The backward theory of Feynman- and Rossi-alpha methods with multiple emission sources

The Feynman- and Rossi-alpha formulas are calculated for subcritical system s driven by a multiple emission source, i.e., one that emits several neutro ns on each source emission event The prime example of such sources is a spa llation 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. Th e essence of the theory is a formula that connects the probability distribu tion of a cascade, induced by one single particle, with that induced by a c ontinuous 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 presen ce of the spallation source does not alter the time-dependence of the formu las, but enhances its amplitude. Hence, both methods appear to be promising to be used in future stationary ADS systems with relatively large subcriti calities.