THE NUMBER OF REFLECTIONS OF A NEUTRON BEAM TRANSMITTED BY A CAPILLARY FIBER

The average number of reflections for radiation transmitted by a strai ght cylindrical channel can be determined analytically for an input be am for which the divergence has polar symmetry. For the case of an inc ident beam with a divergence of Cartesian symmetry (for example, the o utput from a rectangular neutron guide), the number of reflections can be calculated only if the maximum divergence is less than the critica l angle of the cylindrical channel. For larger divergences, the requir ement that the glacing angle is less than the critical angle does not allow a simple analytic solution. This paper reports the calculation o f the number of reflections using an approximation and makes compariso ns with a numerical simulation that gives an estimate of the exact res ult.