Weston M. StaceyNuclear Reactor PhysicsSecond Edition, Completely Revised and Enlarged

Weston M. StaceyNuclear Reactor Physics

1807–Knowledge for GenerationsEach generation has its unique needs and aspirations. When Charles Wiley firstopened his small printing shop in lower Manhattan in 1807, it was a generationof boundless potential searching for an identity. And we were there, helping todefine a new American literary tradition. Over half a century later, in the midstof the Second Industrial Revolution, it was a generation focused on buildingthe future. Once again, we were there, supplying the critical scientific, technical,and engineering knowledge that helped frame the world. Throughout the 20thCentury, and into the new millennium, nations began to reach out beyond theirown borders and a new international community was born. Wiley was there, expanding its operations around the world to enable a global exchange of ideas,opinions, and know-how.For 200 years, Wiley has been an integral part of each generation’s journey,enabling the flow of information and understanding necessary to meet theirneeds and fulfill their aspirations. Today, bold new technologies are changingthe way we live and learn. Wiley will be there, providing you the must-haveknowledge you need to imagine new worlds, new possibilities, and new opportunities.Generations come and go, but you can always count on Wiley to provide youthe knowledge you need, when and where you need it!William J. PescePresident and Chief Executive OfficerPeter Booth WileyChairman of the Board

Weston M. StaceyNuclear Reactor PhysicsSecond Edition, Completely Revised and Enlarged

The AuthorProf. Weston M. StaceyGeorgia Institute of TechnologyNuclear & Radiological Engineering900 Atlantic Drive, NWAtlanta, GA 30332-0425USACoverFour-assembly fuel module for a boiling waterreactor (Courtesy of General ElectricCompany).All books published by Wiley-VCH arecarefully produced. Nevertheless, authors,editors, and publisher do not warrant theinformation contained in these books,including this book, to be free of errors.Readers are advised to keep in mind thatstatements, data, illustrations, proceduraldetails or other items may inadvertently beinaccurate.Library of Congress Card No.:applied forBritish Library Cataloguing-in-PublicationDataA catalogue record for this book is availablefrom the British Library.Bibliographic information published bythe Deutsche NationalbibliothekThe Deutsche Nationalbibliothek lists thispublication in the DeutscheNationalbibliografie; detailed bibliographicdata is available in the Internet. WILEY-VCH Verlag GmbH & Co.KGaA, WeinheimAll rights reserved (including those oftranslation into other languages). No part ofthis book may be reproduced in any form – byphotoprinting, microfilm, or any other means– nor transmitted or translated into amachine language without writtenpermission from the publishers. Registerednames, trademarks, etc. used in this book,even when not specifically marked as such,are not to be considered unprotected by law.Typesetting VTEX, Vilnius, LithuaniaPrinting betz-druck GmbH, DarmstadtBinding Litges & Dopf BuchbindereiGmbH, HeppenheimPrinted in the Federal Republic of GermanyPrinted on acid-free paperISBN 978-3-527-40679-1

To Penny, Helen, Billy, and Lucia

viiContentsPrefacexxiiiPreface to 2nd EditionPART REACTOR PHYSICSNeutron Nuclear Reactions3Neutron-Induced Nuclear Fission3Stable Nuclides3Binding Energy3Threshold External Energy for Fission4Neutron-Induced Fission5Neutron Fission Cross Sections5Products of the Fission Reaction8Energy Release10Neutron Capture13Radiative Capture13Neutron Emission19Neutron Elastic Scattering20Summary of Cross-Section Data24Low-Energy Cross Sections24Spectrum-Averaged Cross Sections24Evaluated Nuclear Data Files24Elastic Scattering Kinematics27Correlation of Scattering Angle and Energy LossAverage Energy Loss2928Neutron Chain Fission Reactors33Neutron Chain Fission Reactions33Capture-to-Fission Ratio33Number of Fission Neutrons per Neutron Absorbed in Fuel33

Contentsviii2.22.32.433. Utilization34Fast Fission34Resonance Escape36Criticality37Effective Multiplication Constant37Effect of Fuel Lumping37Leakage Reduction38Time Dependence of a Neutron Fission Chain AssemblyPrompt Fission Neutron Time Dependence38Source Multiplication39Effect of Delayed Neutrons39Classification of Nuclear Reactors40Physics Classification by Neutron Spectrum40Engineering Classification by Coolant4138Neutron Diffusion Theory43Derivation of One-Speed Diffusion Theory43Partial and Net Currents43Diffusion Theory45Interface Conditions46Boundary Conditions46Applicability of Diffusion Theory47Solutions of the Neutron Diffusion Equation in NonmultiplyingMedia48Plane Isotropic Source in an Infinite Homogeneous Medium48Plane Isotropic Source in a Finite Homogeneous Medium48Line Source in an Infinite Homogeneous Medium49Homogeneous Cylinder of Infinite Axial Extent with Axial LineSource49Point Source in an Infinite Homogeneous Medium49Point Source at the Center of a Finite Homogeneous Sphere50Diffusion Kernels and Distributed Sources in a HomogeneousMedium50Infinite-Medium Diffusion Kernels50Finite-Slab Diffusion Kernel51Finite Slab with Incident Neutron Beam52Albedo Boundary Condition52Neutron Diffusion and Migration Lengths53Thermal Diffusion-Length Experiment53Migration Length55Bare Homogeneous Reactor57Slab Reactor57Right Circular Cylinder Reactor59

