Transport Theory Corrections to the Source-Sink Method for Reactor Lattice Calculations

A new formulation of the source-sink method has been developed in which transport theory is employed rather than the standard diffusion theory approach. A general expression for the flux and criticality condition is derived for a reactor with a finite reflector in one-dimensonal geometry. The problem is solved in detail for the case of an infinite reflector, which enables the infinite medium Fourier transform to be employed. It is found that the general structure of the resulting source-sink equations is similar to that obtained using diffusion theory except, of course, for the presence of aditional transport transients which are important near the fuel plates. By means of an extensive numerical survey, it is shown that the effect of these terms extends well into the moderate region, where it is observed that diffusion theory underestimates the neutron flux. Conversely, diffusion theory is shown to overestimate the effective multiplication factor by amounts which depend upon the plate spacing and the type of moderator. For graphite and heavy water, we have found relatively small errors, whereas for ordinary water they can be unacceptably large. A number of assumptions are made in arriving at the final form of the transport corrected equations and the validity of these is discussed in an Appendix where a consistent derivation of the problem, from the integral equation, is given which highlights the errors involved in the FGH method.