Probabilistic methods in heterogeneous neutronic systems

We consider a slab of moderating material in which are embedded absorbing plates at fixed positions. A fast neutron source is incident on the left hand face and we calculate the transmitted fraction, T, from the far face and the reflected fraction, R, from the source face. The effect of the absorbing plates on the thermal neutron flux is characterised by a plate sink of strength γ, i.e. the Feinberg-Galanin-Horning representation is used. However, instead of the values of γ being prescribed, they are sampled from a probability distribution in the range (γl, γu). Given the probability distribution of the γʹs, we then show how the corresponding probability distribution functions P(T) and P(R) can be obtained. The problem is solved by two methods; in the first, for each realisation of the γʹs we calculate the associated values of T and R. Then, after many realisations (105 in this case), we may construct P(T) and P(R). The second method uses a completely analytical approach which does not involve numerical sampling with random numbers. To proceed we use well-established procedures in the theory of random processes, but because of the algebraic complexity, only two absorbing plates are considered.