The first part of the book covers basic reactor physics, including, but not limited to nuclear reaction data, neutron diffusion theory, reactor criticality and dynamics, neutron energy distribution, fuel burnup, reactor types and reactor safety.
The second part then deals with such physically and mathematically more advanced topics as neutron transport theory, neutron slowing down, resonance absorption, neutron thermalization, perturbation and variational methods, homogenization, nodal and synthesis methods, and space-time neutron dynamics.
For ease of reference, the detailed appendices contain nuclear data, useful mathematical formulas, an overview of special functions as well as introductions to matrix algebra and Laplace transforms.
With its focus on conveying the in-depth knowledge needed by advanced student and professional nuclear engineers, this text is ideal for use in numerous courses and for self-study by professionals in basic nuclear reactor physics, advanced nuclear reactor physics, neutron transport theory, nuclear reactor dynamics and stability, nuclear reactor fuel cycle physics and other important topics in the field of nuclear reactor physics.
Table of Contents
Preface xxiii
Preface to Second Edition xxvii
Preface to Third Edition xxix
Part 1 Basic Reactor Physics 1
1 Neutron–Nuclear Reactions 3
1.1 Neutron-Induced Nuclear Fission 3
1.2 Neutron Capture 12
1.3 Neutron Elastic Scattering 19
1.4 Summary of Cross Section Data 23
1.5 Evaluated Nuclear Data Files 25
1.6 Elastic Scattering Kinematics 25
2 Neutron Chain Fission Reactors 33
2.1 Neutron Chain Fission Reactions 33
2.2 Criticality 37
2.3 Time Dependence of a Neutron Fission Chain Assembly 38
2.4 Classification of Nuclear Reactors 40
3 Neutron Diffusion and Transport Theory 43
3.1 Derivation of One-Speed Diffusion Theory 43
3.2 Solutions of the Neutron Diffusion Equation in Nonmultiplying
3.3 Diffusion Kernels and Distributed Sources in a Homogeneous
3.4 Albedo Boundary Condition 52
3.5 Neutron Diffusion and Migration Lengths 53
3.6 Bare Homogeneous Reactor 57
3.7 Reflected Reactor 62
3.8 Homogenization of a Heterogeneous Fuel–Moderator
3.9 Control Rods 72
3.10 Numerical Solution of Diffusion Equation 76
3.11 Nodal Approximation 82
3.12 Transport Methods 84
4 Neutron Energy Distribution 101
4.1 Analytical Solutions in an Infinite Medium 101
4.2 Multigroup Calculation of Neutron Energy Distribution in an Infinite
4.3 Resonance Absorption 118
4.4 Multigroup Diffusion Theory 127
5 Nuclear Reactor Dynamics 141
5.1 Delayed Fission Neutrons 141
5.2 Point Kinetics Equations 145
5.3 Period–Reactivity Relations 146
5.4 Approximate Solutions of the Point Neutron Kinetics Equations 148
5.5 Delayed Neutron Kernel and Zero-Power Transfer Function 153
5.6 Experimental Determination of Neutron Kinetics Parameters 155
5.7 Reactivity Feedback 160
5.8 Perturbation Theory Evaluation of Reactivity Temperature
5.9 Reactor Stability 171
5.10 Measurement of Reactor Transfer Functions 179
5.11 Reactor Transients with Feedback 184
5.12 Reactor Fast Excursions 187
5.13 Numerical Methods 192
6 Fuel Burnup 197
6.1 Changes in Fuel Composition 197
6.2 Samarium and Xenon 211
6.3 Fertile-to-Fissile Conversion and Breeding 217
6.4 Simple Model of Fuel Depletion 219
6.5 Fuel Reprocessing and Recycling 221
6.6 Radioactive Waste 225
6.7 Burning Surplus Weapons-Grade Uranium and Plutonium 232
6.8 Utilization of Uranium Energy Content 234
6.9 Transmutation of Spent Nuclear Fuel 236
6.10 Closing the Nuclear Fuel Cycle 242
7 Nuclear Power Reactors 247
7.1 Pressurized Water Reactors 247
7.2 Boiling Water Reactors 249
7.3 Pressure Tube Heavy Water–Moderated Reactors 253
7.4 Pressure Tube Graphite-Moderated Reactors 255
7.5 Graphite-Moderated Gas-Cooled Reactors 258
7.6 Liquid Metal Fast Reactors 260
7.7 Other Power Reactors 265
7.8 Characteristics of Power Reactors 266
7.9 Advanced Generation-III Reactors 267
7.10 Advanced Generation-IV Reactors 271
7.11 Advanced Subcritical Reactors 274
7.12 Nuclear Reactor Analysis 276
7.13 Interaction of Reactor Physics and Reactor Thermal Hydraulics 281
8 Reactor Safety 285
8.1 Elements of Reactor Safety 285
