Izvestiya vuzov. Yadernaya Energetika

The peer-reviewed scientific and technology journal. ISSN: 0204-3327

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

Volkov Yu.V.

DOI: 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.

References

  1. Volkov Yu. V. Stohasticheskaja teorija jadernyh reaktorov nulevoj moshhnosti. Chast’
  2. Fizicheskaja i matematicheskaja modeli [Stochastic Theory of Zero Power Nuclear Reactors. Part 1. Physical and Mathematical Models]. Izvestiya vuzov. Yadernaya rnergetika. 2013, no.4, pp. 127-134.
  3. Sevast’yanov B. A. Vetvjashhiesja processy [Branching Processes]. Мoscow, Nauka Publ., 1971. (in Russian)
  4. Sudek G. Problemy kinetiki reaktora. V sb. Teorija jadernyh reaktorov [Aspects of Reactor Kinetics. In Reactor Theory] Мoscow, Gosatomizdat Publ., 1963. (in Russian)
  5. Uhrig R. Statisticheskie metody v fizike jadernyh reaktorov [Statistical Methods in Reactor Physics]. Мoscow, Atomizdat Publ., 1974. (in Russian)
  6. Gnedenko B. V., Kovalenko I. N. Vvedenie v teoriju massovogo obsluzhivanija [Introduction to Queueing Theory]. Мoscow, Nauka Publ., 1966. (in Russian)
  7. Hansen G.E. Assembly of Fissionable Material in the Presence of a Weak Neutron Source. Nucl. Sci. Eng. 1960, v. 8, pp. 709-719.
  8. Hankins D.E. Effect of Reactivity Addition Rate and of Weak Neutron Source on the Fission Yield of Uranium Solutions. Nucl. Sci. Eng. 1966, v. 26, pp. 110-116.
  9. Shabalin E.P. Impul’snye reaktory na bystryh nejtronah [Fast Neutron Pulsed Reactors]. Мoscow, Atomizdat Publ., 1976. (in Russian)

branching process degeneration probability neutron population uncontrolled reactor power excursion due to prompt neutrons nuclear accident model fission process self'sustaining fission chain reaction