Neutronic Analysis For Nuclear Reactor Systems

<div>Table of Contents</div><div>About the Authors </div><div>Preface</div><div>Acknowledgment</div><div>Chapter One: Neutron Physics Background</div><div>1.0 Nuclei – Sizes, Composition, and Binding Energies</div><div>1.1 Decay of a Nucleus</div><div>1.2 Distribution of Nuclides and Nuclear Fission/Nuclear Fusion</div><div>1.3 Neutron-Nucleus Interaction</div><div>1.3.1 Nuclear Reactions Rates and Neutron Cross Sections</div><div>1.3.2 Effects of Temperature on Cross Section</div><div>1.3.3 Nuclear Cross Section Processing Codes</div><div>1.3.4 Energy Dependence of Neutron Cross Sections</div><div>1.3.5 Types of Interactions</div><div>1.4 Mean Free Path</div><div>1.5 Nuclear Cross Section and Neutron Flux Summary</div><div>1.6 Fission</div><div>1.7 Fission Spectra</div><div>1.8 The Nuclear Fuel</div><div>1.6.1 Fertile Material</div><div>1.9 Liquid Drop Model of a Nucleus</div><div>1.10 Summary of Fission Process</div><div>1.11 Reactor Power Calculation</div><div>1.12 Relationship between Neutron Flux and Reactor Power</div><div>1.13 References</div><div>1.14 Problems</div><div>Chapter Two: Modeling Neutron Transport and Interactions</div><div>2.0 Transport Equations</div><div>2.1 Reaction Rates</div><div>2.2 Reactor Power Calculation</div><div>2.3 Relationship between Neutron Flux and Reactor Power</div><div>2.4 Neutron Slowing Down and Thermalization</div><div>2.5 Macroscopic Slowing Down Power</div><div>2.6 Moderate Ratio</div><div>2.7 Integro-Differential Equation (Maxwell-Boltzmann Equation)</div><div>2.8 Integral Equation</div><div>2.9 Multigroup Diffusion Theory</div><div>2.10 The Multigroup Equations</div><div>2.11 Generating the Coefficients</div><div>2.12 Simplifications</div><div>2.13 Nuclear Criticality Concepts</div><div>2.14 Criticality Calculation</div><div>2.15 The Multiplication Factor and a Formal Calculation of Criticality</div><div>2.16 Fast Fission Factor Definition</div><div>2.17 Resonance Escape Probability</div><div>2.18 Group Collapsing<div>2.18.1 Multigroup Collapsing to One Group</div><div>2.18.2 Multigroup Collapsing to Two Group</div><div>2.18.3 Two Group Criticality</div><div>2.19 The Infinite Reactor</div><div>2.20 Finite Reactor</div><div>2.21 Time Dependence</div><div>2.22 Thermal Utilization Factor</div><div>2.23 References</div><div>2.24 Problems</div><div>Chapter Three: Spatial Effects in Modeling Neutron Diffusion – One Group Models</div><div>3.0 Nuclear Reactor Calculations</div><div>3.1.1 Neutron Spectrum</div><div>3.2 Control Rods in Reactors</div><div>3.2.1 Lattice Calculation Analysis</div><div>3.3 An Introduction to Neutron Transport Equation</div><div>3.4 Neutron Current Density Concept in General</div><div>3.5 Neutron Current Density and Fick’s Law</div><div>3.6 Problem Classification and Neutron Distribution</div><div>3.7 Neutron Slowing Down</div><div>3.8 Neutron Diffusion Concept</div><div>3.9 The One Group Model and One Dimensional Analysis</div><div>3.10.1 Boundary Conditions for the Steady-State Diffusion Equation</div><div>3.10.2 Boundary Conditions – Consistent and Approximate</div><div>3.10.3 An Approximate Methods for Solving the Diffusion Equation</div><div>3.10.4 The P1 Approximate Methods in Transport Theory</div><div>3.11 Further Analysis Methods for One Group</div><div>&lt;3.11.1 Slab Geometry</div><div>3.11.2 Cylindrical Geometry</div><div>3.11.3 Spherical Geometry</div><div>3.12 Eigenfunction Expansion Methods and Eigenvalue Equations</div><div>3.12.1 Eigenvalues and Eigenfunctions Problems</div><div>3.13 Multi-Dimensional Models and Boundary Conditions</div><div>3.13.1 The Unreflected Reactor Parallelepiped Core</div><div>3.13.2 The Minimum Volume of the Critical Parallelepiped</div><div>3.13.3 The Peak to Average Flux Ratio</div><div>3.13.4 The Finite Height Cylindrical Core</div><div>3.14 