Energy-higher order mode analyses in Feynman-α method

Highlights: ► This paper focuses on the energy-higher order mode effect in Feynman-α method. ► An analytical formula of Feynman method has been derived for a two-group problem. ► A general higher order Feynman formula has been simplified to a multi-group problem. ► The energy-higher order mode effects are very minor in a thermal system. ► In a fast system, however, the effects are notable except for near-criticality. - Abstract: A subcriticality measurement by the Feynman-α method is generally affected by the spatial and energy-higher order modes. This paper focuses on the energy-higher order modes, which can never be eliminated unless the one-energy group approximation is adopted. An analytical formula of the Feynman Y-function that takes into account the energy-higher order modes has been derived for two-energy group systems based on the stochastic transport theory. A generalized formula for the space and energy-dependent Feynman-α method, which was originally derived by Endo et al. and Muñoz-Cobo et al., has been introduced to the study on the energy-higher order mode effects. The generalized formula used in this study is simplified for multi-group problems in a subcritical infinite multiplying medium. Numerical examples show that the energy-higher order mode effects are very minor in a thermal system with a commonly-used 1/υ detector. Thus, the conventional Feynman-α formula may be accurately applicable to subcriticality measurements. In a fast system, however, the energy-higher order mode effects are notable except when the system is near-critical