- مبلغ: ۸۶,۰۰۰ تومان
- مبلغ: ۹۱,۰۰۰ تومان
The purpose of this work is to elaborate a master equation formalism for the evolution of the probability distribution of the cumulative energy generated by fissions in a multiplying system with delayed neutrons. The formalism accounts for the fact that the fission energy v is also a random variable, thus the fluctuations of the total energy generated are due to both the fluctuations of the number of fissions, as well as to the fluctuations of the energy per fission. By comparing to the case where the fission energy is taken as constant, the significance of the fluctuations of the fission energy can be assessed. The first two moments of the cumulative fission energy are determined explicitly, and the time dependence of the expectation and the variance is calculated for different reactivities. As expected, the variance of the energy per fission does not play a significant role in the variance of the cumulative fission energy
In order to get an insight into the stochastic behaviour of the cumulative fission energy production generated by one starting neutron in a neutron multiplying system, a backward generating function equation was derived, which made it possible to calculate the time dependence of the moments of the cumulative fission energy for the case the fission energy in the individual fissions is a random variable. The expectation and the variance of the cumulative fission energy was determined in systems of various reactivities. In order to assess the significance of the random fission energy, a comparison was made with the case when the fission energy is constant. The difference proved to be very minute, from which one can conclude that the variance of the cumulative fission energy is mainly due to the variance of the number of fissions. This also means that in calculations of the higher order moments of the cumulative fission energy, the fluctuations in the energy generated in individual fissions can be safely neglected.