c p + macc . It follows from the estimate of the energy concentrated in the magnetic compression region
that a fraction of the order of 8 of the total released energy is concentrated in the compression region. The remaining energy will be lost for compression in the region y ^ 428 and field deformation in the surrounding space.
The temporal characteristics of the processes are given by the relation between the pressure decrease in the examined region and the balancing gas-dynamic motion of the plasma. It has been shown in (Syrovatsky, 1966) that the plasma influx cannot balance the decreasing pressure if the basic currents are shifted at velocity u >> us48, where us is the sonic velocity in the plasma. Since the motions in the c c region of the intense field take place at the magneto-hydrodynamic velocity ua >> us, the process considered above may be realized under various conditions in the space.
A further development of this mechanism was given in (Syrovatsky, 1975). It was determined the electric and magnetic fields arising with a discontinuity of the neutral current sheet in connection with the problem of particle acceleration. The neutral sheet is considered to be an infinitely thin and perfectly conducting formation. It has been shown that a weak zero line of a magnetic field was arising with the electric field directed along it.
Syrovatsky (1975) has considered the role of the neutral current sheets in the dynamics of magnetized plasma. The main parameters have been presented which determine the flow near the zero lines of a magnetic field, and their typical values for solar flares and for model experiments. The approximation of a strong magnetic field and the properties of a neutral current sheet in the stationary regime have been examined. It has been noted that there exist two modes of magnetic field dissipation: quasi-stationary, and explosion modes. It was shown that the main effect of a magnetic field's longitudinal component along the zero line comes to a decrease of the effective Mach number of the plasma flow. The interesting model study of plasma behavior in the vicinity of zero lines was carried out by Frank (1975). The results of model laboratory experiments for investigation of magnetic field structure and plasma dynamics in the vicinity of a magnetic zero line were presented in this paper. With the methods of phase location and holographic interferometry it has been shown that the plasma, similarly to a current, transforms into a sheet. Redistribution of electron density over a sheet thickness presents the evidence for a sheet to he broken into separate current filaments. A character of this discontinuity depends on the conditions of an experiment.
4.17.3. A development of magnetic field annihilation models and the model of magnetic force line reconnection; on the role of discharge phenomena in some astrophysical processes and particle acceleration
Priest (1972) has examined the mechanism proposed by Sweet (1958) for magnetic energy transformation into others forms of energy. The method of boundary layer theory was used to obtain the profiles (along a current sheet) of the quantities characterizing a flow. Priest and Sonnerup (1975) have presented a review of the stationary hydro-magnetic models of magnetic field annihilation. The exact three-dimensional solution of magneto-hydrodynamic equations has been described in which a magnetic field was parallel to the jz-plane but varied (depending on the coordinate x) in its value and direction. The application of the theory to the geomagnetic field near the sub-solar point of the magnetopause was considered in the case of slow reconnection of magnetic force lines. The intensity of the induced electric field was calculated depending on the angle between the interplanetary and geomagnetic fields with the condition that the interplanetary field was perpendicular to the Sun-Earth line and plasma density in the current sheet was constant. Yeh
(1976a) has investigated a diffusion hydro-magnetic flow in the vicinity of a neutral point. Yeh (1976a) has shown that the electrical resistance determined the time scale of approaching to the stationary state in the case of hydromagnetic interaction of conducting flood at the merging of magnetic force lines near a neutral point. These proper scales differ from those which are ascribed to the flow when it is observed from outside. In the stationary state a transformation of magnetic energy into kinetic and thermal energy requires that the Alfven number should be less than unit for the upward flow. The solutions in the vicinity of a neutral point show that Ohm's law for a simple resistance is applicable to a modeling of the magnetic field force line reconnection. Rüdiger (1975) has studied the interaction between a homogeneous turbulence and a non-uniform magnetic field in the vicinity of a neutral surface. It was shown that initially uniform and isotropic turbulence field becomes non-uniform and anisotropic in such a magnetic field. The finite correlation length results in the turbulence field being affected also on the neutral surface. The anisotropic decrease of motions in the vicinity of the neutral surface was determined for some special forms of one- and two-dimensional turbulence. Furthermore, the effects of the action of such a non-uniform field of turbulence onto an average magnetic field have been found. Using the Bochner's theorem on the spectral tensor of initially homogeneous turbulence, an additional decrease of an average magnetic field was obtained. Yang and Sonnerup (1976) have generalized a model of the field reconnection in non-compressive fluid for the case of compressive fluid. The properties of two plasma streams ejected from a reconnection region depending on plasma properties and on the inflow velocity were determined by means of numerical integration using the conditions on a shock wave front. The possibility was discussed of the existence of fast transverse shock waves in the outward streams. Fükao and Tsuda (1973) have solved a non-stationary problem of magnetic field line reconnection in the magnetic hydrodynamics of non-compressive fluid. A numerical model experiment has been carried out for a plane of non-compressive viscous conducting fluid in the vicinity of a stagnation line. The velocity and magnetic fields (the magnetic field of a plane current sheet which is orientated along one of the asymptotic directions of plasma flow from the stagnation line) were set as the initial conditions. The results of the solution have been presented; the dependence of the velocity and magnetic field components, the current density, etc, upon the coordinates and time. The magnetic field reconnects in the vicinity of the neutral line arising on the stagnation line of the stream. The velocity of reconnection is increased with the growth of the flow's initial velocity. The interpretation of the results is complicated by the fact that the procedure of calculation itself introduces disturbances which are equivalent to a certain effective diffusion of a magnetic field. The results obtained do not come out of the stationary regime during the time intervals for which the calculating scheme holds. However, some characteristic features (proper to the stationary solutions obtained earlier) can be as well recognized, in the opinion of the authors, in the non-stationary picture obtained.
