Abstract
Industrial reactors have complex geometries, with the nuclear fuel being geometrically separated from the coolant. Furthermore, different materials are used to allow for mechanical and thermal stresses due to the emitted energy. Hence, the homogeneous model cannot be applied in all situations, which leads to more complex neutron models for calculations.
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Notes
- 1.
Isaï Isodorovich Gurevich (1912–1992). This Soviet physicist contributed significantly to the field of reactor and nuclear physics: phase transitions, nuclear repulsion (with Pevzner), and resonance integral theory in heterogeneous reactors. He was a member of the Academy of Sciences of the USSR as of 1968.
- 2.
Isaak Yakovlevich Pomeranchuk (1913–1966) was a Soviet physicist. He obtained his degree from the Institute of chemical technology of Moscow, where he was under the supervision of Alexander Shalnikov. Later on, he worked in Kharkov with Lev Landau and A. Akhiser. In 1937, he followed Landau to the Kapitza Institute and obtained his PhD in 1938. As of 1943, Pomeranchuk and Gurevich worked in the frame of the laboratory 2 of theoretical physics in the Soviet atomic bomb project under Kurchatov. In 1944, he predicted synchrotron radiation and the limit of 1017 eV for the energy of electrons in cosmic rays. With Akhiser, he developed the theory of absorption in a homogeneous medium, which was published in 1947 and used for the construction of the first Russian reactors. He founded the Institute for Theoretical and Experimental Physics (ITEP) with Lev Landau. He is famous for the Landau-Pomeranchuk-Migdal effect for the reduction of the Bethe-Heitler Bremmstrahlung and pair-production cross sections at high energies (or for very dense matter).
- 3.
V. A. Kremnev and A. A. Luk’yanov, Space distribution of neutron resonance absorption in a block, Atomnaya Energiya, Vol. 14, No 2, pp. 216–217, 1963.
- 4.
Alain Guyader : Etude expérimentale de l’effet Doppler de l’uranium dans les milieux multiplicateurs à neutrons thermiques et rapides [Experimental study of the Doppler effect in uranium in multiplying media with thermal and fast neutrons], PhD thesis, University of Orsay (1970). This thesis contains few theoretical aspects, focusing instead on experimental measurements.
- 5.
Albert Amouyal, Pierre Benoist: Nouvelle méthode de détermination du facteur d’utilisation thermique d’une cellule [A new method for determining the thermal utilization factor of a cell], Technical report CEA-571, 1956 and the same authors with Jules Horowitz in: Journal of Nuclear Engineering, 6, p79 (1957), and 23, p. 58 (1965).
- 6.
D.J. Behrens: The effects of holes in a reacting material on the passage of neutrons, Proc. Phys. Soc., 62, 607 (1949). See also: The migration length of neutrons in a reactor, UKAEA report—Atomic Energy Research Establishment, Harwell, R/R.877.
- 7.
D.A. Newmarch: A modification to the diffusion theory of the thermal fine structure in a reactor to account for the effect of air channel, Journal of Nuclear Energy, Vol. 2, pp. 52–58 (1955).
- 8.
I.S. Grant: Neutron streaming in gas-cooled reactors, Report UKEA—Atomic Energy Research Establishment, Harwell, R/R.2568, October 1958. These declassified reports were offered for sale at the time.
- 9.
E. Guggenheim, M. Pryce, Nucleonics, 11, 2–50 (1953).
- 10.
