Itô-calculus based mathematical models for stochastic nuclear reactor kinetics and dynamics simulations of low neutron source nuclear power plant (NPP) start-up

This paper investigates the effect thermal feedback has on the stochastic nuclear reactor dynamics of low neutron source nuclear power plant (NPP) start-ups. Stochastic mathematical and computational models are required to determine the probability of a stochastic power surge occurring during nuclear reactor start-up that would damage the nuclear fuel. The aim is to design the nuclear reactor, the nuclear fuel, and the operational start-up procedures in a manner that minimises the probability of a stochastic power surge occurring, which damages the nuclear fuel, to a prescribed level of probabilistic risk (10−8–10−5). Recently, the Pál-Bell equations have been used for such low neutron source nuclear reactor start-up simulations. However, the stochastic nuclear reactor start-up models, based upon the Pál-Bell equations, cannot accommodate changes in the macroscopic neutron cross-sections arising from feedback processes. An alternative approach that could, in principle, include thermal feedback processes is the forward master equations. However, these are complex to implement for multidimensional and multi-group stochastic nuclear reactor dynamics problems. In addition, time-dependent analog Monte Carlo models could be used but these are computationally prohibitive for most nuclear reactor start-up simulations. This is due to the stringent requirements on the statistical accuracy of the safety probability associated with stochastic power surges. Therefore, this paper uses an alternative Itô-calculus approach to compute the stochastic properties required for low neutron source NPP start-up. The Itô-calculus approach is an approximate mathematical method, compared to the more general Pál-Bell and Monte Carlo methods, for low neutron source nuclear reactor start-up and fast burst systems. Therefore, the implementation of the Itô calculus method is first validated against the Caliban fast burst nuclear reactor experimental wait-time results to understand the accuracy of the method. The implementation of a simple feedback model is also verified against the point neutron kinetics equations. The neutron population CDF calculated using the Pál-Bell equations without thermal feedback, and the safety probabilities computed with, and without, including thermal feedback mechanisms are then analysed and assessed. These results demonstrate that the Itô-calculus approach can be used to gain useful insight into the behaviour of stochastic nuclear kinetics and dynamics during low neutron source NPP start-up. Furthermore, the results suggest that the safety probabilities computed using the Pál-Bell method are not affected by neglecting thermal feedback mechanisms which is an important result from a nuclear reactor safety perspective.