Nuclear Reactor Physics and Engineering

Essential guide to analyzing nuclear energy systems, with focus on reactor physics, fuel cycle, system dynamics, thermal-hydraulics, and economics. Nuclear Reactor Physics and Engineering highlights efforts in utilizing low enrichment uranium fuel as a substitute for carbon-based fuels in energy generation and provides an overview of important aspects of nuclear reactor physics utilizing the neutron diffusion equation for major reactor designs and MATLAB software for system analysis, with exercises illustrating key points and design parameters as supplementary material. This revised and updated Second Edition reflects key findings of the 2023 National Academy of Sciences (NAS) report and discusses physical and engineering characteristics of advanced nuclear reactors, especially in the form of small modular reactors that have the potential to provide enhanced safety and economics, as well as effective long-term management of used nuclear fuel in geological repositories. Key topics explored in the updated edition of Nuclear Reactor Physics and Engineering include: Impact of the use of high-assay low enrichment uranium (HALEU) fuel as a new efficient nuclear fuel Advantages resulting from combined uses of light water reactor and sodium-cooled fast reactor with fuel reprocessing Fundamental nuclear reactor physics, nuclear reactor system analysis, and lattice physics analysis for reactor cores Nuclear fuel cycle analysis, nuclear plant simulation and control, and management of used nuclear fuel Economic analysis of nuclear electricity and thermal-hydraulic analysis of nuclear systems. With a wealth of all-new information detailing the state of the art in the field, Nuclear Reactor Physics and Engineering is an invaluable reference on the subject for undergraduate and graduate students in nuclear engineering, as well as practicing engineers involved with nuclear power plants.