Albert Amouyal read mathematics at BSc level at the Faculty of Sciences in Algiers and obtained an engineering degree from the Ecole Supérieure d’Electricité. He joined the Commissariat à l’Énergie Atomique in 1948 in the Mathematical Physics Department headed by Jacques Yvon, and became head of the Information Technology Department there. In 1972, he was appointed the General Director of the Compagnie Internationale de Services en Informatique (International Company in Information Technology Services, abbreviated as CISI in French—a subsidiary of the Commissariat à l’Énergie Atomique). We reproduce a long but interesting section of an article by Amouyal on the introduction of computers in reactor physics at the CEA: “Initially, the (solitary) work was not rewarding and was restricted to the reading of rare articles published in scientific journals, and contacting some companies or persons—namely M. Couffignal, who was in charge of the subject matter at the Centre National de la Recherche Scientifique (CNRS—National Center for Scientific Research). These contacts were increasingly disappointing, and very discouraging, especially as the needs of the Mathematical Physics Department were met by its calculation studies. The latter employed four qualified persons, who, using Friden calculating machines, had only to solve simple problems for physicists or engineers, thereby illustrating the theoretical models of the time. Hence, in neutron physics, it was common practice to solve most problems in diffusion theory using models having one spatial dimension (slab, spherical or infinite cylindrical geometries), with two or three distinct physical media and with one or two energy groups. The most complex cases rarely led to more than a dozen linear algebra equations involving a dozen unknowns - and yet, at that time, this was considered as being a very difficult task by the calculations department. The first significant contact with the world of computers occurred during a summer school organized in 1954 by the Mathematical Laboratory of the University of Cambridge (United Kingdom), directed by Professor Maurice V. Wilkes. [Amouyal], along with J. Carteron, then at Electricité de France (EDF), was first introduced to programming on the EDSAC. This initiation was followed by a placement in Professor Wilkes’s laboratory lasting several months during the first semester of 1955. [Amouyal] then had the opportunity to deepen his knowledge—thanks especially to the late Stanley Gill and David Wheeler- sufficiently to consider that it was high time that the Mathematical Physics Department should embrace these new technologies by purchasing one of the calculation machines announced by European manufacturers. After analysis, the CEA chose to buy a machine from MERCURY, sold by the British company Ferranti—which seemed very interesting from a technical point of view and in terms of its excellent performance/price ratio. One of these machines was ordered in 1955. At the same time, it was decided to set up a team of specialized persons and to hire young engineers with high-level qualifications. In 1955, two mathematicians were hired immediately after their graduation from the Ecole Normale Supérieure, Rue d’Ulm (the street in which the ENS is located) and sent to England for a one-year training course: one was sent to Manchester University and the other to the University of Cambridge. As of 1956, the specialized team of the Mathematical Physics Department, at that time headed by Jules Horowitz, was composed of twenty persons with a high-level scientific background, but with training that was improvised using the available means for programming or numerical analysis methods applied to computers—French universities did not provide any such training. However, Ferranti had some problems setting up the MERCURY and could not honor the contractual delivery agreements. Thus, under pressure due to the mandatory needs of the Department and the regular shifts in delivery dates of the MERCURY, an IBM650 was ordered hastily and installed at the Nuclear Studies Center in Saclay in July 1957. The MERCURY was finally delivered in December 1957. With these machines, the specialized team of the Mathematical Physics Department was in charge of their operations and of programming the studies to be executed. They were the only ones with the know-how, and thus were the only ones to have access to this equipment. Hence, they were organized into several application sub-groups with one of sub-groups being dedicated to the base programs delivered by the manufacturers, to designing basic sub-programs, and to operating the machines. The application sub-groups were required to design programs to solve problems submitted by the engineers and physicists with the Department on one hand, and more straightforward problems of general value on the other.
The majority of requests came from the neutron physicists in the department, while the others—very few—emanated from the theoretical physics department. The IBM 650, which had a relatively limited capacity, was very useful and was successfully utilized for numerous problems that were too complex for the calculation team. For instance, there were cases of neutron physics problems in diffusion theory with one space variable, but with a nearly infinite number of media, and two neutron groups: this progress was greatly appreciated. MERCURY, was far more powerful than the IBM 650, and opened up new possibilities with the solution of problems involving two spatial variables. However, because of its fragile nature, calculations were restricted to under two hours, otherwise the poor technical inspector responsible for maintenance was in a panic since the probability of unpredictable stoppage of the machine was no longer negligible, and this could lead to appreciable worsening of the monthly breakdown rate, resulting in penalties for the constructor. The operation of the machine was very “low-tech” and simple. Indeed, the working day was essentially dedicated to tests, and each engineer executed his calculations himself on the computer, directly at the workstation of the IBM 650 or the MERCURY. The duration of these calculations was highly unpredictable, as the schedules could only be very approximate. Time loss could not be avoided and affected the cost-effectiveness of the machines, but it was difficult to proceed otherwise as calculations could not be batch-processed at the time. Since it was impossible to answer all the programming requests from all the departments within a reasonable time, the specialized team from the Mathematical Physics Department set up an introductory programming course for all those interested. The latter was simplified on MERCURY thanks to a simple language (the “Autocode”), which was very successful. This led to an increase in the number of users, hence in the number of requirements for calculations. This situation resulted in saturation of the MERCURY machine, but in 1959, the Department of Military Applications bought a new machine, an IBM 704, with 30% of its time being given over to the civil sector of the CEA. This allowed for more time in the acquisition of a new machine. The study of this new project began in 1959, and two choices quickly emerged: a GAMMA 60 from the Bull Company, and an IBM 7090. The GAMMA 60 had very innovative features but was not yet ready for use. It was reminiscent of the situation of the MERCURY machine bought previously, and an IBM 7090 was ordered in 1960 and installed in 1961 in a new building, constructed especially for the occasion, at Saclay.”