Relating k to the Criticality Condition</div><div>3.15 Analytical Solution for the Transient Case for Reactor</div><div>3.16 Criticality</div><div>3.17 Bare Critical Reactor 1-Group Model</div><div>3.18 Bare Critical Reactor 1-Group Model, Finite Geometries</div><div>3.19 Reflected Critical Reactors- 1-Group Model</div><div>3.20 Infinite Reflector Case</div><div>3.21 Criticality for General Bare Geometries</div><div>3.22 Reflected Reactor Geometries</div><div>3.23 Reactor Criticality Calculations</div><div>3.24 References</div><div>3.25 Problems</div><div>Chapter Four: Energy Effects in Modeling Neutron Diffusion – Two Group Models</div><div>4.0 One-Group Diffusion Theory</div><div>4.1 Two-Group Diffusion Theory</div><div>4.2 Few Group Analysis</div><div>4.2.1 2-Group Thermal Reactor Equations</div><div>4.2.2 2-Group Fast Reactor Equations</div><div>4.3 Transverse Buckling Approximation</div><div>4.4 Consistent Diffusion Theory Boundary Conditions</div><div>4.5 Derivation of the One-Dimensional Multi-Group PN Equations</div><div>4.6 Multi-Group Diffusion Equations - Solution Approach</div><div>4.6.1 Infinite Medium for Group Collapse</div><div>4.6.2 Zero-Dimensional Spectrum for Group Collapse</div><div>4.6.3 Group Collapsing</div><div>4.6.4 Group Collapse</div><div>4.7 References</div><div>4.8 Problems<div>Chapter Five: Numerical Methods in Modeling Neutron Diffusion</div><div>5.0 Introduction</div><div>5.1 Problem(s) Solved</div><div>5.1.1 Transport Equation</div><div>5.1.2 Angle Discretization</div><div>5.1.3 Energy Discretization</div><div>5.1.4 Spatial Discretization</div><div>5.1.5 Matrix Formulation</div><div>5.2 Solution Strategy</div><div>5.2.1 Types of Outer Iterations</div><div>5.2.2 Inhomogeneous Source (No Fission)</div><div>5.2.3 Inhomogeneous Source (With Fission)</div><div>5.2.4 Fission Eigenvalue Calculation</div><div>5.2.5 Eigenvalue Search Calculation</div><div>5.3 Middle Iterations</div><div>5.4 Inner Iterations</div><div>5.5 Upscatter Iterations</div><div>5.6 Inhomogeneous Sources</div><div>5.7 Background Concepts</div><div>5.7.1 Mixing Tables</div><div>5.7.2 Cross Section Collapsing</div><div>5.8 Input Description5.9 Output Description</div><div>5.10 References</div><div>5.11 Problems</div><div>Chapter Six: Slowing Down Theory</div><div>6.0 Neutron Elastic and Inelastic Scattering for Slowing Down</div><div>6.1 Derivation of the Energy and Transfer Cross Section</div><div>6.1.1 Elastic Scattering</div><div>6.1.2 Inelastic Scattering</div><div>6.2 Derivation of the Isotropic Flux in an Infinite Hydrogen Moderator</div><div>6.3 Derivation of the Isotropic Flux in a Moderator Other than Hydrogen A &gt; 1</div><div>6.4 Summary of Slowing Down Equations</div><div>6.5 References</div><div>6.6 Problems</div><div>Chapter Seven: Resonance Processing</div><div>7.0 Difficulties Presented by Resonance Cross Sections</div><div>7.1 What is Nuclear Resonance -- Compound Nucleus</div><div>7.1.1 Breit-Wigner Resonance Reaction Cross Sections</div><div>7.1.2 Resonance and Neutron Cross Section</div><div>7.2 Doppler Effect and Doppler Broadening of Resonance</div><div>7.3 Doppler Coefficient in Power Reactors<div>7.4 Infinite Resonance Integrals and Group Cross Section</div><div>7.4.1 The Flux Calculator Method</div><div>7.4.2 The Bondarenko Method - The Bondarenko Factor</div><div>7.4.3 The CENTRM Method</div><div>7.5 Infinite Resonance Integrals and Group Cross Sections</div><div>7.6 Dilution Cross Section - Dilution Factor</div><div>7.7 Resonance Effects</div><div>7.8 Homogeneous Narrow Resonance Approximation</div><div>7.9 Homogeneous Wide Resonance Approximation</div><div>7.10 Heterogeneous Narrow Resonance Approximation</div><div>7.11 Heterogeneous Wide Resonance Approximation</div><div>7.12 References</div><div>7.13 Problems</div><div>Chapter Eight: Heterogeneous Reactors and Wigner Seitz