Table of Contents:
List of Tables xv List of Figures xvii Preface xxix Preface to the Second Edition xxxi Permissions and Copyrights xxxiii About the Companion Website xxxv 1 Nuclear Power Plants 1 1.1 History and Current Status of Nuclear Power Plants 1 1.2 Basic Features of Nuclear Power Plants 3 1.3 Pressurized Water Reactor Systems 4 1.4 Boiling Water Reactor Systems 10 1.5 Advanced Reactor Designs 17 References 30 Problems 32 2 Neutron–Nucleus Reaction and Neutron Cross Section 33 2.1 Neutron–Nucleus Reaction Probability and Neutron Cross Section 34 2.2 Mechanisms of Neutron–Nucleus Interaction 35 2.3 Nuclear Fission Process 38 2.4 Two-Body Collision Mechanics and Center-of-Mass System 44 2.5 Single-Level Breit–Wigner Formula for Resonance Reaction 48 2.6 Differential Scattering Cross Section and Scattering Kernel 51 2.7 Further Remarks on Neutron Cross Section 55 References 60 Problems 61 3 Neutron Flux, Reaction Rate, and Effective Cross Section 65 3.1 Neutron Flux and Current 66 3.2 Rate of Neutron–Nucleus Interaction 72 3.3 Neutron Energy Distribution and Effective Thermal Cross Section 75 3.4 Application to a 1∕V-Absorber 79 References 80 Problems 80 4 Derivation of the Neutron Diffusion Equation 83 4.1 Basic Assumptions for Neutron Balance Statement 84 4.2 Neutron Balance Equation 85 4.3 Neutron Source Term 89 4.4 Fick’s Law of Neutron Current 90 4.5 Neutron Transport Equation and P1 Approximation 93 4.6 Remarks on Diffusion Coefficient 98 4.7 Limitations of Neutron Diffusion Theory 100 4.8 One-Group Neutron Diffusion Equation 100 4.9 Summary Discussion of Diffusion Equation 102 References 102 Problems 103 5 Applications of the One-Group Neutron Diffusion Equation 105 5.1 Boundary Conditions for Diffusion Equation 106 5.2 Solution of Steady-State Diffusion Equation 110 5.3 Neutron Flux in Multiplying Medium and Criticality Condition 120 5.4 Four- and Six-Factor Formulas for Multiplication Factor 129 5.5 Concluding Remarks 131 References 131 Problems 132 6 Numerical Solution of the Neutron Diffusion Equation 137 6.1 Finite Difference Form of Diffusion Equation 138 6.2 Flux Solution Algorithm: Inner Iteration 142 6.3 Boundary Conditions for Difference Equation 144 6.4 Source or Outer Iteration 146 6.5 Relative Power Distribution and Overall Flow Chart 148 6.6 Single-Channel Flux Synthesis 151 6.7 Multidimensional Finite Difference Formulation 154 6.8 Coarse-Mesh Diffusion Equation Solver 160 6.9 Krylov Subspace Method as a Diffusion Equation Solver 164 References 168 Problems 169 7 Applications of the Two-Group Neutron Diffusion Equation 171 7.1 Derivation of Multigroup Neutron Diffusion Equation 172 7.2 Steady-State Multigroup Diffusion Equation 176 7.3 Two-Group Form of Effective Multiplication Factor 178 7.4 General Two-Group Diffusion Analysis 181 References 184 Problems 184 8 Nuclear Reactor Kinetics 189 8.1 Derivation of Point Kinetics Equation 190 8.2 Solution of Point Kinetics Equation without Feedback 194 8.3 State Space Representation of Point Kinetics Equation 205 8.4 Point Kinetics Equation with Feedback 208 8.5 Reactivity Measurements 214 8.6 System Stability Analysis 217 8.7 Point Reactor and Space-Dependent Reactor Kinetics 221 References 223 Problems 223 9 Fast Neutron Spectrum Calculation 227 9.1 Neutron Balance Equation and Slowing Down Density 228 9.2 Elastic Scattering and Lethargy Variable 232 9.3 Neutron Slowing Down in Infinite Medium 234 9.4 Resonance Escape Probability 243 9.5 Doppler Broadening of Resonances 250 9.6 Fermi Age Theory 256 9.7 Comments on Lattice Physics Analysis 260 References 261 Problems 262 10 Perturbation Theory and Adjoint Flux 265 10.1 Operator Notation for Neutron Diffusion Equation 265 10.2 Adjoint Operator and Adjoint Flux 267 10.3 First-Order Perturbation Theory 269 10.4 Adjoint Flux for Control Rod Worth Calculation 271 10.5 Adjoint Flux for Variational Formulation 273 10.6 Adjoint Flux for Detector Response Calculation 274 10.7 Adjoint Formulation for Flux Perturbation Calculation 276 10.8 Concluding Remarks on Adjoint Flux 280 References 280 Problems 281 11 Lattice Physics Analysis of Heterogeneous Cores 283 11.1 Material Heterogeneity and Flux Distribution in Unit Cell 285 11.2 Neutronic Advantages of Fuel Lumping 287 11.3 Diffusion Theory Model for Thermal Utilization 291 11.4 Improved Method for Thermal Disadvantage Factor 296 11.5 Resonance Escape Probability for Heterogeneous Cell 300 11.6 Thermal Spectrum Calculation 310 11.7 Integral Transport Methods 313 11.8 B1 Formulation for Spectrum Calculation 316 11.9 Lattice Physics Methodology for Fast Reactor 322 11.10 Monte Carlo Lattice Physics Analysis 325 11.11 Overall Reactor Physics Analysis 326 References 327 Problems 330 12 Nuclear Fuel Cycle Analysis and Management 333 12.1 Nuclear Fuel Cycle Analysis 334 12.2 Nuclear Transmutation Formulation 337 12.3 Equilibrium Cycle and Mass Balance 347 12.4 Simplified Cycling Model 353 12.5 Fission Product Xenon Buildup 359 12.6 General Incore Management Considerations 365 12.7 Fission Products and Radioactive Waste 371 12.8 Management of Used Nuclear Fuel 376 12.9 Key Considerations for Geological Disposal 396 References 404 Problems 409 13 Thermal-Hydraulic Analysis of Reactor Systems 413 13.1 Empirical Laws for Energy and Momentum Transport 415 13.2 Derivation of Fluid Conservation Equations 418 13.3 Simple Solutions of Fluid Conservation Equations 426 13.4 Conservation Equations for Channel Flow 443 13.5 Axial Temperature Distribution in Reactor Core 446 13.6 Boiling Heat Transfer and Two-Phase Flow 456 13.7 Thermal Hydraulic Limitations and Power Capability 471 13.8 Thermal-Hydraulic Models for Nuclear Plant Analysis 479 13.9 Advances in Nuclear Plant Modeling System 488 References 489 Problems 493 14 Power Coefficients of Reactivity 499 14.1 Physical Phenomena Affecting Core Reactivity 500 14.2 Relationship Between Reactivity Coefficients 502 14.3 Two-Group Representation of Reactivity Feedback 503 14.4 Parametric Dependence of LWR Reactivity Coefficients 505 14.5 Reactivity Coefficients in Sodium-Cooled Fast Reactor 508 14.6 Reactivity Feedback Model for Sodium-Cooled Fast Reactor 510 References 512 Problems 513 15 Nuclear Energy Economics 515 15.1 Electrical Energy Cost 516 15.2 Overview of Engineering Economics 519 15.3 Calculation of Nuclear Electricity Generation Cost 521 15.4 Impact of Increased Capital and O&M Costs 530 15.5 Energy Generation Efficiency of Various Technologies 533 References 536 Problems 539 16 Space-Time Kinetics and Reactor Control 541 16.1 Space-Time Reactor Kinetics 542 16.2 Space-Time Power Oscillations due to Xenon Poisoning 551 16.3 Time-Optimal Reactor Control 564 16.4 Model-Based Reactor Control 572 16.5 Alternate Reactor Control Techniques 581 16.6 Kalman Filtering for Optimal System Estimation 585 References 588 Problems 592 17 Elements of Neutron Transport Theory 595 17.1 Collision Probability Method 595 17.2 First-Flight Escape Probability and Dirac Chord Method 600 17.3 Flux Depression Calculation and Blackness 605 17.4 Numerical Solution of Neutron Transport Equation 610 References 621 Problems 623 Appendix A Key Physical Constants 627 Appendix B Comparison of Major Reactor Types 629 References 633 Appendix C Special Mathematical Functions 635 C.1 Gamma Function 635 C.2 Legendre Polynomial and Spherical Harmonics 637 C.3 Bessel Function 639 C.4 Dirac Delta Function 642 References 642 Appendix D Integral Transforms 643 D.1 Laplace Transform 643 D.2 Fourier Transform 645 D.3 Jordan’s Lemma 645 References 647 Appendix E Calculus of Variation for Optimal Control Formulation 649 E.1 Euler–Lagrange and Hamilton Equations 649 E.2 Pontryagin’s Maximum Principle 650 References 656 Appendix F Kalman Filter Algorithm 657 F.1 Linear Kalman Filter 657 F.2 Unscented Kalman Filter 660 References 662 Answers to Selected Problems 663 Index 679

About the Author :
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.