Stochastic theory of zero-power nuclear reactors. Part 2. Probability of the branching process degeneration and issues of estimating the probability of a nuclear accident

AbstractA formula has been derived to estimate the degeneration probability in which the conditional probability that the fission process will not stop by the time t is determined by using a system of nonlinear differential equations presented in the paper. It follows from the formula that whatever the breeding ratio, a branching process with a probability of unity will never arise in a nuclear reactor without an external excitation.A general relationship has been found for an asymptotic value of the probability that the fission process will stop in the nuclear reactor. It has been shown that Hansen's model is a quadratic approximation of the general model and always overestimates this probability.The paper presents a theoretical analysis showing that Hansen's model underestimates the probability of a nuclear accident as compared to the estimates obtained by using the general model presented in the paper