A theory of low source start-up based on the Pál-Bell equations

• Published in: Annals of nuclear energy Vol. 102; pp. 317 - 348
• Main Authors: Williams, M.M.R., Eaton, M.D.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.04.2017
• ISSN: 0306-4549; 1873-2100
• DOI: 10.1016/j.anucene.2016.12.014

•Use of Pál-Bell equation to calculate low source strength.•Comparison of saddlepoint method with exact inversion method.•Derivation of mean and variance for space and energy dependence. The safe start-up of a nuclear reactor depends upon the presence of a steady neutron source in the core. This source, however, does not always have to be physically inserted into the reactor because there exist in the core natural neutron sources from spontaneous fission, cosmic rays, photo neutrons, fission products, etc. Nevertheless, so that the source magnitude is well defined, it is generally thought judicious to have a specially constructed source of the (α,n) type present. From an operational point of view, it is vital to assess the strength of the natural sources to see if they will be sufficient in magnitude to ensure safe stochastic startup without the addition of an extraneous source. The most important case for source evaluation is that of a reactor starting up with fresh, unirradiated fuel because then the natural background sources will be at a minimum. It is the purpose of this paper to examine the criteria necessary to ensure that the source strength is high enough to reduce the probability of any undesirable stochastic transient occurring to a specified value, e.g. 10−8; it may also be considered as an update of the classic work of Hurwitz and co-workers (1963). To carry out the calculations, we use the Pál-Bell backward formalism (Pázsit and Pál, 2008) and apply it to the point model in order to make comparisons with the earlier work of Hurwitz. We also extend the study to include space and energy dependence which are found to have a not insignificant influence on the results. The usefulness of the Gamma distribution is explored and its accuracy assessed. Tables and figures are given to illustrate the conclusions.