The moment method in the task of cosmic rays transport with finite speed in the framework of fractal Galaxy model
The task of cosmic rays transport with finite speed in framework of fractal Galaxy model have considered. The moment method have been used for analysis of space characteristics of process. The asymptotic moments (at t → ∞) have been obtained in the task of random walk with finite speed and with power law distributions of free path races p�(x) = �xx � 1 , x → ∞, 0 < � < 2. Accounting a finite speed led to necessity divide the original task into two separate tasks. The former consist in propagation of cosmic rays with finite mathematical expectation of free path races (1 < � < 2), and the latter consist in the propagation of cosmic rays with infinite mathematical expectation of free path races (0 < � < 1). In the former case the asymptotic distribution is described by stable law and influence of finite speed reduced to decrease of diffusivity. In the latter case a situation cardinally is changing. The asymptotic distribution has U-shape or W-shape form. Distributions of cosmic rays is reconstructed by using the obtained moments.