Jan Dufek: Progress of Monte Carlo methods in reactor physics calculations

Simulation of neutron transport in nuclear reactors is a cumbersome task due to the spatial and neutron energy dependence in various macroscopic cross-sections of many nuclides present in the reactor. This problem is classically approached by homogenizing the macroscopic cross-section dependence over a number of spatial nodes and collapsing its energy dependence over a number of energy groups. Calculations can be carried out in this fashion relatively fast (once the nuclear data are homogenized and collapsed), and the bias due to the simplifications can be made acceptably small for some applications. Nevertheless, once the reactor geometry or materials are modified, the whole procedure must start from the beginning, which requires a tremendous amount of time. Hence, the deterministic approach is not suitable for R&D of new reactors where the reactor design is being constantly iterated.

A solution to the above problem can be provided by Monte Carlo methods that simulate transport of a large number of individual neutrons in the reactor. The Monte Carlo approach does not require any cross-section space and energy dependence treatment for a specific reactor. A single nuclear data library can be used for practically all reactor designs, which greatly simplifies the neutron transport simulations. Moreover, the correct treatment of the spatial and energy dependence ensures almost no bias in the results.

While the results from Monte Carlo simulations are not biased, they do contain a statistical error. Depending on the actual computed quantity of interest, the statistical error coming from a quick simulation may be relatively large; in this case, more neutron histories must be simulated, which requires a longer computing time. The large computational time for achieving small statistical errors is the major drawback of the Monte Carlo methods.

The presentation summarizes the current status of development of Monte Carlo methods in reactor physics, and outlines the challenges that need to be solved in order to establish the Monte Carlo methods not only in R&D, but in the whole nuclear industry.