1.9.5. Transport path of scattering by cylindrical fibers with field h = M/rn in the two-dimensional case
Consider first the case n = 3 (scattering by magnetic dipoles). Then the Eq. 1.8.14 will be used for the impact parameters r1 > ro (considering that do << 1, see Section 1.8.5) and numerical averaging will be carried out for r1 < ro using the plot of Fig. 1.8.3. The resultant expression is
Similarly, it can be easily shown that at an arbitrary n
This result follows physically from the simple observation. If the field h = M/rn the effective size of the scatter X are as if dependent on pc. The value of X may be estimated as the distance at which the Lorentz force equals the centrifugal force:
Since in the two-dimensional case A = /2/X , it is the Eq. 1.9.23 that follows from Eq. 1.9.25.
1.9.6. The transport path in the three-dimensional case of scattering by fields of the type h = M/rn
Since in the three-dimensional case X is also determined by the Eq. 1.9.25 and the mean path of collisions with inhomogeneities of effective size X is determined by the Eq. 1.9.1, then approximately
Thus it should be expected in the three-dimensional case of CR scattering by the dipole type of fields that A will be proportional to particle rigidity R. For the field of the type of quadruple (n = 4) A ^ at n = 5 A ^ R1/2. etc., i.e. the dependence of A on R weakens as the field becomes more complicated.
1.9.7. Transport path of scattering by inhomogeneities of the type h = (o, h(x ),0) against the background of the regular field Ho = (Ho ,0,0 )
Let us now find the transport path for the inhomogeneities the elementary scattering by which is set by the Eq. 1.8.19. According to Eq. 1.9.1 and considering Eq. 1.9.4, we shall obtain for inhomogeneities of type j (j = 1, 2, 3):
V 0max J
2njh 2 A2
Assuming that we have a spectrum of inhomogeneities in the range between X1 and X2 with the dependence of l and h on X in the form described by Eq. 1.9.6. In this case we shall obtain similarly to Eq. 1.9.9:
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