Extract from “Deuxième Colloque sur l’Histoire de l’Informatique en France” (Second conference on the history of computing in France), Papers edited by Philippe Chatelin and Pierre-E. Mounier-Kuhn, Conservatoire National des Arts et Métiers, Paris, March 1990; 2 vol. (366+368 pages + 21p. additional) ISBN 2-9502887-3-1, pp. 11–28.
- 11.
P. Benoist: Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités [Neutron diffusion coefficient theory in a lattice with cavities], PhD thesis (1964) and CEA technical report CEA-R 2278 (1964).
- 12.
B. Bailly du Bois, Influence de la forme des cellules sur le Laplacien et structure fine du flux thermique dans une pile hétérogène [Influence of cell geometry on buckling and pin-by-pin thermal flux distribution in a heterogeneous reactor], CEA Report No 740 (1957).
- 13.
This is equivalent to expanding the sources on parallel rods that are uniformly distributed, thus forming a periodic lattice in both directions of the plane perpendicular to the rods.
- 14.
Pierre J. Benoist (1926–): Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités [Neutron Diffusion coefficient theory in a lattice with cavities], PhD thesis (1964) and CEA technical report CEA-R 2278 (1964). This PhD was presided over by Jacques Yvon, seconded by Jules Horowitz and Austin Blaquière as reviewers. It is considered a masterpiece of French know-how in theoretical neutron physics in the 1960s. It was even translated into English in the USA, an extremely rare exploit at that time, which led to many spin-offs and to the founding of very fertile heterogeneous diffusion theories. Benoist, who obtained the ANS Wigner prize in 1996, is internationally regarded as a leading expert in transport and diffusion theory.
- 15.
Frederick Seitz (1911–2008) was an American physicist. He obtained his BSc from Stanford University in 1932, and later specialized in solid-state physics, writing a book on the subject, The Modern Theory of Solids, in 1940. He made significant contributions on the migration energy of faults in metals. He worked at several American universities before being appointed professor at the University of Illinois. He presided over the American Academy of Sciences from 1962 to 1969. From 1968 to 1978, he was president of Rockfeller University. Although he received many awards, his position in favor of the tobacco lobbyists, his pro-Vietnam war stance and his skepticism about global warming all tarnished his image in part.
(Public domain) - 16.
J. R. Askew : Some boundary condition problems arising in the application of collision probability methods, Proceedings of a seminar on numerical reactor calculations held in Vienna by the AIEA, January 17–21, 1972, pp. 343–356 (1972).
- 17.
T. Ushio, T. Takeda: The characteristic and subgroup methods in square light reactor cell calculations, Nuclear Science and Engineering, 143, 61–80 (2003).
- 18.
Sydney Michael Dancoff (1913–1951) was an American theoretical physicist, the son of a Russian refugee of the pogrom period in 1905. After receiving an MSc from the University of Pittsburgh in 1936, he obtained a PhD in 1939 from the University of Berkeley under the supervision of Robert Oppenheimer. He worked on a renormalization method in quantum electrodynamics known as the Tamm-Dancoff approximation. During the war, he worked on the Manhattan Project in the reactor team, where he focused on the shadowing effect of one fuel on another in heterogeneous reactors, after having contributed to the CP1 pile with Fermi’s team. After the war, he worked at the University of Illinois at Urbana-Champaign. He struck up a scientific relationship with the physician and radiologist Henry Quastler in the field of information theory in biology, which resulted in a posthumous paper “The Information Content and Error Rate of Living Things.” The expression for Dancoff’s law is found inside this article in the form of: “The greatest growth occurs when the greatest number of mistakes are made consistent with survival.” He died of a lymphoma in 1951.
- 19.
S.M. Dancoff, M. Ginsburg: Surface resonance absorption in close packed lattices, Manhattan Project Report CP-2157 (1944).
- 20.
Yuzo Fukai: New analytical formula for Dancoff correction for cylindrical fuel lattices, Nuclear Science and Engineering, 9, pp. 370–376 (1961).