Cells</div><div>8.0 Homogeneous and Heterogeneous Reactors</div><div>8.1 Spectrum Calculation in Heterogeneous Reactors</div><div>8.2 Cross Section Self Shielding and Wigner-Seitz Cells</div><div>8.3 References</div><div>8.4 Problems</div><div>Chapter Nine: Thermal Spectra and Thermal Cross Sections</div><9.0 Coupling to Higher Energy Sources</div><div>9.1 Chemical Binding and Scattering Kernels</div><div>9.1.1 Scattering Materials</div><div>9.1.2 Thermal Cross Section Average</div><div>9.2 Derivation of the Maxwell-Boltzmann Spectrum</div><div>9.3 References</div><div>9.4 Problems</div><div>Chapter Ten: Perturbation Theory for Reactor Neutronics</div><div>10.0 Perturbation Theory</div><div>10.1 Zero Dimensional Methods<div>10.2 Spatial Method (1 Group)</div><div>10.3 References</div><div>10.4 Problems</div><div>Chapter Eleven: Reactor Kinetics and Point Kinetics</div><div>11.0 Time Dependent Diffusion Equation</div><div>11.1 Derivation of Exact Point Kinetics Equations (EPKE)</div><div>11.2 The Point Kinetics Equations</div><div>11.3 Dynamic versus Static Reactivity</div><div>11.4 Calculating the Time Dependent Shape Function</div><div>11.5 Point Kinetics Approximations</div><div>11.5.1 Level of Approximation to the Point Kinetics Equations</div><div>11.6 Adiabatic Approximation<div>11.7 Adiabatic Approximation with Pre-Computed Shape Functions</div><div>11.8 Quasi-Static Approximation</div><div>11.9 Zero Dimensional Reactors</div><div>11.10 References</div><div>11.11 Problems</div><div>Chapter Twelve: Reactor Dynamics</div><div>12.0 Background on Nuclear Reactor</div><div>12.1 Neutron Multiplication</div><div>12.2 Simple Feedbacks</div><div>12.3 Multiple Time Constant Feedbacks</div><div>12.4 Fuchs-Nordheim models</div><div>12.5 References</div><div>12.6 Problems</div><div>Chapter Thirteen: Reactor Stability</div><div>13.0 Frequency Response</div><div>13.1 Nyquist Plots</div><div>13.2 Non-Linear Stability</div><div>13.3 References</div><div>13.4 Problems</div><div>Chapter Fourteen: Numerical Modeling for Time Dependent Problems</div><div>14.0 Fast Breeder Reactor History and Status</div><div>14.1 The Concept of Stiffness</div><div>14.2 The Quasi-Static Method</div><div>14.3 Bethe-Tait Models</div><div>14.4 References</div><div>14.5 Problems<div>Chapter Fifteen: Fission Product Buildup and Decay</div><div>15.0 Background Introduction</div><div>15.1 Nuclear Fission and the Fission Process</div><div>15.2 Radioactivity and Decay of Fission Product</div><div>15.3 Poisons Produced by Fission</div><div>15.4 References</div><div>15.5 Problems</div><div>Chapter Sixteen: Fuel Burnup and Fuel Management</div><div>16.0 The World’s Energy Resources</div><div>16.1 Today’s Global Energy Market</div><div>16.2 Fuel Utilization and Fuel Burnup</div><div>16.3 Fuel Reprocessing</div><div>16.3.1 PUREX Process</div><div>16.3.2 Transuranium Elements</div><div>16.3.3 Vitrification</div><div>16.4 Fuel Management for Nuclear Reactors</div><div>16.5 Nuclear Fuel Cycle</div><div>16.6 Store and Transport High Burnup Fuel</div><div>16.7 Nuclear Reactors for Power Production</div><div>16.8 Future Nuclear Power Plants Systems</div><div>16.9 Next Generation of Nuclear Power Reactors for Power Production</div><div>16.10 References</div>16.11 Problems<div>Appendix A: Laplace Transforms</div><div>A-1 Definition of Laplace Transform</div><div>A-2 Basic Transforms</div><div>A-3 Fundamental Properties</div><div>A-4 Inversion by Complex Variable Residue Theorem</div><div>Appendix B: Transfer Functions and Bode Plots</div><div>B-1 Transfer Functions</div><div>B-2 Sample Transforms</div><div>B-3 Fourier Transforms</div><div>B-4 Transfer Functions</div><div>B-4 Feedback and Control</div><div>B-5 Graphical Representation (Bode and Nyquist Diagram)</div><div>B-6 Root Locus Construction Rules</div><div>B-7 References</div><div>INDEX</div></div></div>