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It should be again emphasized that the results obtained are valid for the isotropic scattering of particles by inhomogeneities which is determined by the Eq. 1.9.3 (or, approximately, by Eq. 1.9.4).

1.9.4. Transport path in a plane perpendicular to cylindrical fibers with a homogeneous field

Let us estimate the transport path for particle scattering by an ensemble of inhomogeneities of the type of the simplest two-dimensional and three-dimensional models considered above (see Section 1.8.4). In the general case for non-isotropic scattering

where N is the density of scatters, a is the effective cross section of scatters, 0is the scattering angle. If the mean distance between the axes of the scattering cylinders is l, then N ~ l~2 . Let cosO and then cosO be found. Considering that r = ro cosx (where x is the particle incidence angle varying from 0 to n) and after trigonometric transformations of the Eq. 1.8.7 we obtain cos0 = 1 - 2sin2 x{rLlro ) - 2(rL/ro )cosx+ 1 (1.9.17)

Integrating Eq. 1.9.17 over r = ro cosx from -ro to +ro, we shall find that

The Eq. 1.9.18 gives the following asymptotic representations:

= J(4/3)(/r0)-2 if rL/r0 >> 1, [4/3 if i/o << 1.

Substituting Eq. 1.9.18 in Eq. 1.9.16 we find that

i2 L

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