Fundamentals of Nuclear Reactor Physics (eBook)

Front Cover 1
Fundamentals of Nuclear Reactor Physics 4
Copyright Page 5
Table of Contents 8
Preface 14
Chapter 1 Nuclear Reactions 18
1.1 Introduction 18
1.2 Nuclear Reaction Fundamentals 19
Reaction Equations 20
Notation 22
Energetics 22
1.3 The Curve of Binding Energy 24
1.4 Fusion Reactions 25
1.5 Fission Reactions 26
Energy Release and Dissipation 27
Neutron Multiplication 29
Fission Products 30
1.6 Fissile and Fertile Materials 33
1.7 Radioactive Decay 35
Saturation Activity 37
Decay Chains 38
Chapter 2 Neutron Interactions 46
2.1 Introduction 46
2.2 Neutron Cross Sections 46
Microscopic and Macroscopic Cross Sections 47
Uncollided Flux 49
Nuclide Densities 50
Enriched Uranium 52
Cross Section Calculation Example 53
Reaction Types 53
2.3 Neutron Energy Range 55
2.4 Cross Section Energy Dependence 57
Compound Nucleus Formation 58
Resonance Cross Sections 59
Threshold Cross Sections 63
Fissionable Materials 64
2.5 Neutron Scattering 65
Elastic Scattering 66
Slowing Down Decrement 67
Inelastic Scattering 69
Chapter 3 Neutron Distributions in Energy 74
3.1 Introduction 74
3.2 Nuclear Fuel Properties 75
3.3 Neutron Moderators 78
3.4 Neutron Energy Spectra 80
Fast Neutrons 82
Neutron Slowing Down 83
Thermal Neutrons 87
Fast and Thermal Reactor Spectra 89
3.5 Energy-Averaged Reaction Rates 90
Fast Cross Section Averages 92
Resonance Cross Section Averages 95
Thermal Cross Section Averages 96
3.6 Infinite Medium Multiplication 98
Chapter 4 The Power Reactor Core 102
4.1 Introduction 102
4.2 Core Composition 102
Light Water Reactors 105
Heavy Water Reactors 108
Graphite-Moderated Reactors 109
RBMK Reactors 110
Fast Reactors 111
4.3 Fast Reactor Lattices 111
4.4 Thermal Reactor Lattices 115
The Four Factor Formula 116
Pressurized Water Reactor Example 125
Chapter 5 Reactor Kinetics 132
5.1 Introduction 132
5.2 Neutron Balance Equations 133
Infinite Medium Nonmultiplying Systems 133
Infinite Medium Multiplying Systems 134
Finite Multiplying Systems 136
5.3 Multiplying Systems Behavior 137
5.4 Delayed Neutron Kinetics 140
Kinetics Equations 141
Reactivity Formulation 143
5.5 Step Reactivity Changes 143
Reactor Period 144
Prompt Jump Approximation 148
5.6 Prologue to Reactor Dynamics 150
Chapter 6 Spatial Diffusion of Neutrons 156
6.1 Introduction 156
6.2 The Neutron Diffusion Equation 157
Spatial Neutron Balance 157
Diffusion Approximation 159
6.3 Nonmultiplying Systems—Plane Geometry 160
Source Free Example 160
Uniform Source Example 161
6.4 Boundary Conditions 162
Vacuum Boundaries 163
Reflected Boundaries 164
Surface Sources and Albedos 164
Interface Conditions 165
Boundary Conditions in Other Geometries 166
6.5 Nonmultiplying Systems—Spherical Geometry 166
Point Source Example 167
Two Region Example 168
6.6 Diffusion Approximation Validity 170
Diffusion Length 171
Uncollided Flux Revisited 172
6.7 Multiplying Systems 174
Subcritical Assemblies 174
The Critical Reactor 177
Chapter 7 Neutron Distributions in Reactors 184
7.1 Introduction 184
7.2 The Time-Independent Diffusion Equation 184
7.3 Uniform Reactors 186
Finite Cylindrical Core 187
Reactor Power 189
7.4 Neutron Leakage 191
Two Group Approximation 191
Migration Length 195
Leakage and Design 196
7.5 Reflected Reactors 197
Axial Reflector Example 198
Reflector Savings and Flux Flattening 201
7.6 Control Poisons 203
Reactivity Worth 203
Partially Inserted Control Rod 205
Control Rod Bank Insertion 207
Chapter 8 Energy Transport 216
8.1 Introduction 216
8.2 Core Power Distribution 216
Finite Cylindrical Core 217
Uniform Cylindrical Core Example 220
8.3 Heat Transport 221
Heat Source Characterization 221
Steady State Temperatures 222
Pressurized Water Reactor Example 226
8.4 Thermal Transients 228
Fuel Temperature Transient Examples 229
Coolant Temperature Transients 230
Chapter 9 Reactivity Feedback 238
9.1 Introduction 238
9.2 Reactivity Coefficients 238
Fuel Temperature Coefficient 240
Moderator Temperature Coefficient 242
Fast Reactor Temperature Coefficients 244
9.3 Composite Coefficients 244
Prompt Coefficient 245
Isothermal Temperature Coefficient 245
Power Coefficient 246
Temperature and Power Defects 247
9.4 Excess Reactivity and Shutdown Margin 247
9.5 Reactor Transients 249
Reactor Dynamics Model 250
Transient Analysis 251
Chapter 10 Long-Term Core Behavior 260
10.1 Introduction 260
10.2 Reactivity Control 260
10.3 Fission Product Buildup and Decay 262
Xenon Poisoning 264
Samarium Poisoning 267
10.4 Fuel Depletion 269
Fissionable Nuclide Concentrations 269
Burnable Poisons 272
10.5 Fission Product and Actinide Inventories 274
Appendices 280
Appendix A Useful Mathematical Relationships 282
Derivatives and Integrals 282
Definite Integrals 282
Hyperbolic Functions 283
Expansions 283
Integration by Parts 283
Derivative of an Integral 284
First-Order Differential Equations 284
Second-Order Differential Equations 285
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Appendix B Bessel’s Equation and Functions 286
Appendix C Derivation of Neutron Diffusion Properties 290
Appendix D Fuel Element Heat Transfer 296
Appendix E Nuclear Data 300
Index 304