Monte Carlo Calculation Method for Reactor Period Utilizing the Differential Operator Sampling Technique

Abstract

The inverse reactor period α is a fundamental mode eigenvalue of the α-mode nonlinear Boltzmann eigenvalue equation that considers delayed neutron contributions. Thus far, several Monte Carlo methods, including the α-k, weight balancing, and transition rate matrix methods, have been developed to calculate α. This study presents a new Monte Carlo method for predicting α by using the derivatives of the k-eigenvalue with respect to α. Formulae are derived to calculate the first and second derivatives using the differential operator sampling method. The key feature of the new proposed method is its ability to estimate the uncertainty of the predicted α by considering the uncertainty of the k-eigenvalue and its derivatives with respect to α.

Keywords:

• Monte Carlo
• reactor period
• differential operator sampling
• delayed neutron

Disclosure Statement

No potential conflict of interest was reported by the authors.

Notes

^a If α in Eq. (1)(1) $\begin{array}{rl}& \frac{\alpha }{\mathrm{v}}{\varphi }_{\alpha }\left(\mathbf{r},\mathbf{v}\right)+\mathbf{L}{\varphi }_{\alpha }\left(\mathbf{r},\mathbf{v}\right)\\ & =\frac{1}{\mathit{k}\left(\mathit{\alpha }\right)}\left({\mathbf{F}}_{\mathrm{p}}{\varphi }_{\alpha }\left(\mathbf{r},\mathbf{v}\right)+\sum _i\frac{{\lambda }_i}{{\lambda }_i+\mathit{\alpha }}{\mathbf{F}}_{\mathrm{d},\mathrm{i}}{\varphi }_{\alpha }\left(\mathbf{r},\mathbf{v}\right)\right),\end{array}$(1) is equal to the inverse reactor period of the system, $\mathit{k}\left(\mathit{\alpha }\right)$ is exactly equal to unity. Thus, $\mathit{k}\left(\mathit{\alpha }\right)$ does not appear explicitly in the regular α-mode eigenvalue equation.

^b This is a fictitious eigenvalue that is introduced to iteratively search for the true inverse reactor period α.