Yeh (1976b) has studied reconnection of magnetic lines of force in a viscous conducting fluid. Two-dimensional solutions of the equations of non-compressible magnetic hydrodynamics including the terms of viscosity and conductivity have been considered. The solutions were obtained describing the flow which is typical for the case of the reconnection of magnetic force lines. These solutions do not contain any discontinuity. It has been shown that magneto-hydrodynamic flows in the problem of magnetic field line reconnection which were obtained in a non-dissipative approximation can be substantially different from the flows which were obtained in the case in which viscosity and conductivity are tending to zero in a dissipative flow. The properties of the solution obtained confirm the substantial role of boundary conditions far from the neutral point on the character of magnetic field line reconnection.
The paper of Bruce (1975), in which the results of more than hundred publications during the thirty years are summarized, is devoted to a study of the role of the process of electric discharge in various astrophysical phenomena. The phenomena have been described related to electric discharges: the propagation velocity, magnetic fields which are circular with respect to a discharge axis, pinch-effect; plasma jets; radiation of whistlers; and so on. An attempt was made to identify the electric discharges with a wide class of astrophysical phenomena. It is adopted that electric discharges give a certain contribution to the solar flares where a current of ~ 104 A is reached and the magnetic fields of the order of 104-105 Gs are required which are not observable with solar magnetometer owing to localization and absence of the neutral atoms. The variation of long period variable stars, a filamentary structure of the Crab nebula, the abrupt changes in the brightness curves of Novae, the giant scale eruptions in the radio galaxies and some other astrophysical processes following particle acceleration are explained basing on the electrical discharges.
4.17.4. Particle acceleration in the neutral current sheets
Bulanov and Syrovatsky (1972) have considered two models of charged particle acceleration by electric fields near the neutral current sheets. For the first example, particle acceleration by the electric field arising at the instantaneous decay of the sheet was considered. It was shown that a considerable share of magnetic field energy can be transferred to the particles energy. In the second case the interaction of a stepped electromagnetic impulse of finite amplitude with a neutral current sheet has been examined. If the impulse amplitude is sufficiently high, non-limited particle acceleration will take place in the sheet.
Levine (1974) has studied the behavior of thermal particles in the vicinity of a neutral sheet. It has been shown that the field compression towards the neutral sheet would produce particle acceleration. A mean energy increase was calculated both with no account of and including the Coulomb losses. Coulomb losses complicate the picture to a high degree. In particular, acceleration does not take place in certain directions of particle motion; the acceleration of electrons is far more complicated problem than that of proton acceleration. The case is possible in which practically only the protons will be accelerated. The case of very rapid field compression was considered separately.
Particle acceleration in the vicinity of magnetic field neutral line has been studied as well by Bulanov and Sasorov (1974, 1975). Charged particle acceleration in a hyperbolic magnetic and uniform electric field has been investigated. The acceleration process consists from the direct acceleration by an electric field in a non-adiabatic region near the neutral line and from the betatron acceleration in a drift region. The characteristic energy of accelerated particles in non-relativistic and super-relativistic limits was determined. In the high energy region the energy spectra have an exponential form.
Bulanov and Syrovatsky (1976) have studied analytically and computed numerically the motion equations of charged particles in a uniform electric field which is directed along the zero of a hyperbolic magnetic field. The region of substantially non-adiabatic motion is located near the zero line, in which the particles are directly accelerated by electric field. Outside this region the particles are in a drift motion consisting of oscillation along the force lines and of a displacement across them; the oscillation amplitude is slowly increased (decreased) with moving away from (approaching to) the zero line. When approaching the zero line the adiabatic cooling of particles takes place and their heating takes place in the case of moving away.
