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The average number of reflections for radiation transmitted by a straight cylindrical channel can be determined analytically for an input beam for which the divergence has polar symmetry. For the case of an incident beam with a divergence of Cartesian symmetry (for example, the output from a rectangular neutron guide), the number of reflections can be calculated only if the maximum divergence is less than the critical angle of the cylindrical channel. For larger divergences, the requirement that the glacing angle is less than the critical angle does not allow a simple analytic solution. This paper reports the calculation of the number of reflections using an approximation and makes comparisons with a numerical simulation that gives an estimate of the exact result.

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