energy release, numerical simulations of a random resistive network are needed, taking into account lifetime effects, current feed-back influence, and the high self-induction of the magnetic fields in the normal domains in the sheet.

4.19. Particle acceleration in shear flows of space plasma

4.19.1. Space plasma's shear flows in different objects

In papers of Berezhko (1981, 1982), Berezhko and Krymsky (1981) there was assumed a particle acceleration mechanism in shear flows of space plasma. The shear flows of space plasma can be realized at boundaries of the magnetospheres of the Earth and other planets, at boundaries of the Heliosphere and stellar winds, and other astrophysical objects in regions of interactions of plasma flows with different velocities. In all these cases there are formatted shear flows of space plasma with regular changes of velocities of frozen in magnetic inhomogeneities which can be considered as scattering centers for energetic charged particles.

4.19.2. Particle acceleration in the two-dimensional shear flow of collisionless plasma

Berezhko (1981) investigates the idealized picture of the two-dimensional shear flow of collisionless plasma that is characterized by the presence of scattering centers whose role is played the magnetic field inhomogeneities. It was supposed that the hydrodynamic velocity u of the plasma is directed along the x axis and its magnitude varies as a function of the coordinate y (see Fig. 4.19.1).

In order to establish the energy variation law of a particle which, after scattering elastically, moves in the medium with a velocity v >> u, it is convenient to represent this motion in the form of a population of vibrations between two scattering centers with an appropriate averaging over all possible pairs. Thus if the particle vibrates between the centers A and B and uA > uB and xA < xB, as shown in Fig. 4.19.1, then its energy will increase since the centers A and B are brought together. However, for the center B there is a center B' that is placed symmetrically with respect to A (yB = yB, xA - xB' = xB -xA) so that the particle moving between the centers A and B' with the same velocity loses energy if only the quantities of the order of u/v are taken into account. In other words, within the framework of the adiabatic approximation no changes occur in the particle energy: < dE/dt > = 0 (the angular brackets denote averaging).

From other hand, if the terms ~ (u/v)2 are taken into account, an analysis of the particle motion between the two scattering centers, which are moving with a relative velocity dl/dt = w, leads to the expression

where I is the distance between the scattering centers. It can be seen from this that the total contribution of the centers A, B, and B' to dE/dt is positive and equal to 4Ew2/(lv). An averaging of this expression over the locations of the B center with allowance for the fact that the probability of the particle traversing a path length without scattering is exp(-//À) gives dE dt

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