hydrodynamic flows with mass loading

We study the influence of mass loading on the formation of shocks employing a time-dependent hydrodynamic model. Numerical examples illustrate in which way the formation and propagation of shocks in the plasma is affected by variations of the ionization rate (due to changes of solar wind parameters or of neutral gas production). It is found that mass loading may be an efficient mechanism to prevent the formation of discontinuities in hydrodynamic flows.     

Theory of magnetic reconnection in three dimensions

Magnetic reconnection in traditional, two-dimensional theory can be closely associated with topological properties of the magnetic field, separatrices, neutral lines, or separators. Such well-defined topological properties may no longer exist, or become hopelessly complicated, in more general three-dimensional configurations, that otherwise behave physically quite similarly to the two-dimensional configurations. We discuss generalized definitions of reconnection applied to such situations and illustrate typical properties with simulations of three-dimensional reconnection in the magnetotail.     

Imaging of reconnection processes in hard X-rays

The Hard X-ray Spectrometer aboard the SMM detected several events of energy release late in the development of two-ribbon flares. One such event, at 21:12 UT on 21 May, 1980 (～ 20 min after the flare onset and 15 min after the peak of the impulsive phase) is studied in detail. The site of new brightening first became visible in hard X-rays (> 22 keV) and only afterwards showed up at lower energies. It was clearly located high in the corona so that one can identify it with energy release at the tops of newly formed post-flare loops. Thus, if the Kopp and Pneuman model of the loop formation is adopted, we may have imaged here a reconnection process in the solar corona. An attempt is made to estimate physical parameters at the reconnection site.     

Ion dynamics of magnetic reconnection in the magnetotail

We discuss the kinetic processes of plasma thermalization, acceleration, and mixing in magnetic reconnection. Non-Maxwellian, gyrotropic ion distribution functions such as anisotropic ion beams in the plasma sheet boundary layer (PSBL) and counter-streaming ions (CSIs) in the plasma sheet are often observed during a plasmoid passage of a satellite in the Earth's magnetotail. Non-gyrotropic ion distribution functions are also sometimes observed just after the passage of the plasmoid. We study the behavior of non-Maxwellian ion distribution functions observed by GEOTAIL. We further study theoretically the ion dynamics by using a particle-in-cell simulation, and discuss the role of non-Maxwellian distribution functions in magnetic reconnection.     

The role of helicity in the reconnection process

The change of helicity for magnetic reconnection is calculated with the help of a kinematic model. The results confirm the approximate conservation of magnetic helicity for reconnection in an almost ideal plasma as e. g. the solar corona. Different examples show the contributions of twist or linkage of flux tubes to the total helicity change in the process. However, they also show that helicity may be produced for reconnection processes in more extended non-ideal regions which is due to new magnetic flux linked to the reconnected flux tubes.     

Interaction of shocks with a current sheet and reconnection in the solar corona

Interaction of shocks with a current sheet is investigated within a 2D MHD model based on an improved FCT numerical scheme. Basic parameters of the problem are chosen to correspond to situations in the solar corona with low plasma β and moderate shock strength. Slow and fast MHD shocks are introduced with shock normal parallel to magnetic field lines. The interaction with the current sheet causes distortion of the shock front and this distorts the magnetic field lines and generates electric current. Large current densities are generated especially when the fast MHD shock becomes the intermediate MHD shock at the current sheet. Then peak values of the current density are about 3–4 times larger than the initial undisturbed values in the current sheet.