8.2 Reactor Safety Analysis 287
8.3 Quantitative Risk Assessment 289
8.4 Reactor Accidents 294
8.5 Passive Safety 300
Part 2 Advanced Reactor Physics 305
9 Neutron Transport Theory 307
9.1 Neutron Transport Equation 307
9.2 Integral Transport Theory 312
9.3 Collision Probability Methods 323
9.4 Interface Current Methods in Slab Geometry 327
9.5 Multidimensional Interface Current Methods 336
9.6 Spherical Harmonics (PL) Methods in One-Dimensional
9.7 Multidimensional Spherical Harmonics (PL) Transport Theory 357
9.8 Discrete Ordinates Methods in One-Dimensional Slab Geometry 362
9.9 Discrete Ordinates Methods in One-Dimensional Spherical
9.10 Multidimensional Discrete Ordinates Methods 372
9.11 Even-Parity Transport Formulation 379
9.12 Monte Carlo Methods 380
10 Neutron Slowing Down 395
10.1 Elastic Scattering Transfer Function 395
10.2 P1 and B1 Slowing-Down Equations 400
10.3 Diffusion Theory 407
10.4 Continuous Slowing-Down Theory 411
10.5 Multigroup Discrete Ordinates Transport Theory 423
11 Resonance Absorption 429
11.1 Resonance Cross Sections 429
11.2 Widely Spaced Single-Level Resonances in a Heterogeneous
11.3 Calculation of First-Flight Escape Probabilities 439
11.4 Unresolved Resonances 444
11.5 Multiband Treatment of Spatially Dependent Self-Shielding 449
11.6 Resonance Cross Section Representations 456
12 Neutron Thermalization 469
12.1 Double Differential Scattering Cross Section for Thermal Neutrons 469
12.2 Neutron Scattering from a Monatomic Maxwellian Gas 470
12.3 Thermal Neutron Scattering from Bound Nuclei 473
12.4 Calculation of the Thermal Neutron Spectra in Homogeneous Media 478
12.5 Calculation of Thermal Neutron Energy Spectra in Heterogeneous Lattices 492
12.6 Pulsed Neutron Thermalization 494
13 Perturbation and Variational Methods 501
13.1 Perturbation Theory Reactivity Estimate 501
13.2 Adjoint Operators and Importance Function 504
13.3 Variational/Generalized Perturbation Reactivity Estimate 508
13.4 Variational/Generalized Perturbation Theory Estimates of Reaction Rate Ratios in Critical Reactors 512
13.5 Variational/Generalized Perturbation Theory Estimates of Reaction Rates 515
13.6 Variational Theory 516
13.7 Variational Estimate of Intermediate Resonance Integral 519
13.8 Heterogeneity Reactivity Effects 521
13.9 Variational Derivation of Approximate Equations 522
13.10 Variational Even-Parity Transport Approximations 524
13.11 Boundary Perturbation Theory 527
14 Homogenization 535
14.1 Equivalent Homogenized Cross Sections 536
14.2 ABH Collision Probability Method 537
14.3 Blackness Theory 541
14.4 Fuel Assembly Transport Calculations 543
14.5 Homogenization Theory 551
14.6 Equivalence Homogenization Theory 553
14.7 Multiscale Expansion Homogenization Theory 556
14.8 Flux Detail Reconstruction 560
15 Nodal and Synthesis Methods 563
15.1 General Nodal Formalism 564
15.2 Conventional Nodal Methods 567
15.3 Transverse Integrated Nodal Diffusion Theory Methods 570
15.4 Transverse Integrated Nodal Integral Transport Theory Models 577
15.5 Transverse Integrated Nodal Discrete Ordinates Method 585
15.6 Finite-Element Coarse-Mesh Methods 586
15.7 Variational Discrete Ordinates Nodal Method 595
15.8 Variational Principle for Multigroup Diffusion Theory 605
15.9 Single-Channel Spatial Synthesis 608
15.10 Multichannel Spatial Synthesis 614
15.11 Spectral Synthesis 616
16 Space–Time Neutron Kinetics 623
16.1 Flux Tilts and Delayed Neutron Holdback 623
16.2 Spatially Dependent Point Kinetics 626
16.3 Time Integration of the Spatial Neutron Flux Distribution 635
16.4 Stability 651
16.5 Xenon Spatial Oscillations 667
16.6 Stochastic Kinetics 680
Appendices
A Physical Constants and Nuclear Data 695
B Some Useful Mathematical Formulas 703
C Step Functions, Delta Functions, and Other Functions 705
C.1 Introduction 705
C.2 Properties of the Dirac δ-Function 706
Alternative Representations 706
Properties 706
Derivatives 707
D Some Properties of Special Functions 709
E Introduction to Matrices and Matrix Algebra 713
E.1 Some Definitions 713
E.2 Matrix Algebra 715
F Introduction to Laplace Transforms 717
F.1 Motivation 717
F.2 “Cookbook” Laplace Transforms 719
Index 723
