Nuclear Reactor Physics and Engineering

John C. Lee, PhD, has been on the nuclear engineering faculty at the University of Michigan since 1974 and served as the department chair for six years. He has published two Wiley books, Risk and Safety Analysis of Nuclear Systems (with N.J. McCormick, 2011, 2017 second printing) and Nuclear Reactor Physics and Engineering (2020). He has served on two U.S. National Academy of Sciences committees, including the recent committee on advanced nuclear reactors and used nuclear fuel. Dr. Lee is a Fellow of the American Nuclear Society.

• List of Tables xvList of Figures xviiPreface xxixPreface to the Second Edition xxxiPermissions and Copyrights xxxiiiAbout the Companion Website xxxv1 Nuclear Power Plants 11.1 History and Current Status of Nuclear Power Plants 11.2 Basic Features of Nuclear Power Plants 31.3 Pressurized Water Reactor Systems 41.4 Boiling Water Reactor Systems 101.5 Advanced Reactor Designs 17References 30Problems 322 Neutron–Nucleus Reaction and Neutron Cross Section 332.1 Neutron–Nucleus Reaction Probability and Neutron Cross Section 342.2 Mechanisms of Neutron–Nucleus Interaction 352.3 Nuclear Fission Process 382.4 Two-Body Collision Mechanics and Center-of-Mass System 442.5 Single-Level Breit–Wigner Formula for Resonance Reaction 482.6 Differential Scattering Cross Section and Scattering Kernel 512.7 Further Remarks on Neutron Cross Section 55References 60Problems 613 Neutron Flux, Reaction Rate, and Effective Cross Section 653.1 Neutron Flux and Current 663.2 Rate of Neutron–Nucleus Interaction 723.3 Neutron Energy Distribution and Effective Thermal Cross Section 753.4 Application to a 1∕V-Absorber 79References 80Problems 804 Derivation of the Neutron Diffusion Equation 834.1 Basic Assumptions for Neutron Balance Statement 844.2 Neutron Balance Equation 854.3 Neutron Source Term 894.4 Fick’s Law of Neutron Current 904.5 Neutron Transport Equation and P1 Approximation 934.6 Remarks on Diffusion Coefficient 984.7 Limitations of Neutron Diffusion Theory 1004.8 One-Group Neutron Diffusion Equation 1004.9 Summary Discussion of Diffusion Equation 102References 102Problems 1035 Applications of the One-Group Neutron Diffusion Equation 1055.1 Boundary Conditions for Diffusion Equation 1065.2 Solution of Steady-State Diffusion Equation 1105.3 Neutron Flux in Multiplying Medium and Criticality Condition 1205.4 Four- and Six-Factor Formulas for Multiplication Factor 1295.5 Concluding Remarks 131References 131Problems 1326 Numerical Solution of the Neutron Diffusion Equation 1376.1 Finite Difference Form of Diffusion Equation 1386.2 Flux Solution Algorithm: Inner Iteration 1426.3 Boundary Conditions for Difference Equation 1446.4 Source or Outer Iteration 1466.5 Relative Power Distribution and Overall Flow Chart 1486.6 Single-Channel Flux Synthesis 1516.7 Multidimensional Finite Difference Formulation 1546.8 Coarse-Mesh Diffusion Equation Solver 1606.9 Krylov Subspace Method as a Diffusion Equation Solver 164References 168Problems 1697 Applications of the Two-Group Neutron Diffusion Equation 1717.1 Derivation of Multigroup Neutron Diffusion Equation 1727.2 Steady-State Multigroup Diffusion Equation 1767.3 Two-Group Form of Effective Multiplication Factor 1787.4 General Two-Group Diffusion Analysis 181References 184Problems 1848 Nuclear Reactor Kinetics 1898.1 Derivation of Point Kinetics Equation 1908.2 Solution of Point Kinetics Equation without Feedback 1948.3 State Space Representation of Point Kinetics Equation 2058.4 Point Kinetics Equation with Feedback 2088.5 Reactivity Measurements 2148.6 System Stability Analysis 2178.7 Point Reactor and Space-Dependent Reactor Kinetics 221References 223Problems 2239 Fast Neutron Spectrum Calculation 2279.1 Neutron Balance Equation and Slowing Down Density 2289.2 Elastic Scattering and Lethargy Variable 2329.3 Neutron Slowing Down in Infinite Medium 2349.4 Resonance Escape Probability 2439.5 Doppler Broadening of Resonances 2509.6 Fermi Age Theory 2569.7 Comments on Lattice Physics Analysis 260References 261Problems 26210 Perturbation Theory and Adjoint Flux 