Neutronic Analysis For Nuclear Reactor Systems pp 101-212 | Cite as

# Spatial Effects in Modeling Neutron Diffusion: One-Group Models

## Abstract

The fundamental aspect of keeping a reactor critical was discussed in Chap. 2, and we found out that the most principal evaluation quantity of the nuclear design calculation is the effective multiplication factor \( \left(\overline{\sigma}\left(\mathrm{v},T\right)=\frac{1}{\mathrm{v}}\int {d}^3V\left|\mathrm{v}-V\right|\sigma \left(\left|\mathrm{v}-V\right|\right)M\Big(V,T\Big)\right) \) and neutron flux distribution. We also so far have noticed that the excess reactivity, control rod worth, reactivity coefficient, power distribution, etc. are undoubtedly inseparable from the nuclear design calculation. Some quantities among them can be derived by secondary calculations from the effective multiplication factor or neutron flux distribution that was also discussed in Sect. 2.15 of Chap. 2 so far. In this chapter we treat the theory and mechanism to be able to analyze and calculate the effective multiplication factor and neutron flux distribution and possibly show numerical analysis and computer codes involved with solving the diffusion equation in one-dimensional and one-group models. The goal of this chapter is also for the reader to understand simple reactor systems, the notion of criticality, what it means both physically and mathematically, how to analytically solve for the steady-state flux for simple geometries, and finally how to numerically solve the steady state for more arbitrarily complex geometries.

## Supplementary material

## References

- 1.Y. Oka, T. Kiguchi,
*Nuclear Reactor Design (An Advanced Course in Nuclear Engineering)*(Springer, Tokyo, June 2014)Google Scholar - 2.J.R. Lamarsh,
*Introduction to Nuclear Reactor Theory*(Addison-Wesley, Reading, 1966)Google Scholar - 3.K. Okumura, T. Kugo, K. Kaneko, K. Tsuchihashi,
*SRAC2006: A Comprehensive Neutronic Calculation Code System, JAEA-Data/Code 2007-004*(Japan Atomic Energy Agency, Tokai-mura, 2007)Google Scholar - 4.A.F. Henry,
*Nuclear-Reactor Analysis*. Chapter 2 (MIT Press, Cambridge, MA, 1975)Google Scholar - 5.J.J. Duderstadt, L.J. Hamilton,
*Nuclear Reactor Analysis*(Wiley, New York, 1976)Google Scholar - 6.P.M. Morse, H. Feshbach,
*Method of Theoretical Physics*. Chapter 6 (McGraw-Hill, New York, 1963)zbMATHGoogle Scholar