On the other hand, at v < cs the particles are accelerated in the electric field without being scattered on the ion sound plasmons (in this case, the ionization losses are negligibly low). Each gain in the velocity is permanent up to where the particle energy is exchanged with the ion-sound plasmons. As it was shown just above, however, the particles in these regions are immediately affected by the quasidiffusion acceleration. Thus, the chemical composition of the accelerated particles should be similar to that of the plasma in which the acceleration occurs, in agreement with the observation data (Dorman and Miroshnichenko, M1968; Dorman, M1972, M1978; Miroshnichenko, M2001). It can be seen when summarizing the above discussion that the inclusion of the particle-plasmon elastic collisions will unambiguously give the quasi-diffusive particle acceleration in the elastic field the main characteristics of which coincide with the observation data. This makes it possible to expect that this description of the processes resulting in particle acceleration in the current sheet of a flare is adequate.
4.18.11. Development of solar flare models and mechanisms of particle acceleration in the turbulent current sheet
In papers of Pustil'nik (1997, 1999a,b,c, 2001) given the development of discussed above solar flare models and mechanisms of particle acceleration in the turbulent current sheet. In more details are investigated the problem of the stability of a turbulent current sheet. Pustil'nik (1997) note that after successful progress in our understanding of the equilibrium state of a flare current sheet, it is natural to ask whether this equilibrium state is stable. This leads us to the unfortunate conclusion that the generally accepted equilibrium state of a turbulent current sheet is not stable, and this picture of a flare cannot be considered final. The instability of a turbulent current sheet forces us to drastically reconsider our approach to flare energy release, and to obtain a new, stable equilibrium state taking into account properties of dynamical instabilities. Let us first consider the main instabilities of a turbulent flare current sheet.
Tearing mode instability. These instabilities (Fürth et al., 1963) lead to the redistribution of the flat current in a plasma with finite conductivity into a set of parallel current strings (see Fig. 4.18.6).
The most unstable mode (tearing) has a development time
where Ta = a/va = 10-5 ■ 10-3 sec is the Alfven time, ReH =Td lza is the magnetic Reynolds number, and td = a V (c2/W) is the diffusion time.
For standard current sheet parameters H2 5 = 102 5Gs, «g = 108cm -3, t6 = 106 K, this corresponds to a time for splitting of a flat current sheet into a system of strings of about 10-100 sec for Coulomb conductivity and 1-10 msec for turbulent conductivity. The tearing mode is very important, since it, has no threshold in the flare condition, and cannot be suppressed (stabilization by the rapid evacuation of plasma from the sheet, according to Bulanov and Sasorov (1978) does not act effectively for a thin current sheet). In the nonlinear state of the tearing mode, the opposite process of coalescence occurs. This leads to the joining of numerous generation strings, with additional energy release on the same tearing time scale. The final structure is determined by the competition between the coalescence of magnetic islands (current strings) and the ejection of plasma from the current sheet by magnetic tension.
Pinch type instabilities (sausage, kink, etc.). Current strings are in a Z pinch state, with the external pressure of azimuthally fields H0 balanced by the internal pressure of the plasma nkT and the longitudinal field H2 /4n. This state is unstable to a set of MHD fast instabilities (Priest, 1982) (sausage, kink, and other more complicated instabilities), which result in the collapse of a local current strings and their disruption at numerous points, with the generation of an electrostatic double layers (in the sausage mode) and/or the formation of a current kink and straightening of its braided field lines (in the kink mode). There is some stabilization of the pinch mode by the influence of the longitudinal magnetic field on the length of the pinch
according to criteria of Kruskal and Schwarzschild (1954) and Shafranov (1957). However, this stabilization is not effective for the thin, long current strings with lla > 102 ■ 103 produced by the tearing mode in the turbulent current sheets of solar flares. The following two processes (c) and (d) disrupt the steady state of a current sheet under the action of a specific property of plasma turbulence, namely, the very narrow threshold for plasma turbulence generation: the directed velocity in the current must exceed the phase velocity of the excited waves. For the opposite sign of the ratio (even for 1 - ujVph << 1), we have very rapid dissipation of the plasma waves in the same plasma. This can easily be seen from the example of the growth rate of the ion-acoustic wave instability in plasma with longitudinal current (Mikhailovsky, M1977):
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