Applying the derivative source method to flux derivatives in Monte Carlo fixed source problems caused by interface shifts between spontaneous fission materials

Abstract

Derivative source method (DSM) determines neutron flux derivatives by solving the transport equation obtained by differentiating the fixed source Boltzmann neutron transport equation with respect to cross sections or interface positions. This study proposes a method for analyzing neutron flux derivatives using the DSM when the interface between spontaneous fission materials shifts. Since the cross section and source distribution in this case are given by Heaviside functions, the derivative due to the interface shift is obtained using a Dirac delta function at the interface. In the DSM, derivative source particles given by the delta function are emitted from both sides of the interface and undergo a random walk; however, we propose a method, applicable to multi-group Monte Carlo calculations, to integrate these two into a single particle. The DSM is conducted in the course of an ordinary fixed source calculation for cross section changes due to interface shifts. During the calculation, each time a particle crosses a shifting interface, a derivative source particle is emitted from the crossing point and its random walk is subsequently performed. Furthermore, an additional calculation is conducted when the interface of spontaneous fission source material shifts, in which derivative source particles are emitted from the interface due to the spontaneous fission source shift and subjected to a random walk. Test calculations demonstrate the DSM’s effectiveness in terms of computational accuracy and efficiency in comparison to neutron flux derivatives obtained from differences in neutron flux before and after a minute displacement of the interface.