4.19.3. Some examples of possible particle acceleration in shear flows
According to Sergeev and Tsyganenko (M1980) it has been established that a layer consisting of a shear flow of solar wind plasma exists at the boundary of the Earth's magnetosphere. The hydrodynamic velocity of the plasma in the layer varies from zero at the inside boundary to ~ 400 km/sec at the outside boundary. The characteristic thickness of the layer is l ~ re and its longitudinal dimension is L > 100re, where re is the Earth's radius. Particles which have path lengths X << l are accelerated efficiently by means of the mechanism discussed in Section 4.19.2. The condition X << l can be satisfied only for electrons, since X ~ p ~ 100 km for thermal protons, where p is the gyro-radius. It was assumed that the range of accelerated electrons is E < 1 MeV if X ~ p (the magnetic field at the boundary of the magnetosphere is ~ 10-4 Gs). Since the electrons usually cannot penetrate the interior boundary of the acceleration region, which is formed by the regular magnetospheric magnetic field, a density gradient of accelerated electrons, which is directed toward the Earth, is formed. A corresponding diffusion flow is directed from the Earth, which accounts for the anisotropy of high energy electrons that is recorded in the experiments (Sergeev and Tsyganenko, M1980). The following can be said about the shape of their energy spectrum. Gnedin et al. (1972) have analyzed the formation of the spectrum of particles, which have been accelerated by means of a mechanism for which the characteristic acceleration time t = Ej(dE/dt)<x E(4.19.3)
They showed that at 0> 0 a power spectrum ^ EY is formed with an exponent
at energies E >> Eo where Eo is the initial energy of the particles. For the case considered in Section 4.19.2 the condition described by Eq. 4.19.3 means that X <x E0. It can be assumed that X ~ p (i.e. X <x E) for most of the electrons energy range, and that X ^ E at high energies. Thus obtain a spectrum exponent Yin the limits from -3 to -1.5, consistent with the experiment: Y = -2 to -1.5 for E = 18-120 keV and y = -4.5 to -3 fore E > 100 keV (Sergeev and Tsyganenko, M1980). The values of y < -2 may be attributed to the influence of energy losses.
Universality of the spectrum produced is a characteristic feature of the discussed mechanism. An important feature of this mechanism is that it involves regular, large scale plasma motion, which sets it favorably apart from the other mechanisms, in particular, the mechanism of acceleration by turbulent pulsations (see Section 4.9).
A shear plasma flows can frequently occur under space conditions in different objects. A typical example for interplanetary space is the high velocity flows in the solar wind. Because of this the acceleration process of charged particles in a shear flows can be important in the production CR in different energy ranges.
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