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Introduction to neutron distribution theory
Journalof Nuclear EnergyParts A/B, 1964,Vol. 18, p. 709. PergamonPress Ltd. Printedin NorthernIreland
BOOK REVIEW
Introduction to Neutron Distribution Theory, L. C. WOODS, Methuen, 1964, 132 pp., 28s. IN HIS Preface, the author says “There has not been space enough in the book to include any account of the applications of the theory to reactor kinetics or to heterogeneous reactors, but in any case such topics properly belong to the derived subject of reactor analysis”. In the reviewer’s opinion, this choice of emphasis is a grave error of judgement which has led the author largely to ignore the vast developments of neutron transport theory which have taken place in the last fifteen years. These developments have been impelled by the need to design reactors to tight margins, and have been made possible by improvements in cross-section data and by the availability of large digital computers. They have led to improvements in the underlying mathematics, which can now be presented in a more attractive and coherent manner than Dr. Woods’ exposition would suggest. For instance, a neutron cannot change its position and its energy simultaneously. This implies that an energy-dependent problem can always be regarded as a set of one-group spatial problems, the source at any energy being provided by fissions and scatters from other energies; in particular, collision probabilities can always be calculated on a one-group basis. The book does not seem to bring out this fundamental point. Indeed, although it devotes six pages to the integral transport equation it does not mention collision probabilities at all, in spite of the light which has been thrown on the structure of the transport equation by modern investigation of these quantities. Again, the PN spherical harmonics method is now largely discredited because of its low accuracy and great complexity in cylindrical geometry, Nonetheless, 9 pages are devoted to this method while Carlson’s SN method is dismissed in 8 lines with the statement that “Although this method (Carlson) is less elegant than the spherical harmonics method, it has the advantage of being more suited to large-scale digital computing machinery”. The uninstructed reader would never guess that the SN method gives a much better approximation to the angular distribution than does the PN method, and that most of the serious solutions of the Boltzmann equation have been obtained with it. Having turned his back on heterogeneous reactor theory, the author could either have expounded the theory of homogeneous reactors, or he could have given the usual treatment of the Boltzmann equation in homogeneous media. In fact, he has tried to do both, and neither of the discussions is really satisfactory. The only cross section which is shown in a figure is that of indium. Slowing-down theory is developed with almost no reference to resonances, and the only reference to resonance integral is the quotation of an empirical formula which is no longer used in practical work. The omission of the Chernick theory of resonance escape,* and of the NR and WR approximations, is particularly regrettable since these are simple and physically vivid. The section called “Thermalisation theory” is devoted to a deduction of the transfer cross sections of a free gas. No use is made of these cross sections, and nothing is said about their relation to the Maxwellian spectrum. Diffusion theory is introduced twice, once on page 62 during an over-long discussion of age theory and again in a discussion of multigroup theory. On the credit side, there is an adequate treatment of anisotropy of scattering in the c-system and a good treatment of the criticality of a homogeneous multiplying medium on the lines pioneered by HELLENS.? Unfortunately, having inferred a proper two-group criticality equation from this treatment the author then introduces the four-factor formula. This has now been largely discarded because of the difficulty of defining the four factors rigorously. D. C. LESLIE * CHERNICK J. and VERNON R. Nucl. Sci. Engng. 4,649 (1958). HELLENS R. L. Neutron Slowing Down in Group D@sion Theory,
t
709
Report WAPD-114.
BOOK REVIEW
Introduction to Neutron Distribution Theory, L. C. WOODS, Methuen, 1964, 132 pp., 28s. IN HIS Preface, the author says “There has not been space enough in the book to include any account of the applications of the theory to reactor kinetics or to heterogeneous reactors, but in any case such topics properly belong to the derived subject of reactor analysis”. In the reviewer’s opinion, this choice of emphasis is a grave error of judgement which has led the author largely to ignore the vast developments of neutron transport theory which have taken place in the last fifteen years. These developments have been impelled by the need to design reactors to tight margins, and have been made possible by improvements in cross-section data and by the availability of large digital computers. They have led to improvements in the underlying mathematics, which can now be presented in a more attractive and coherent manner than Dr. Woods’ exposition would suggest. For instance, a neutron cannot change its position and its energy simultaneously. This implies that an energy-dependent problem can always be regarded as a set of one-group spatial problems, the source at any energy being provided by fissions and scatters from other energies; in particular, collision probabilities can always be calculated on a one-group basis. The book does not seem to bring out this fundamental point. Indeed, although it devotes six pages to the integral transport equation it does not mention collision probabilities at all, in spite of the light which has been thrown on the structure of the transport equation by modern investigation of these quantities. Again, the PN spherical harmonics method is now largely discredited because of its low accuracy and great complexity in cylindrical geometry, Nonetheless, 9 pages are devoted to this method while Carlson’s SN method is dismissed in 8 lines with the statement that “Although this method (Carlson) is less elegant than the spherical harmonics method, it has the advantage of being more suited to large-scale digital computing machinery”. The uninstructed reader would never guess that the SN method gives a much better approximation to the angular distribution than does the PN method, and that most of the serious solutions of the Boltzmann equation have been obtained with it. Having turned his back on heterogeneous reactor theory, the author could either have expounded the theory of homogeneous reactors, or he could have given the usual treatment of the Boltzmann equation in homogeneous media. In fact, he has tried to do both, and neither of the discussions is really satisfactory. The only cross section which is shown in a figure is that of indium. Slowing-down theory is developed with almost no reference to resonances, and the only reference to resonance integral is the quotation of an empirical formula which is no longer used in practical work. The omission of the Chernick theory of resonance escape,* and of the NR and WR approximations, is particularly regrettable since these are simple and physically vivid. The section called “Thermalisation theory” is devoted to a deduction of the transfer cross sections of a free gas. No use is made of these cross sections, and nothing is said about their relation to the Maxwellian spectrum. Diffusion theory is introduced twice, once on page 62 during an over-long discussion of age theory and again in a discussion of multigroup theory. On the credit side, there is an adequate treatment of anisotropy of scattering in the c-system and a good treatment of the criticality of a homogeneous multiplying medium on the lines pioneered by HELLENS.? Unfortunately, having inferred a proper two-group criticality equation from this treatment the author then introduces the four-factor formula. This has now been largely discarded because of the difficulty of defining the four factors rigorously. D. C. LESLIE * CHERNICK J. and VERNON R. Nucl. Sci. Engng. 4,649 (1958). HELLENS R. L. Neutron Slowing Down in Group D@sion Theory,
t
709
Report WAPD-114.