Contents3. of Criticality Condition60Optimum Geometries61Reflected Reactor62Reflected Slab Reactor62Reflector Savings64Reflected Spherical, Cylindrical, and Rectangular ParallelepipedCores65Homogenization of a Heterogeneous Fuel–Moderator AssemblySpatial Self-Shielding and Thermal Disadvantage Factor65Effective Homogeneous Cross Sections69Thermal Utilization71Measurement of Thermal Utilization72Local Power Peaking Factor73Control Rods73Effective Diffusion Theory Cross Sections for Control Rods73Windowshade Treatment of Control Rods76Numerical Solution of Diffusion Equation77Finite Difference Equations in One Dimension78Forward Elimination/Backward Substitution Spatial SolutionProcedure79Power Iteration on Fission Source79Finite-Difference Equations in Two Dimensions80Successive Relaxation Solution of Two-DimensionalFinite-Difference Equations82Power Outer Iteration on Fission Source82Limitations on Mesh Spacing83Nodal Approximation83Transport Methods85Transmission and Absorption in a Purely Absorbing Slab ControlPlate87Escape Probability in a Slab87Integral Transport Formulation87Collision Probability Method88Differential Transport Formulation89Spherical Harmonics Methods90Discrete Ordinates Method94Neutron Energy Distribution101Analytical Solutions in an Infinite Medium101Fission Source Energy Range102Slowing-Down Energy Range102Moderation by Hydrogen Only103Energy Self-Shielding103Slowing Down by Nonhydrogenic Moderators with No Absorption65104ix

Contentsx4.24.34.455. Density105Slowing Down with Weak Absorption106Fermi Age Neutron Slowing Down107Neutron Energy Distribution in the Thermal Range108Summary111Multigroup Calculation of Neutron Energy Distribution in an InfiniteMedium111Derivation of Multigroup Equations111Mathematical Properties of the Multigroup Equations113Solution of Multigroup Equations114Preparation of Multigroup Cross-Section Sets115Resonance Absorption117Resonance Cross Sections117Doppler Broadening119Resonance Integral122Resonance Escape Probability122Multigroup Resonance Cross Section122Practical Width122Neutron Flux in Resonance123Narrow Resonance Approximation123Wide Resonance Approximation124Resonance Absorption Calculations124Temperature Dependence of Resonance Absorption127Multigroup Diffusion Theory127Multigroup Diffusion Equations127Two-Group Theory128Two-Group Bare Reactor129One-and-One-Half-Group Theory129Two-Group Theory of Two-Region Reactors130Two-Group Theory of Reflected Reactors133Numerical Solutions for Multigroup Diffusion Theory137Nuclear Reactor Dynamics143Delayed Fission Neutrons143Neutrons Emitted in Fission Product Decay143Effective Delayed Neutron Parameters for Composite MixturesPhotoneutrons146Point Kinetics Equations147Period–Reactivity Relations148Approximate Solutions of the Point Neutron Kinetics EquationsOne Delayed Neutron Group Approximation150Prompt-Jump Approximation153Reactor Shutdown154145150

Contents5. Neutron Kernel and Zero-Power Transfer Function155Delayed Neutron Kernel155Zero-Power Transfer Function155Experimental Determination of Neutron Kinetics Parameters156Asymptotic Period Measurement156Rod Drop Method157Source Jerk Method157Pulsed Neutron Methods157Rod Oscillator Measurements158Zero-Power Transfer Function Measurements159Rossi-α Measurement159Reactivity Feedback161Temperature Coefficients of Reactivity162Doppler Effect162Fuel and Moderator Expansion Effect on Resonance EscapeProbability164Thermal Utilization165Nonleakage Probability166Representative Thermal Reactor Reactivity Coefficients166Startup Temperature Defect167Perturbation Theory Evaluation of Reactivity TemperatureCoefficients168Perturbation Theory168Sodium Void Effect in Fast Reactors169Doppler Effect in Fast Reactors169Fuel and Structure Motion in Fast Reactors170Fuel Bowing171Representative Fast Reactor Reactivity Coefficients171Reactor Stability171Reactor Transfer Function with Reactivity Feedback171Stability Analysis for a Simple Feedback Model172Threshold Power Level for Reactor Stability174More General Stability Conditions175Power Coefficients and Feedback Delay Time Constants178Measurement of Reactor Transfer Functions179Rod Oscillator Method179Correlation Methods179Reactor Noise Method181Reactor Transients with Feedback183Step Reactivity Insertion (ρex β): Prompt Jump184Step Reactivity Insertion (ρex β): Post-Prompt-Jump Transient185Reactor Fast Excursions186Step Reactivity Input: Feedback Proportional to Fission Energy186Ramp Reactivity Input: Feedback Proportional to Fission Energy187xi

