Boundary Conditions in Gap Geometry

It is shown that the most suitable boundary conditions connecting the moments of the angular flux at the two faces of an annular void surrounding the fuel in a reactor lattice cell are obtained from the consistent use of the transport-theory P_N approximation in the void as well as in the other media, when N is not restricted to very low values. A different procedure, which is particularly appropriate in diffusion theory, had been used previously by Newmarch and extended to N = 3 and N = 5 by Tait and Clendenin. However, the algebraic difficulties are considerable, and, although their method is preferable to the systematic use of the P_N approxi- mation in all media for the lowest values of N, it is not capable of generalization to higher N. Comparisons of the different approaches are given for the lowest-order approximations; the method based on applying the P_N approximation to all regions is given in a form suitable for any odd value of N, and numerical results are presented up to N = 11 to show that it converges rapidly.