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Nuclear reactor theory and design
by Roger A. Rydin
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This edition was published in 1977 by University Publications in Blacksburg, Va.
Written in English
— 385 pages
Table of Contents Page
CHAPTER 1 INTRODUCTION 1
1.1 Background 1
1.2 Historical Approach 2
1.3 Neutron Density 5
1.4 Reaction Rates 6
1.5 Design Approximations 11
1.6 Reactor Design Implications 12
CHAPTER 2 INTERACTIONS OF NEUTRONS
WITH MATTER 17
2.1 Compound Nucleus  Cross Sections 17
2.2 Nuclear Systematics of Naturally Occurring
Isotopes 23
2.3 Level Widths and Partial Cross Sections 25
2.3 Cross Section for Formulation of the Compound
Nucleus 26
2.5 Reaction Probabilities 28
2.6 Kinematics in the CenterofMass System 30
2.7 Relationships Between the Scattering
Angles in the LAB and CM Systems 36
CHAPTER 3 NUCLEAR FISSION 45
3.1 Binding Energy 45
3.2 Liquid Drop Model of Fission 48
3.3 Fission Product Yields 55
3.4 Fission Neutron Spectrum 57
3.5 Prompt Neutrons 59
3.6 Delayed Neutrons 62
3.7 Energy Production in Fission 64
CHAPTER 4 DERIVATION OF THE NEUTRON
DIFFUSION EQUATION 69
4.1 Fick's Law Derivation of the Diffusion Equation 69
4.2* The OneSpeed Transport Equation 74
4.3* OneDimensional, OneSpeed Transport Equation 80
4.4* Derivation of the P1 Equations 86
4.5 The P1 Diffusion Theory Approximation 89
4.6 Comments on the P1 Equations of Diffusion Theory 92
4.7* Alternate Derivation of the Diffusion Equation 94
CHAPTER 5 ANALYTIC SOLUTIONS TO THE
ONESPEED DIFFUSION EQUATION 99
5.1 Partial Currents and the Extrapolated Boundary
Condition 99
5.2 Source Plane Boundary Conditions 107
5.3 Two Region Planar Problem 111
5.4 Point and Line Sources 113
5.5 Solution to the Inhomogeneous Source Problem 120
5.6* General Derivation of the Green's Function
Superposition Integral 123
5.7 Diffusion Length 126
5.8 Critical Reactors 128
5.9 Homogeneous Bare Critical Slab Reactor 131
5.10 Two Region Slab Reactor 135
5.11 OneDimensional Bare Homogeneous Cylindrical Reactor 138
5.12 Bare Homogeneous Spherical Reactor 141
5.13 Comments on Multiregion OneDimensional
Reactors 145
5.14 Multidimensional Reactors 149
5.15* Diffusion Length Experiment 152
CHAPTER 6 FEWGROUP EQUATIONS AND
NUMERICAL SOLUTION METHODS 165
6.1 EnergyDependent Diffusion Equation 165
6.2 FewGroup Diffusion Equations 167
6.3 Finite Difference FewGroup Equations in
One Dimension 172
6.4 Specification of Boundary Conditions 180
6.5 Direct Solution of the Source Problem 182
6.6* Iterative Solution of the Source Problem 187
6.7 Iterative Solution of the Critical Reactor
Problem 193
6.8* Convergence of the Outer Iteration to the
Fundamental Mode Solution 198
6.9 Qualitative Comparison Between OneSpeed
and TwoGroup Solutions 202
CHAPTER 7 PERTURBATION THEORY 211
7.1 Adjoint Equations 211
7.2 Matrix Form of the Adjoint Equations 217
7.3 FirstOrder Perturbation Theory 220
7.4* Perturbation Effects on Higher Harmonic
Modes 224
7.5 Control Rod Worth 226
7.6* Inhomogeneous Case 230
CHAPTER 8 REACTOR KINETICS 239
8.1 Multigroup Reactor Kinetics Equation 240
8.2 Interpretation of Spatial Kinetics Results 246
8.3 Point Kinetics Equations 249
8.4 Results for One Group of Delayed Neutrons 255
8.5 Experimental Measurement of Control Rod Worth 261
8.6* "Point" Kinetics Equations Derivation 263
8.7 Method of Obtaining and 267
CHAPTER 9 POISONING, TEMPERATURE EFFECTS,
AND DEPLETION IN REACTORS 275
9.1 The Fission Product Xenon135 276
9.2 Xenon Poisoning 277
9.3 General Transient Solution for Buildup
of Xenon and Iodine 279
9.4 Spatial Xenon Transients 283
9.5 XenonInduced Spatial Power Oscillations 284
