Nuclear Science and Engineering / Volume 179 / Number 4 / April 2015 / Pages 460-476
Technical Paper / dx.doi.org/10.13182/NSE14-42
Analytical Greenâ€™s functionâ€“based diffusion Monte Carlo (MC) methods have been applied earlier for simulation of reactor noise experiments for measuring the degree of subcriticality in accelerator-driven systems. In this method analytical solution of the diffusion equation is used to construct the probability distribution function for neutron absorption in a medium. This method has several advantages such as speed, elegance, and exactitude but was applicable to a rather restricted class of problems, such as an infinite or bare homogeneous medium.
In the present paper, we further develop the analytical Greenâ€™s function (analytical diffusion kernel) approach to demonstrate its utility in a wider class of problems like a heterogeneous medium with the same or different diffusion coefficients. We provide mathematical and numerical proofs of the validity of certain recipes that were proposed for heterogeneous systems. We also investigate whether and to what extent the diffusion theoryâ€“based MC can be improved to give results closer to transport theory, particularly in situations wherein diffusion theory methods are otherwise inapplicable.