On the Validity of the Second Fundamental Theorem for Small Reactors
- 1 April 1959
- journal article
- research article
- Published by Taylor & Francis in Nuclear Science and Engineering
- Vol. 5 (4), 248-253
- https://doi.org/10.13182/nse59-a25592
Abstract
The second fundamental theorem of reactor theory gives a general expression for the nonescape probability. To check the validity of this expression for small sizes, first-flight nonescape probabilities are calculated for neutrons which have originated from either a persisting or a uniform stationary distribution in slabs of half-widths ranging from 0.1 to 10 mean free paths. Exact values computed directly from the integral formulation are compared with the approximate values obtained by expanding the distributions in eigen solutions of the wave equation and applying the general theorem, assuming that the linear extrapolation of the final flux vanishes on the extrapolation surface. It is found that the nonescape probabilities given by the fundamental theorem remain quite accurate even when the size of the reactor is decreased to the order of the mean free path. For a slab which is only two mean free paths wide, the fractional difference from the exact value is 1.5 per cent for the persisting distribution and 2.5 per cent for the uniform distribution.Keywords
This publication has 1 reference indexed in Scilit:
- The Physical Theory of Neutron Chain ReactorsPhysics Today, 1959