Title Details

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