Tf Tr cot dr bdp and Tf is the time scale for fragmentation and Tr is the time scale for the radioactivity decay. The Eq. 2.11.58 for index p = 4 gives:
which in the case when the convection velocity v is a constant and N ^ 0, has solution w+w = -bp2 J Jpjp -^p.
If the CR source has an exponential dependence of the form Q(p)<* J p Ydp, the solution for differential energy spectrum of CR density according to Eq. 2.11.62 will be d(w+w)= Y- 2 ( E^-(r-1) dE y(y —1)1 c
2.I2. Phenomenological description of CR anisotropic diffusion
In some cases, the approximation of anisotropic diffusion is sufficient for the study of CR propagation and their energy variations (CR propagation in the galactic arms, interaction of CR of moderate energy with solar wind etc.). The matter is that CR distribution is isotropic in the first approximation, a relative variance from isotropy (so called anisotropy) is very small; as a rule it is < 1%, and in this case a distribution of CR in space can be described, with good accuracy, by a particle density n(r,p,t) instead of a distribution function f(r,p,t) (Dorman, 1965, 1967).
Thus a density of CR in space is n(r, R, Ze, t), where r is the spherical coordinates with the center in the Sun, R and Ze are the particle rigidity and charge, t is the time. Then in the approximation of anisotropic diffusion n will be determined by a continuity equation
Cosmic Ray Propagation in Space Plasmas
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