9.6 Samarium Poisoning 289
9.7 Temperature Effects on Reactivity 293
9.8 Effect of Thermal Feedback on Reactor Kinetics 297
9.9 Depletion 308
CHAPTER 10 NEUTRON MODERATION 321
10.1 Scattering Collisions 322
10.2 Slowing Down Problem 329
10.3 Slowing Down in Hydrogen With No Absorption 330
10.4 The Slowing Down Density in Hydrogen,
No Absorption 333
10.5 Moderation for A > 1, No Absorption 335
10.6 Asymptotic Slowing Down Theory, A > 1,
No Absorption 339
10.7* Slowing Down in Hydrogen With Absorption 343
10.8* Special Cases of Slowing Down With
Absorption, A > 1 347
10.9 Final Comments 353
CHAPTER 11 SLOWING DOWN IN THE PRESENCE
OF RESONANCES 357
11.1 Resonance Cross Sections 358
11.2 Doppler Effect 365
11.3 Slowing Down in the Presence of Resonances 373
11.4 HomogeneousMedium Resonance Absorption 376
11.5 Homogeneous Resonance Integrals 385
11.6* Heterogeneous System Resonance Absorption 391
11.7 Reactor Design Implications of
Heterogeneous Lumping 407
11.8 The GAM Multigroup Slowing Down Equations 412
CHAPTER 12 THERMALIZATION 429
12.1 Neutron Balance Equation 430
12.2* Monatomic Gas Moderator Cross Sections 432
12.3 Solution to the Monatomic Gas
Thermalization Problem 443
12.4 General Case Solution 446
12.5 Spatial Effects in the Thermalization
Problem 451
APPENDIX A. THE SINGULARITY FUNCTIONS 461
APPENDIX B. THE LAPLACE TRANSFORM 465
APPENDIX C. MATRIX RELATIONSHIPS 473
APPENDIX D. SPHERICAL HARMONICS 479
APPENDIX E. DIFFERENTIATION OF AN
INTEGRAL 483
INDEX 485
Subjects
Design and construction, Nuclear reactors
Edition  Availability 

1 
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Nuclear reactor theory and design
First published in 1977
Subjects
Design and construction, Nuclear reactorsNuclear reactor theory and design
This edition was published in 1977 by University Publications in Blacksburg, Va.
Edition Description
Table of Contents Page
CHAPTER 1 INTRODUCTION 1
1.1 Background 1
1.2 Historical Approach 2
1.3 Neutron Density 5
1.4 Reaction Rates 6
1.5 Design Approximations 11
1.6 Reactor Design Implications 12
CHAPTER 2 INTERACTIONS OF NEUTRONS
WITH MATTER 17
2.1 Compound Nucleus  Cross Sections 17
2.2 Nuclear Systematics of Naturally Occurring
Isotopes 23
2.3 Level Widths and Partial Cross Sections 25
2.3 Cross Section for Formulation of the Compound
Nucleus 26
2.5 Reaction Probabilities 28
2.6 Kinematics in the CenterofMass System 30
2.7 Relationships Between the Scattering
Angles in the LAB and CM Systems 36
CHAPTER 3 NUCLEAR FISSION 45
3.1 Binding Energy 45
3.2 Liquid Drop Model of Fission 48
3.3 Fission Product Yields 55
3.4 Fission Neutron Spectrum 57
3.5 Prompt Neutrons 59
3.6 Delayed Neutrons 62
3.7 Energy Production in Fission 64
CHAPTER 4 DERIVATION OF THE NEUTRON
DIFFUSION EQUATION 69
4.1 Fick's Law Derivation of the Diffusion Equation 69
4.2* The OneSpeed Transport Equation 74
4.3* OneDimensional, OneSpeed Transport Equation 80
4.4* Derivation of the P1 Equations 86
4.5 The P1 Diffusion Theory Approximation 89
4.6 Comments on the P1 Equations of Diffusion Theory 92
4.7* Alternate Derivation of the Diffusion Equation 94
CHAPTER 5 ANALYTIC SOLUTIONS TO THE
ONESPEED DIFFUSION EQUATION 99
5.1 Partial Currents and the Extrapolated Boundary
Condition 99
5.2 Source Plane Boundary Conditions 107
5.3 Two Region Planar Problem 111
5.4 Point and Line Sources 113
5.5 Solution to the Inhomogeneous Source Problem 120
5.6* General Derivation of the Green's Function
Superposition Integral 123
5.7 Diffusion Length 126
5.8 Critical Reactors 128
5.9 Homogeneous Bare Critical Slab Reactor 131
5.10 Two Region Slab Reactor 135
5.11 OneDimensional Bare Homogeneous Cylindrical Reactor 138