- 21.
Alberto Talamo: Analytical calculation of the average Dancoff factor for prismatic high-temperature reactors, Nuclear Science and Engineering, 156, pp. 346–356 (2007).
- 22.
E.E. Bende, A.H. Hogenbirk: Analytical calculation of the average Dancoff factor for a fuel kernel in a pebble bed high-temperature reactor, Nuclear Science and Engineering, 133, pp. 147–162 (1999).
- 23.
Jean-Yves Doriath : Méthodes numériques adaptatives pour des problèmes de transport dans les réacteurs nucléaires de sûreté par l’utilisation de signatures et de procédés de perturbations [Adaptive numerical methods for transport problems in safety nuclear reactors using the signatures and perturbation processes], PhD thesis from the University of Aix-Marseille (1983). This PhD work develops the S i j method.
- 24.
I. Carlvik, A method for calculating collision probabilities in general cylindrical geometry and application to flux distribution and Dancoff factors, Proc. Int. Conf. On peaceful use of atomic energy, 1964, p. 681.
- 25.
R. Stamm’ler et al: Equivalence relations for resonance integral calculations, Jour. of Nuclear Energy, 27, 1973, p. 885
- 26.
F. Storrer, A. Khairallah, M. Cadilhac, P. Benoist: Heterogeneity calculation for fast reactors by a perturbation method, Winter meeting of the American Nuclear Society, 30 Nov./3 Dec. 1964, San Francisco, USA (1964).
- 27.
Evans (1967) contains an article presenting numerical results using both the model and the PERHET code in which it is contained.
- 28.
In France, the code used is APOLLO2 developed at CEA.
- 29.
Philippe Finck’s thesis presents an interesting review of homogenization adapted to Nodal Expansion Method. Philippe Jean Finck: Homogenization and dehomogenization schemes for BWR assemblies, PhD at the Massachusetts Institute of Technology, January 1983.
- 30.
Michel Soldevila : Contribution à l’étude du problème de l’équivalence transport-diffusion [Contribution to the study of the transport-diffusion equivalence problem], PhD thesis, University of Orsay (1978).
- 31.
Alain Kavenoky: The SPH homogenization method, Proceedings of the specialists’ meeting on Homogenization methods in reactor physics organized by the IAEA held in Lugano, 13–15 November 1978, technical document issued by the AIEA, Vienna, 1980, pp. 181–187.
- 32.
Alain Hébert: Développement de la méthode SPH: homogénéisation de cellules dans un réseau non uniforme et calcul des paramètres réflecteur [Development of the SPH method: homogenization of cells in a non-uniform lattice and calculation of reflector parameters], PhD thesis University of Orsay (1981).
- 33.
Alain Hébert: A consistent technique for the pin-by-pin homogenization of a pressurized water reactor assembly, Nuclear Science and Engineering 113, pp. 227–238 (1993).
- 34.
Alain Hébert: Development of a third-generation superhomogénéisation method for the homogenization of a pressurized water reactor assembly, Nuclear Science and Engineering 115, pp. 129–141 (1993).
- 35.
The coefficient D g can be evaluated using the B 1 method, which will be seen later.
- 36.
Carlos José Gho : Homogénéisation du coefficient de diffusion: influence de la modélisation et du Laplacien pour les réacteurs rapides de puissance et les maquettes expérimentales [Homogenization of the diffusion coefficient: influence of the model used for the buckling calculation in high-power fast reactors and experimental reactors], PhD thesis, University of Grenoble (1984).
- 37.
Hongbin Zhang, Rizwan-uddin, J.J. Dorning: A multiple-scales systematic theory for the simultaneous homogenization of lattice cells and fuel assemblies, Transport theory and statistical physics, 26 (7), 763–811 (1997).
- 38.
Ivan Petrovic: Amélioration du modèle de fuites de neutrons dans le schéma de calcul des conditions critiques et des paramètres homogénéisés d’un réacteur nucléaire [Improving the neutron leakage model in a calculation scheme for critical conditions and homogenized parameters for a nuclear reactor], PhD thesis, University of Orsay (1993). This PhD work was supervised by Pierre Benoist. Petrovic developed the TIBERE model, which is a simplified heterogeneous B 1 model. The clear illustrations from Petrovic’s work for the homogeneous B 0 and B 1 equations are used to reproduce the equations here.
- 39.