4.17.5. Mechanism of magnetic field dissipation in a current sheet including non-anti-parallelism of the magnetic field, instabilities, and turbulence
Cowley (1976) has examined the phenomenon of reconnection of non antiparallel magnetic fields. Some modifications of the existing models of magnetic field line reconnection in the vicinity of the x-line (where the effects of finite conductivity are substantial) have been considered. In the models of this kind (for non-compressible conducting fluid) the magnetic fields and the stream velocities in the 'convective region' are less restricted than was assumed earlier. In the general case it can be argued that:
1) the magnetic field components and stream velocities normal to the x-line should change their sign to the opposite of that in the current sheet and its vicinity, the absolute values of the field and velocity, however, can be different on both sides of the sheet;
2) the components parallel to the x-line are arbitrary and can undergo arbitrary jumps in the sheet;
3) the second statement results in that the current in the sheet is not obligatory parallel to the x-line.
The mechanism of fast magnetic field dissipation in the current sheets, which are formed by the velocity gradients in the solar wind and in the magnetosphere's tail was considered by Vainshtein and Tomozov (1975). Since plasma with these conditions is collisionless, the dissipation processes are determined by the effective electric conductivities that are formed at a development of current sheets of ionsound turbulence in plasma. The characteristic energies of electrons accelerated in the solar wind in the process of outflow of the magnetosphere have been estimated. Galeev and Zeleny (1976) have considered a development of the tearing mode of instability in plasma with a diffusive neutral sheet at the presence of a magnetic field normal to the sheet component with a small, but finite, value. The influence of this component on the electron orbits in the vicinity of the neutral sheet results in a stabilization of the electron-tearing mode even at very small amplitudes of the normal field. A development of the ion tearing mode of an instability of a given wave length is possible only in a 'slot'. This slot is a limited range of the normal magnetic field component for which it is on the ion orbits in the neutral sheet can be neglected but a stabilizing contribution to plasma dielectric properties (produced by the magnetized electrons) becomes small. It has been shown that the slot formation is possible only in the case of a neutral sheet with sufficient current. The states of plasma with the values of normal to the sheet of magnetic field component which are under the instability region appeared to be the metastable states with respect to generation of the main discontinuity mode.
Basing on the analysis of a tearing instability in a neutral sheet region, Pustil'nik (1973, 1976, 1977a,b, 1978, 1980, 1999a,b,c, 2001), Pustil'nik and Stasyuk (1973, 1974) have developed detailed models of solar flares (chromospheric and coronal) and the corresponding mechanisms of solar CR acceleration. This problem will be consider in detail in the next Section 4.18.
4.18. Tearing instability in neutral sheet region, triggering mechanisms of solar flares, turbulence, percolation, and particle acceleration
4.18.1. The problem of solar flare origin, particle acceleration and ejection into solar wind
The studies of solar flares (Kaplan et al., 1974; Syrovatsky, 1972; Pustil'nik, 1976) have shown that the flare occurs due to an anomalously rapid dissipation of the magnetic field in the solar atmosphere. Such dissipation takes place in the current sheet in the magnetic field shear zone between two magnetic tubes. The anomalous dissipation is triggered when the plasma of the initial 'thick' sheet become turbulent owing to a strong current corresponding to the electric field mevT
e where v^ is the velocity of thermal electrons and vf is the effective frequency of collisions. According to Pustil'nik (1977a), the problem of flare origin is thereby reduced to the search for the initial disturbance resulting in the abrupt increase of the current and electric field in the sheet. Three types of hypotheses about the nature of such disturbances are considered: (1) an abrupt disturbance of the photospheric magnetic field (is at variance with the observations of Rust (1968) which show that the field is not disturbed before the flares); (2) transition of the field into an unstable state with the discontinuity modes of the tearing type (faces the difficulties of principle owed to stabilization of such instabilities by the longitudinal magnetic field and due to a slow mode of their occurrence (Fürth et al., 1962; Biskamp et al., 1970); (3) the instability of plasma formations hanging in the solar atmosphere near the initial sheet. Version (3), described in detail by Pustil'nik (1976), will be treated in detail here. Only two types of such formations exist in the solar atmosphere, namely the quiescent prominence and the coronal condensation.
The appearance of new magnetic fluxes in an active region should result, on the one hand, in a storage of the energy of the non-potential strength-less magnetic field, and, on the other hand, in a depression of the upper arc of the force lines (Kiepenhahn and Shindler, 1957; Syrovatsky, 1966). As it was shown by Pikelner (1971), such depression should leak to the quiescent prominence within a period Tsyphon = 10 ■ 30 hours. In other words, a situation takes place in this region which is sufficiently unstable relative to the balloon modes of the flute instability, i.e. a
npr > 10 cm j above the light corona ncor = 10 cm j. As it was shown by Pustil'nik (1973), when a prominence exceeds the critical value
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