accelerated particles is sufficiently dependent on the index in the power spectrum of turbulent pulsations.

2.10. CR diffusion in the pitch-angle space

If we neglect the action of electric fields of oscillations on the particles in the initial kinetic Eq. 2.6.13 (or if we equate to zero the coefficients D2 and D3 in the collision integral of Eq. 2.6.13), we shall obtain the equation describing the process of particle diffusion in angular space which passes with energy conservation. In this case one should solve directly the kinetic Eq. 2.5.1 because the diffusion approximation with respect to coordinates certainly is not applicable. In the general case this problem presents serious mathematical complications; however, if the regular magnetic field is sufficiently strong so that a perturbation of particle movement by a stochastic field during the time of the order of cyclotron rotation is small, one can average the Eq. 2.5.1 over the angle of particle rotation, pass to the drift approximation (Sivukhin, 1963). The collisional term of the kinetic Eq. 2.5.1 is determined in this case by the Eq. 2.9.1 at D2 = D3 = 0 and the averaging of the right side of Eq. 2.5.1 is known from the drift theory (Sivukhin, 1963; Galperin et. al., 1971):

dF „dF v . / xdF 1 d . „dF ^ ^ -+ vcos e---sin e(Vh)-=--Dl sin e-. (2.10.1)

An analytical solution of Eq. 2.10.1 can be obtained for the angles fitting the condition e << 1. In this case Eq. 2.5.1 takes the form:

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