Michel Lam-Hime: Homogénéisation: résolution de l’équation de transport en mode fondamental, définition et calcul de coefficient de diffusion des neutrons dans un réseau de cellules hétérogènes unidimensionnelles planes [Homogenization: solving the fundamental mode transport equation, defining and calculating the diffusion coefficient for neutrons in a heterogeneous lattice of 1D slabs], PhD thesis University of Orsay (1981). This PhD follows in the footsteps of Pierre Benoist’s work. Analytical calculations are developed for a slab lattice. Michel Lam-Hime (1952–) spent his entire career at EDF, where he worked in all the divisions in which reactor calculations were performed (Nuclear Calculation Division, SEPTEN, R&D/Reactor Physics). His knowledge of the calculation chain along with a tremendous and legendary appetite for work in the company makes him a leading French expert in neutron physics.
(Courtesy Lam Hime) - 40.
Pierre Benoist: Formalisme pour le calcul de l’effet de la vidange de sodium sur les fuites de neutrons dans un réacteur rapide [Formalism for calculation of the sodium void effect on neutron leakage in a fast reactor], technical report CEA-R-5121 (1981).
- 41.
Christian Robert: Recherche et mise en œuvre d’une nouvelle formulation du coefficient de diffusion pour prendre en compte les effets de juxtaposition de réseaux réguliers différents dans les réacteurs à neutrons rapides [Investigation and implementation of a new formulation of the diffusion coefficient taking into account the effects of adjacent and different regular lattices in fast neutron reactors], PhD thesis, Lyon (1980).
- 42.
C. Robert prefers to use dimensions divided by the mean free path 1/Σ ti , thus modifying the usual formalism of the diffusion equation.
- 43.
C. Garzenne: Equivalence transport-diffusion: présentation des méthodes utilisées au CEA et à EDF [Transport-diffusion equivalence: an illustration of the methods used at CEA and EDF], HT-12-92018 B, 1992. Claude Garzenne (1956–). After his engineering studies at Ecole Centrale at Lyon (France), he joined EDF/DER in January 1981. He spent his entire career there as an expert in reactor physics, save for a 3-year period at CEA Cadarache, where he participated in experimental programs on the MINERVE and EOLE reactors. He developed the homogenization and transport-diffusion equivalence method, HOMERE, which allows calculation of PWR cores using assembly calculations in SN transport. He subsequently specialized in fuel cycle physics, especially within the framework of the Bataille law of 1991 on the management of nuclear waste. He was appointed a Senior Engineer on these matters.
(Courtesy Garzenne) - 44.
It would appear inappropriate to use the term leakage for an infinite lattice: this misnomer is formed by analogy with the DΔΦ term.
- 45.
If the fluxes are expressed per unit lethargy (\( {\varphi}_m^j \)), weighting should be performed using lethargy increments: \( {\varPhi}_m^g=\Delta {u}_g{\varphi}_m^g\equiv \sum \limits_{j\in g}{\varPhi}_m^j=\sum \limits_{j\in g}\Delta {u}_j{\varphi}_m^j \), as shown in (Silvennoinen 1976, p. 174).
- 46.
François Malige: Etude mathématique et numérique de l’homogénéisation des assemblages combustibles d’un cœur de réacteur nucléaire [Mathematical and numerical analysis of the homogenization of fuel assemblies in a reactor core], PhD thesis, Ecole Polytechnique (1996).
- 47.
It should be emphasized that power is created in inactive structures by photon attenuation and neutron slowing-down in water, meaning that there is also power in guide thimbles.
- 48.
Farzad Rahnema is an American physicist. After his PhD at the University of California in 1981, he worked for 10 years at the nuclear division of General Electrics on Monte Carlo methods in neutron transport and on the PANACEA core code for BWR. In 1992, he joined the Georgia Institute of Technology, where he is professor of nuclear engineering in the field of medical physics and radiology.
- 49.
F. Rahnema, C.L. Martin , S. Congdon : A boundary condition perturbation method for predicting pin power distribution in light water reactors, Proc Topical meeting Reactor physics and shielding, Chicago 1984, Vol. 1, p. 394.
- 50.
F. Rahnema: A perturbation technique of the reconstruction of local power and flux distribution in nodal methods, Proc Topical meeting Advances in reactor physics, Chicago 1984, Vol. II, p. 204.
- 51.
