Feynman-alpha and Rossi-alpha formulas with spatial and modal effects

[EN] Feynman-α and Rossi-α formulas including multiple α-modes are derived for stochastic and continuous neutron sources. The presented formalism is further developed to achieve spatial correction factors for the single α-mode point kinetics representations of the Feynman-α and Rossi-α formulas. As a natural extension of the multiple α-mode formalism, delayed neutrons are included in the Feynman-α formula. The obtained formulas are validated experimentally in a strongly heterogeneous system obeying multiple α-modes, resulting in good agreement with the presented theoretical framework.