The relationship between the backward and forward equations of stochastic neutron transport and associated matters

Abstract

The relationship between the forward and backward equations of probability balance for neutron transport are discussed and, in particular, we show the close relationship between the characteristics of the forward equation to the main equations of the backward approach. The well-known failure of the backward method to handle feedback is also noted and possible origins proposed, although this curious feature remains an open question. A comparison of the backward and forward approaches is gone into in some detail and their relative advantages and disadvantages highlighted. We illustrate the matter by the discussion of a problem of an energy burst due to a ramp insertion of reactivity. This problem leads to a transition from the stochastic region to the deterministic one and shows how the backward equation may be used in tandem with a deterministic set of equations without violating the restriction on the backward method. The problems arising from a spatially varying source are also discussed with reference to the backward equations and their undoubted superiority over the forward equations is stressed.