The Backward Theory of Feynman- and Rossi-Alpha Methods with Multiple Emission Sources

Abstract

The Feynman- and Rossi-alpha formulas are calculated for subcritical systems driven by a multiple emission source, i.e., one that emits several neutrons on each source emission event. The prime example of such sources is a spallation source, which will be used in future accelerator-driven subcritical systems (ADS), such as the energy amplifier. The Feynman- and Rossi-alpha formulas are calculated with backward master equations for such systems. The essence of the theory is a formula that connects the probability distribution of a cascade, induced by one single particle, with that induced by a continuous source of particles. Compact and consistent expressions are found for both the Feynman- and Rossi-alpha formulas. In agreement with earlier forward-theory–based or heuristic calculations, it is shown that the presence of the spallation source does not alter the time-dependence of the formulas, but enhances its amplitude. Hence, both methods appear to be promising to be used in future stationary ADS systems with relatively large subcriticalities.