26510.1 Operator Notation for Neutron Diffusion Equation 26510.2 Adjoint Operator and Adjoint Flux 26710.3 First-Order Perturbation Theory 26910.4 Adjoint Flux for Control Rod Worth Calculation 27110.5 Adjoint Flux for Variational Formulation 27310.6 Adjoint Flux for Detector Response Calculation 27410.7 Adjoint Formulation for Flux Perturbation Calculation 27610.8 Concluding Remarks on Adjoint Flux 280References 280Problems 28111 Lattice Physics Analysis of Heterogeneous Cores 28311.1 Material Heterogeneity and Flux Distribution in Unit Cell 28511.2 Neutronic Advantages of Fuel Lumping 28711.3 Diffusion Theory Model for Thermal Utilization 29111.4 Improved Method for Thermal Disadvantage Factor 29611.5 Resonance Escape Probability for Heterogeneous Cell 30011.6 Thermal Spectrum Calculation 31011.7 Integral Transport Methods 31311.8 B1 Formulation for Spectrum Calculation 31611.9 Lattice Physics Methodology for Fast Reactor 32211.10 Monte Carlo Lattice Physics Analysis 32511.11 Overall Reactor Physics Analysis 326References 327Problems 33012 Nuclear Fuel Cycle Analysis and Management 33312.1 Nuclear Fuel Cycle Analysis 33412.2 Nuclear Transmutation Formulation 33712.3 Equilibrium Cycle and Mass Balance 34712.4 Simplified Cycling Model 35312.5 Fission Product Xenon Buildup 35912.6 General Incore Management Considerations 36512.7 Fission Products and Radioactive Waste 37112.8 Management of Used Nuclear Fuel 37612.9 Key Considerations for Geological Disposal 396References 404Problems 40913 Thermal-Hydraulic Analysis of Reactor Systems 41313.1 Empirical Laws for Energy and Momentum Transport 41513.2 Derivation of Fluid Conservation Equations 41813.3 Simple Solutions of Fluid Conservation Equations 42613.4 Conservation Equations for Channel Flow 44313.5 Axial Temperature Distribution in Reactor Core 44613.6 Boiling Heat Transfer and Two-Phase Flow 45613.7 Thermal Hydraulic Limitations and Power Capability 47113.8 Thermal-Hydraulic Models for Nuclear Plant Analysis 47913.9 Advances in Nuclear Plant Modeling System 488References 489Problems 49314 Power Coefficients of Reactivity 49914.1 Physical Phenomena Affecting Core Reactivity 50014.2 Relationship Between Reactivity Coefficients 50214.3 Two-Group Representation of Reactivity Feedback 50314.4 Parametric Dependence of LWR Reactivity Coefficients 50514.5 Reactivity Coefficients in Sodium-Cooled Fast Reactor 50814.6 Reactivity Feedback Model for Sodium-Cooled Fast Reactor 510References 512Problems 51315 Nuclear Energy Economics 51515.1 Electrical Energy Cost 51615.2 Overview of Engineering Economics 51915.3 Calculation of Nuclear Electricity Generation Cost 52115.4 Impact of Increased Capital and O&M Costs 53015.5 Energy Generation Efficiency of Various Technologies 533References 536Problems 53916 Space-Time Kinetics and Reactor Control 54116.1 Space-Time Reactor Kinetics 54216.2 Space-Time Power Oscillations due to Xenon Poisoning 55116.3 Time-Optimal Reactor Control 56416.4 Model-Based Reactor Control 57216.5 Alternate Reactor Control Techniques 58116.6 Kalman Filtering for Optimal System Estimation 585References 588Problems 59217 Elements of Neutron Transport Theory 59517.1 Collision Probability Method 59517.2 First-Flight Escape Probability and Dirac Chord Method 60017.3 Flux Depression Calculation and Blackness 60517.4 Numerical Solution of Neutron Transport Equation 610References 621Problems 623Appendix A Key Physical Constants 627Appendix B Comparison of Major Reactor Types 629References 633Appendix C Special Mathematical Functions 635C.1 Gamma Function 635C.2 Legendre Polynomial and Spherical Harmonics 637C.3 Bessel Function 639C.4 Dirac Delta Function 642References 642Appendix D Integral Transforms 643D.1 Laplace Transform 643D.2 Fourier Transform 645D.3 Jordan’s Lemma 645References 647Appendix E Calculus of Variation for Optimal Control Formulation 649E.1 Euler–Lagrange and Hamilton Equations 649E.2 Pontryagin’s Maximum Principle 650References 656Appendix F Kalman Filter Algorithm 657F.1 Linear Kalman Filter 657F.2 Unscented Kalman Filter 660References 662Answers to Selected Problems 663Index 679