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

7/14/2014 2014 - #02 Physics and technology of nuclear reactors

https://doi.org/10.26583/npe.2014.2.13

### UDC: 621.039.516

A 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 non’linear differential equations presented in the paper. It follows from the formula that whatever the breeding ratio, a branching process with a probability of one will never arise in a nuclear reactor without an external excitation.

A general relationship has been found for an asymptotic value of 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 which shows that Hansen’s model underestimates the probability of a nuclear accident as compared to the estimates derived by using the general model presented in the paper.

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