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The Effect of Fuel Depletion on Stochastic Behaviour in Supercritical Systems

  • M. M. R. Williams

Abstract

Extensive studies have been carried out of the probability distribution of neutron number in multiplying systems and a comprehensive list of references is available! Essentially, the procedure involves the construction of a probability balance equation for P(n,t), the probability that exactly n neutrons are present in the system at time t. Various extensions to this distribution may easily be developed which include delayed neutron precursors, number of counts recorded, etc. An aspect of this general problem that has by and large been neglected is the inclusion of burn-up of the fissile material. That is, the destruction of nuclei that occurs when fission takes place. The justification for such neglect is that during the time of measurement the number of nuclei destroyed is negligible compared with those remaining. This is indeed true except in one special case; namely that of a nuclear explosion. In this case, the time scale is such (10-7s) that a large fraction of the fissile material is consumed before the period of interest is over.

Keywords

Gaussian Approximation Nuclear Explosion Moment Equation Neutron Number Probability Generate Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    M. M. R. Williams, “Random Processes in Nuclear Reactors,” Pergamon Press, Oxford (1974).Google Scholar
  2. 2.
    N. T. J. Bailey, “The Elements of Stochastic Processes,” John Wiley, NY (1964)MATHGoogle Scholar
  3. 3.
    S. Chandrasekhar, “Stochastic Problems in Physics and Astronomy,” Rev. Mod. Phys. 115:1(1943).MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    N. G. Van Kampen, “Birth and Death Processes in Large Populations,” Biometrika, 60:419 (1973).CrossRefMATHGoogle Scholar

Copyright information

© Plenum Press, New York 1989

Authors and Affiliations

  • M. M. R. Williams
    • 1
  1. 1.Nuclear Engineering DepartmentThe University of MichiganAnn ArborUSA

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