K. Koebke: Advances in homogeneization and dehomogeneization, Proc. International Topical meeting: advances in mathematical methods for the solution of nuclear engineering problems, Munich, 1981, Vol. 2 p. 59.
- 52.
K. Koebke, H. Haase, L. Hetzel, H.J. Winter: Application and verification of the simplified equivalence theory for burn-up states, Nuclear Science and Engineering, 92, pp. 56–65 (1986).
(Public domain)
(Courtesy Lam Hime)
(Courtesy Garzenne)Bibliography
Milton Abramowitz, Irene Stegun, Handbook of mathematical functions, Dover, USA, ISBN 0-486-61272-4, re-edition of the 1972 version, 1046 pages. This thick textbook constitutes a complete mathematical handbook. The Dover edition makes it accessible to everyone.
Robert Barjon, Physique des réacteurs nucléaires [The physics of nuclear reactors], autoedition, Grenoble, ISBN 2-7061-0508-9, 1993. This work along with [Bussac and Reuss 1985], is one the two most complete references in French. Unfortunately, this self-edition is out of stock and very hard to find at present. Robert Barjon started his career at the Faculty of Alger, translated the famous [Halliday, 1957], and taught at Grenoble for several years. It is most unfortunate that this book is no longer edited.
Daniel Blanc, Les réacteurs atomiques [Atomic reactors], Que sais-je collection, PUF, Paris, 1986, 126 pages. This famous collection proposes very interesting popularizing books. The first three chapters explain theoretical aspects, while the rest of the book deals with technological matters.
Kenneth M. Case, Frederic de Hoffmann, George Placzek, Introduction to the theory of neutron diffusion Volume 1, Los Alamos Scientific Laboratory, Government printing office, Washington D.C., USA, 1953, 174 pages. It is one of the first books of pure neutron physics or neutronics. It established the formalism of leakage probability calculations and tabulated several functions that are found in transport theory. The Volume 2 was never edited but it can be imagined that [Case et Zweifel, 1967] is a good successor.
Lawrence Dresner, Resonance absorption in nuclear reactors, International series of monograph in nuclear energy, Vol. 4, Pergamon press, USA, Library of Congress card number 60-14191, 1960, 132 pages. This volume is a classical text for resonance absorption. Crystal clear, it is THE reference for chapter 5.
James J. Duderstadt, Louis J. Hamilton, Nuclear reactor analysis, John Wiley, USA, ISBN 0-471-22363-8, 1976, 650 pages. Complete reference. I appreciate the clear notations. James Duderstadt is a great transport specialist.
M.M. El-Wakil, Nuclear power engineering, McGraw-Hill, USA, ISBN 07-019300-2, 1962, 556 pages. Deals with thermal hydraulic aspects and technologies. The first part deals with ractor physics. More relevant in thermal hydraulics than neutronics (the plots on page 67 on activity are not correct, a confusion with concentrations perhaps?).
Harold Etherington (Editor), Nuclear Engineering Handbook, McGraw-Hill, New-York, USA, 1957. 14 locally numbered chapters. Chapter 6: Reactor physics is within our framework.
P.V. Evans (Editor), Fast breeder reactors, proceedings of the London conference organized by the British Nuclear Energy Society, May 1966, Pergamon Press, London, United Kingdom, Library of Congress Card Number 67-15631, 1967, 951 pages. especially: F. Storrer, A. Khairallah, M. Cadilhac, J.M. Chaumont, P.P. Clauzon, et al : Physics, kinetics and shielding of fast breeder reactors –survey of recent work done in France, Fast Breeder Reactors, p 685–710.
Jeol H. Ferziger, Paul F. Zweifel, The theory of neutron slowing-down in nuclear reactor, MIT press, Massachussets, USA, Library of Congress Card Number 66-13806, 1966, 307 pages. In my opinion, the best textbook on slowing-down. I recommend the notations.
Alain Hébert, Applied reactor physics, Presses internationales polytechniques, ISBN 978-2-553-01436-9, 2009, 414 pages. After his Ph. D., Alain Hébert has worked at the CEA on transport problems and homogenization methods.
Heavy water lattices, specialists meeting held in Vienne, September 1959, IAEA, STI/PUB/17, Vienne, Autriche, 1960, 142 pages. Logically, Canadians from Chalk River present most papers at this meeting dedicated to heavy water reactors.