p Reactivity Input: Nonlinear Feedback Proportional toCumulative Energy Release187Bethe–Tait Model188Numerical Methods190Fuel Burnup197Changes in Fuel Composition197Fuel Transmutation–Decay Chains198Fuel Depletion–Transmutation–Decay Equations199Fission Products203Solution of the Depletion Equations204Measure of Fuel Burnup205Fuel Composition Changes with Burnup205Reactivity Effects of Fuel Composition Changes206Compensating for Fuel-Depletion Reactivity Effects208Reactivity Penalty208Effects of Fuel Depletion on the Power Distribution209In-Core Fuel Management210Samarium and Xenon211Samarium Poisoning211Xenon Poisoning213Peak Xenon215Effect of Power-Level Changes216Fertile-to-Fissile Conversion and Breeding217Availability of Neutrons217Conversion and Breeding Ratios219Simple Model of Fuel Depletion219Fuel Reprocessing and Recycling221Composition of Recycled LWR Fuel221Physics Differences of MOX Cores222Physics Considerations with Uranium Recycle224Physics Considerations with Plutonium Recycle225Reactor Fueling Characteristics225Radioactive Waste226Radioactivity226Hazard Potential226Risk Factor226Burning Surplus Weapons-Grade Uranium and PlutoniumComposition of Weapons-Grade Uranium and PlutoniumPhysics Differences Between Weapons- and Reactor-GradePlutonium-Fueled Reactors234Utilization of Uranium Energy Content235Transmutation of Spent Nuclear Fuel237Closing the Nuclear Fuel Cycle244233233

1388.18.2Nuclear Power Reactors249Pressurized Water Reactors249Boiling Water Reactors250Pressure Tube Heavy Water–Moderated Reactors255Pressure Tube Graphite-Moderated Reactors258Graphite-Moderated Gas-Cooled Reactors260Liquid-Metal Fast Breeder Reactors261Other Power Reactors265Characteristics of Power Reactors265Advanced Generation-III Reactors265Advanced Boiling Water Reactors (ABWR)266Advanced Pressurized Water Reactors (APWR)267Advanced Pressure Tube Reactor268Modular High-Temperature Gas-Cooled Reactors (GT-MHR)268Advanced Generation-IV Reactors269Gas-Cooled Fast Reactors (GFR)270Lead-Cooled Fast Reactors (LFR)271Molten Salt Reactors (MSR)271Super-Critical Water Reactors (SCWR)272Sodium-Cooled Fast Reactors (SFR)272Very High Temperature Reactors (VHTR)272Advanced Sub-critical Reactors273Nuclear Reactor Analysis275Construction of Homogenized Multigroup Cross Sections275Criticality and Flux Distribution Calculations276Fuel Cycle Analyses277Transient Analyses278Core Operating Data279Criticality Safety Analysis279Interaction of Reactor Physics and Reactor Thermal Hydraulics280Power Distribution280Temperature Reactivity Effects281Coupled Reactor Physics and Thermal-Hydraulics Calculations281Reactor Safety283Elements of Reactor Safety283Radionuclides of Greatest Concern283Multiple Barriers to Radionuclide ReleaseDefense in Depth285Energy Sources285Reactor Safety Analysis285Loss of Flow or Loss of Coolant287Loss of Heat Sink287283xiii

Contentsxiv8.38.48.5Reactivity Insertion287Anticipated Transients without ScramQuantitative Risk Assessment288Probabilistic Risk Assessment288Radiological Assessment291Reactor Risks291Reactor Accidents293Three Mile Island294Chernobyl297Passive Safety299Pressurized Water Reactors299Boiling Water Reactors299Integral Fast Reactors300Passive Safety Demonstration300PART REACTOR PHYSICSNeutron Transport Theory305Neutron Transport Equation305Boundary Conditions310Scalar Flux and Current310Partial Currents310Integral Transport Theory310Isotropic Point Source311Isotropic Plane Source311Anisotropic Plane Source312Transmission and Absorption Probabilities314Escape Probability314First-Collision Source for Diffusion Theory315Inclusion of Isotropic Scattering and Fission315Distributed Volumetric Sources in Arbitrary Geometry316Flu