5.12 Bare Homogeneous Spherical Reactor 141
5.13 Comments on Multiregion OneDimensional
Reactors 145
5.14 Multidimensional Reactors 149
5.15* Diffusion Length Experiment 152
CHAPTER 6 FEWGROUP EQUATIONS AND
NUMERICAL SOLUTION METHODS 165
6.1 EnergyDependent Diffusion Equation 165
6.2 FewGroup Diffusion Equations 167
6.3 Finite Difference FewGroup Equations in
One Dimension 172
6.4 Specification of Boundary Conditions 180
6.5 Direct Solution of the Source Problem 182
6.6* Iterative Solution of the Source Problem 187
6.7 Iterative Solution of the Critical Reactor
Problem 193
6.8* Convergence of the Outer Iteration to the
Fundamental Mode Solution 198
6.9 Qualitative Comparison Between OneSpeed
and TwoGroup Solutions 202
CHAPTER 7 PERTURBATION THEORY 211
7.1 Adjoint Equations 211
7.2 Matrix Form of the Adjoint Equations 217
7.3 FirstOrder Perturbation Theory 220
7.4* Perturbation Effects on Higher Harmonic
Modes 224
7.5 Control Rod Worth 226
7.6* Inhomogeneous Case 230
CHAPTER 8 REACTOR KINETICS 239
8.1 Multigroup Reactor Kinetics Equation 240
8.2 Interpretation of Spatial Kinetics Results 246
8.3 Point Kinetics Equations 249
8.4 Results for One Group of Delayed Neutrons 255
8.5 Experimental Measurement of Control Rod Worth 261
8.6* "Point" Kinetics Equations Derivation 263
8.7 Method of Obtaining and 267
CHAPTER 9 POISONING, TEMPERATURE EFFECTS,
AND DEPLETION IN REACTORS 275
9.1 The Fission Product Xenon135 276
9.2 Xenon Poisoning 277
9.3 General Transient Solution for Buildup
of Xenon and Iodine 279
9.4 Spatial Xenon Transients 283
9.5 XenonInduced Spatial Power Oscillations 284
9.6 Samarium Poisoning 289
9.7 Temperature Effects on Reactivity 293
9.8 Effect of Thermal Feedback on Reactor Kinetics 297
9.9 Depletion 308
CHAPTER 10 NEUTRON MODERATION 321
10.1 Scattering Collisions 322
10.2 Slowing Down Problem 329
10.3 Slowing Down in Hydrogen With No Absorption 330
10.4 The Slowing Down Density in Hydrogen,
No Absorption 333
10.5 Moderation for A > 1, No Absorption 335
10.6 Asymptotic Slowing Down Theory, A > 1,
No Absorption 339
10.7* Slowing Down in Hydrogen With Absorption 343
10.8* Special Cases of Slowing Down With
Absorption, A > 1 347
10.9 Final Comments 353
CHAPTER 11 SLOWING DOWN IN THE PRESENCE
OF RESONANCES 357
11.1 Resonance Cross Sections 358
11.2 Doppler Effect 365
11.3 Slowing Down in the Presence of Resonances 373
11.4 HomogeneousMedium Resonance Absorption 376
11.5 Homogeneous Resonance Integrals 385
11.6* Heterogeneous System Resonance Absorption 391
11.7 Reactor Design Implications of
Heterogeneous Lumping 407
11.8 The GAM Multigroup Slowing Down Equations 412
CHAPTER 12 THERMALIZATION 429
12.1 Neutron Balance Equation 430
12.2* Monatomic Gas Moderator Cross Sections 432
12.3 Solution to the Monatomic Gas
Thermalization Problem 443
12.4 General Case Solution 446
12.5 Spatial Effects in the Thermalization
Problem 451
APPENDIX A. THE SINGULARITY FUNCTIONS 461
APPENDIX B. THE LAPLACE TRANSFORM 465
APPENDIX C. MATRIX RELATIONSHIPS 473
APPENDIX D. SPHERICAL HARMONICS 479
APPENDIX E. DIFFERENTIATION OF AN
INTEGRAL 483
INDEX 485
Edition Notes
Includes bibliographies and index. Third edition available from author in pdf form, rar@virginia.edu
Classifications
The Physical Object
ID Numbers
History
 Created October 20, 2008
 6 revisions
April 13, 2010  Edited by Open Library Bot  Linked existing covers to the edition. 
April 2, 2010  Edited by 65.40.126.56  Edited without comment. 
April 2, 2010  Edited by 65.40.126.56  Edited without comment. 
March 27, 2010  Edited by 65.40.126.56  Edited without comment. 
October 20, 2008  Created by ImportBot  Imported from University of Toronto MARC record. 