Rossi-α and Feynmann Y functions for non-Poissonian pulsed sources of neutrons in the stochastic pulsing method: Application to subcriticality monitoring in ADS and comparison with the results of Poissonian pulsed neutron sources

In this paper, analytical expressions for the Rossi-α and the Feynmann Y functions are deduced for the case of Poissonian and non-Poissonian neutron sources when the stochastic pulsing method is used. These analytical expressions are used to fit the experimental data and to obtain the prompt neutron time constant. Also we perform in this paper a comparison of the results obtained for the Rossi-α and Feynmann Y functions with Poissonian and non-Poissonian neutron sources, and we study how much change the shape of these functions when the fission probability decreases and the capture probability increases due to the depletion with time of the fuel, and the increase of the fission products. Some comparisons with experimental data and with the results of other authors have been performed. Another important question analyzed in this paper and that it is interesting from an academic point of view is that the average number of detected counts induced by one single neutron injected in the system at an arbitrary time t′, should obey in point kinetics theory an adjoint equation in the time domain. Also the cross-factorial moment of the number of counts induced by one neutron in two counting intervals should obey also an adjoint equation in the time domain with a source term that depends on the first moments. These results are a consequence of more general results that have been obtained using stochastic transport theory for the one particle probability generating function or Kernel generating function.