It can be seen from Table 1.8.1.that the particles with 0.5.Rmax < R < 3Rmax are scattered through the largest angles and that the scattering by inhomogeneities of the first type is in the largest rigidity interval, whilst that by the third type of inhomogeneities is in the smallest rigidity interval (Dorman, 1969). The inhomogeneities may also be in the form of condensations and rarefactions of magnetic force lines, the magneto-hydrodynamic and shock waves, the strengthens magnetic formation etc. We shall not dwell here on these cases and only note that the abovementioned formations may also be characterized by the size X (for the condensations and rarefactions of the field and for the strengthens closed formations this is merely their effective size; for the magneto-hydrodynamic or magneto-sonic wave this is the wavelength; for the shock wave this is the width of the front) and field h. The scattering by such formations will be determined, as a first approximation, by the Eq. 1.8.8, 1.8.14, 1.8.19.
1.9. The transport path of CR particles in space magnetic fields
1.9.1. The transport path of scattering by magnetic inhomogeneities of the type of isolated magnetic clouds of the same scale
Let N be the concentration of magnetic inhomogeneities of size X; the mean path of particle interaction with inhomogeneity is then
where l = N 13 is the mean distance between inhomogeneities. If the scattering through an angle 6<0o and do << 1 is on the average of equal probability in each interaction, the particle after n interactions will be scattered with equal probability through an angle 0<0oyfn . Thus after n = (2/0o )2 collisions the scattering will be practically isotropic and the transport path will be
Examine first the inhomogeneities of the same scale of the type of isolated magnetic clouds. It was shown above that in such case do ~ 2 if R/h = rL <<A and do ~ 2A/rL if rL > A . Taking account of Eq. 1.9.2 we shall obtain
The Eq. 1.9.3 may be rewritten, accurate to within a factor of ~ 2, in the form
1.9.2. Transport scattering path in case of several scales of magnetic inhomogeneities
Let it now be assumed that the space contains some spectrum of magnetic inhomogeneities filling the entire space, l ~ A. If the field strength in inhomogeneities of all scales is approximately the same, the following simple observations (Dorman, 1959) will make it possible to estimate the dependence of A on R. Consider the motion of particles whose curvature radius in a field H is rL .
The scattering by inhomogeneities for which rL ~ A will be determined by the path A1 ~ rL ~ A. At the same time, the scattering by big inhomogeneities of size Ab >> rL will be determined by the path A2 ~Ab >>A1, and that by small inhomogeneities of size As << rL by the path A3 ~(rL/As )2 As >> A1, in both last cases the scattering proves to be much less effective and may be neglected as compared with the scattering by inhomogeneities with A ~ rL (resonance scattering).
If we have a set of inhomogeneities within A1 ^A2, then, in compliance with the above simple observations, the diffusion path will be
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