Several authors, Homogenization methods in reactor physics, Proceedings of a specialists meeting on homogenization methods in reactor physics held in Lugano, Suisse, 13–15 November 1978. AIEA-TECDOC-231. Vienne, 1980, 670 pages. It is a compilation of articles on homogenization and equivalence methods for transport-diffusion calculations. Methods for reactors other than PWR are also presented: BWR, etc.
Théo Kahan, M. Gauzit, Physique et calcul des réacteurs nucléaires [Reactor physics and calculations], Dunod, Paris, 1957, 388 pages. Several elements on the dimensioning of the French graphite-gas reactors. Indeed, since France relied more on those reactors at that time, there is no mention of PWR.
Nordine Kerkar, Philippe Paulin, Exploitation des cœurs REP [Operating PWR cores], EDP Sciences-INSTN, Paris, ISBN 978-2-86883-3, 2008, 304 pages. It is a specialized work which presents the essential knowledge to operate PWR. The glossary is complete and gives an overview of the jargon with trigrams (thrre-letter abbreviations) which are often unfriendly to beginners.
John Lamarsh, Anthony J. Barrata, Introduction to nuclear engineering, Prentice Hall, ISBN 0-201-82498-1, 3rd edition, 2001, 783 pages. More of an engineering textbook where few physical or mathematical proofs are illustrated.
Jacques Ligou, Installations nucléaires []Nuclear installations], Presses Polytechniques Universitaires Romandes, ISBN 2-88074-011-8, 1982, 2nd edition, 430 pages. Indeed, a very technology-oriented book, although it contains some theoretical background on fusion (chapter 2) and reactor physics (chapter 4).
J. Littler, J.F. Raffle, An introduction to reactor physics, Pergamon Press, London, United Kingdom, 1997, 2nd edition, 208 pages.
Gurii I. Marchuk, Numerical methods for nuclear reactor calculations, Consultants bureau inc., New-York, USA, Library of Congress Card Number 59-9229, 1959. Translated from Russian as from no. 3–4 of the Russian journal Atomnaya Energiya of 1958. Probably the first book of numerical methods applied to reactors. Especially for the numerical solution of slowing-down.
Robert V. Meghreblian, David K. Holmes, Reactor analysis, McGraw-Hill, New-York, Library of Congress Catalog Card Number 59-15469, 1964, 807 pages. This work is entirely devoted to reactor physics and neutron physics and is within the framework of this textbook. No technology or operating details. One of the best references on the subject.
Jacques Planchard, Méthodes mathématiques en neutronique [Mathematical method in neutron physics], Eyrolles, Paris, ISBN 0399-4198, 1995, 431 pages. Especially for theorems on the critical equation and for cases with neutron sources. Jacques Planchard unfortunately died in 2009 – he was an expert at EDF R&D.
D.R. Poulter (Editor), The design of gas-cooled graphite-moderated reactors, Oxford University Press, London, United Kingdom, 1963, 692 pages. The theoretical chapters are mostly relevant to our book: Steady-state reactor physics by B. Cutts and Reactor kinetic and control by F.W. Fenning.
Paul Reuss, Précis de neutronique [Neutron physics], EDP Sciences, collection INSTN, Paris, ISBN 2-86883-637-2, 2003, essential elements from [Bussac and Reuss 1985], with a more modern typography but simplified content (directed towards students in a more didactic form). The only textbook of pure neutron physics still available in French.
P. Silvennoinen, Reactor core fuel management, Pergamon Press, Oxford, United Kingdom, ISBN 0-08-019853-8, 1976, 257 pages. Curiously, this book hardly deals with fuel management.
Weston M. Stacey, Nuclear reactor physics, John Wiley, USA, ISBN 0-471-39127-1, 2001, 707 pages.
Rudi J.J. Stamm’ler, Maximo J. Abbate, Methods of steady state reactor physics in nuclear design, Academic Press, USA, ISBN 0-12-663320-7, 1983, 506 pages. This book is very interesting although, chapter 2 is quite surprising with programming recommendations in Fortran which is not very appropriate considering the general framework of the book (?).
G.N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, Cambridge, United Kingdom, ISBN 0-521-09382, 1980, 804 pages. This book was written in 1922 and had several re-editions since it is essential on the subject matter. It is hard to believe that so much has been published on these functions! The reactor physicist working with cylindrical geometries will find everything in that reference!
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Marguet, S. (2017). Heterogeneous Reactors. In: The Physics of Nuclear Reactors. Springer, Cham. https://doi.org/10.1007/978-3-319-59560-3_14
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