Abstract
The physics of a reactor is significantly improved by surrounding it with a neutron reflector, i.e. structural elements that enclose the fissile zone, rather than just a bare reactor with a vacuum around it. It will also be seen that the properties of this reflector impact the neutron economy of the reactor. In 1939, Francis Perrin was the first to suggest the idea of surrounding a reactor with graphite blocks to reduce the size of the fissile zone. This idea was successfully implemented by Enrico Fermi for the CP1 pile, then for the first French reactor with heavy water, Zoé [acronym for Zero energy, Oxide, Heavy water [“Eau lourde” in French], (Nahmias 1953, p. 134; Lefebvre 2002, p. 35)]. The neutron reflector of PWR is mainly constituted of water and steel. It reflects back thermal neutrons towards the core and leads to an “economy” (or a gain) in fissile matter compared to a bare core. Another advantage is that it greatly improves the form factor by flattening the power distribution. Calculation of the neutron properties of the reflector is a key step in the calculation scheme for a reactor, a topic not often discussed in the standard references, despite the fact that a significant amount of theoretical research work has been carried out on this subject.
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Notes
- 1.
With the notable exception of (Meghreblian and Holmes 1960), which contains a full chapter on this question.
- 2.
J.P. Argaud: Modélisation du réflecteur pour les calculs de diffusion en neutronique [Modeling a reflector for neutron diffusion calculations], PhD thesis.
- 3.
Henri Poincaré (1854–1912) was one of the most brilliant French mathematicians/physicists. In 1873, he was first in the very competitive examination for enrolment at the Ecole Polytechnique and obtained his engineering degree from the prestigious “Corps de Mines” in 1875. He obtained his PhD in mathematics in 1879, and in 1886 he was awarded the Mathematical physics and probability calculations chair of the Faculty of Paris. In 1887, he was elected to the Académie des Sciences. His work in mechanics makes him the “father” of chaos theory. Furthermore, he was one of the pioneers of relativity theory, to which he made significant mathematical contributions. Further, in mathematics, he is the author of the famous Poincaré conjecture that was formally proved by Grigori Perelman in 2003.
Vladimir A. Steklov (1864–1926) was a Ukrainian mathematician, and a member of the Academy of Sciences of the USSR, and he seems to have been the first to use the notion of vector and operator in mechanics, thereby converting several physical problems in potential theory into problems concerning Dirichlet boundary conditions.
- 4.
Guy Beltranda : Etude des couvertures et réflecteurs des réacteurs de la filière à neutrons rapides [Study of blankets and reflectors for fast-neutron reactors], thesis presented to the University of Grenoble (1974).
- 5.
R.T. Ackroyd and J.D. McCullen: Albedo methods, Proc 2nd Peaceful uses of atomic energy, 1958, Volume 12, pp. 38–47.
- 6.
Ronald Tunstall Ackroyd (1921–2005) was an English neutron physicist. He taught neutron physics at Imperial College and became a member of the London Mathematical Society in 1950. He is also the author of an excellent work on the use of the finite element method in particle transport (Ackroyd 1997).
- 7.
Ph. Lebigot, J.C. Lefebvre: Tranches PWR—études de cœur: nouveau mode de calcul des réflecteurs [PWR—core studies: a new model for reflector calculations], technical report EDF/SEPTEN E-SE-TB-78-02, March 1978.
- 8.
Indeed, this relation allows calculation of β 2 and χ 2 in terms of the fuel properties. It is not a true critical equation from the neutron point of view since a critical equation would link the properties and size of the reactor. The usual critical equation is obtained using a studied combination of the continuity equations at the core/reflector interface, and couples the properties of the core and reflector, and their respective sizes.
- 9.
APOLLO2 in the case of EDF.
- 10.
E.Z. Muller: Environment-insensitive equivalent diffusion theory group constants for pressurized water reactor radial reflector regions, Nuclear Science and Engineering, 103, pp. 359–376 (1989).
- 11.
J. Ragusa, R. Sanchez, S. Santandrea: Application of duality principles to reflector homogenization, Nuclear Science and Engineering, 157, pp. 299–315 (2007).
- 12.
P. Reuss, S. Nisan: Une nouvelle méthode pour le calcul de l’interface cœur-réflecteur [A new method for calculating the core/reflector interface], technical report CEA/SERMA 265 T (1976) as well as the previous work of A. Jolly and P. Reuss of 1980, illustrated in (Bussac and Reuss 1985).
- 13.
J. Mondot: BETA—une méthode d’équivalence pour le calcul neutronique des réflecteurs en théorie de la diffusion multigroupe [BETA- an equivalence method for neutron calculation of reflectors in multi-group diffusion theory], technical report CEA SEN/LPN-83/1646 (1983). Jacques Mondot (1948–1993) spent all of his (too) brief career at the CEA, first at the Saclay center, then at Cadarache, where he established an original model that bears his name. After an MSc in reactor physics in 1971, followed by a PhD in 1973, he specialized in calculation schemes for reactors.
- 14.
E. Richebois, C. Fedon-Magnaud, P. Magat, G. Mathonnière, S. Mengelle, A. Nicolas: Determination of multi-group and multi-operator reflector constants: application to a power reactor transport calculation, International Conference on the Physics of Nuclear Science and Technology, pp. 1018–1025 Long Island, USA (1998).
- 15.
Ronald C. Brockhoff, J. Kenneth Shultis: A new approach for the neutron albedo, Nuclear Science and Engineering, 155, pp. 1–17 (2007). The authors propose empirical albedo laws for several materials at an equivalent surrounding dose.
Bibliography
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Marguet, S. (2017). Neutron Reflectors. In: The Physics of Nuclear Reactors. Springer, Cham. https://doi.org/10.1007/978-3-319-59560-3_13
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