Neutronic Analysis For Nuclear Reactor Systems

Table of ContentsAbout the AuthorsPrefaceAcknowledgmentChapter One: Neutron Physics Background1.0Nuclei - Sizes, Composition, and Binding Energies1.1Decay of a Nucleus1.2Distribution of Nuclides and Nuclear Fission/Nuclear Fusion1.3Neutron-Nucleus Interaction1.3.1Nuclear Reactions Rates and Neutron Cross Sections1.3.2Effects of Temperature on Cross Section1.3.3Nuclear Cross Section Processing Codes1.3.4Energy Dependence of Neutron Cross Sections1.3.5Types of Interactions1.4Mean Free Path1.5Nuclear Cross Section and Neutron Flux Summary1.6Fission1.7Fission Spectra1.8The Nuclear Fuel1.6.1Fertile Material1.9Liquid Drop Model of a Nucleus1.10Summary of Fission Process1.11Reactor Power Calculation1.12Relationship between Neutron Flux and Reactor Power1.13References1.14ProblemsChapter Two: Modeling Neutron Transport and Interactions2.0Transport Equations2.1Reaction Rates2.2Reactor Power Calculation2.3Relationship between Neutron Flux and Reactor Power2.4Neutron Slowing Down and Thermalization2.5Macroscopic Slowing Down Power2.6Moderate Ratio2.7Integro-Differential Equation (Maxwell-Boltzmann Equation)2.8Integral Equation2.9Multigroup Diffusion Theory2.10The Multigroup Equations2.11Generating the Coefficients2.12Simplifications2.13Nuclear Criticality Concepts2.14Criticality Calculation2.15The Multiplication Factor and a Formal Calculation of Criticality2.16Fast Fission Factor Definition2.17Resonance Escape Probability2.18Group Collapsing2.18.1Multigroup Collapsing to One Group2.18.2Multigroup Collapsing to Two Group2.18.3Two Group Criticality2.19The Infinite Reactor2.20Finite Reactor2.21Time Dependence2.22Thermal Utilization Factor2.23References2.24ProblemsChapter Three: Spatial Effects in Modeling Neutron Diffusion - One Group Models3.0Nuclear Reactor Calculations3.1.1Neutron Spectrum3.2Control Rods in Reactors3.2.1Lattice Calculation Analysis3.3An Introduction to Neutron Transport Equation3.4Neutron Current Density Concept in General3.5Neutron Current Density and Fick's Law3.6Problem Classification and Neutron Distribution3.7Neutron Slowing Down3.8Neutron Diffusion Concept3.9The One Group Model and One Dimensional Analysis3.10.1Boundary Conditions for the Steady-State Diffusion Equation3.10.2Boundary Conditions - Consistent and Approximate3.10.3An Approximate Methods for Solving the Diffusion Equation3.10.4The P1 Approximate Methods in Transport Theory3.11Further Analysis Methods for One Group<3.11.1Slab Geometry3.11.2Cylindrical Geometry3.11.3Spherical Geometry3.12Eigenfunction Expansion Methods and Eigenvalue Equations3.12.1Eigenvalues and Eigenfunctions Problems3.13Multi-Dimensional Models and Boundary Conditions3.13.1The Unreflected Reactor Parallelepiped Core3.13.2The Minimum Volume of the Critical Parallelepiped3.13.3The Peak to Average Flux Ratio3.13.4The Finite Height Cylindrical Core3.14Relating k to the Criticality Condition3.15Analytical Solution for the Transient Case for Reactor3.16Criticality3.17Bare Critical Reactor 1-Group Model3.18Bare Critical Reactor 1-Group Model, Finite Geometries3.19Reflected Critical Reactors- 1-Group Model3.20Infinite Reflector Case3.21Criticality for General Bare Geometries3.22Reflected Reactor Geometries3.23Reactor Criticality Calculations3.24References3.25ProblemsChapter Four: Energy Effects in Modeling Neutron Diffusion - Two Group Models4.0One-Group Diffusion Theory4.1Two-Group Diffusion Theory4.2Few Group Analysis4.2.12-Group Thermal Reactor Equations4.2.22-Group Fast Reactor Equations4.3Transverse Buckling Approximation4.4Consistent Diffusion Theory Boundary Conditions4.5Derivation of the One-Dimensional Multi-Group PN Equations4.6Multi-Group Diffusion Equations - Solution Approach4.6.1Infinite Medium for Group Collapse4.6.2Zero-Dimensional Spectrum for Group Collapse4.6.3Group Collapsing4.6.4Group Collapse4.7References4.8ProblemsChapter Five: Numerical Methods in Modeling Neutron Diffusion5.0Introduction5.1Problem(s) Solved5.1.1Transport Equation5.1.2Angle Discretization5.1.3Energy Discretization5.1.4Spatial Discretization5.1.5Matrix Formulation5.2Solution Strategy5.2.1Types of Outer Iterations5.2.2Inhomogeneous Source (No Fission)5.2.3Inhomogeneous Source (With Fission)5.2.4Fission Eigenvalue Calculation5.2.5Eigenvalue Search Calculation5.3Middle Iterations5.4Inner Iterations5.5Upscatter Iterations5.6Inhomogeneous Sources5.7Background Concepts5.7.1Mixing Tables5.7.2Cross Section Collapsing5.8Input Description5.9Output Description5.10References5.11ProblemsChapter Six: Slowing Down Theory6.0Neutron Elastic and Inelastic Scattering for Slowing Down6.1Derivation of the Energy and Transfer Cross Section6.1.1Elastic Scattering6.1.2Inelastic Scattering6.2Derivation of the Isotropic Flux in an Infinite Hydrogen Moderator6.3Derivation of the Isotropic Flux in a Moderator Other than Hydrogen A > 16.4Summary of Slowing Down Equations6.5References6.6ProblemsChapter Seven: Resonance Processing7.0Difficulties Presented by Resonance Cross Sections7.1What is Nuclear Resonance -- Compound Nucleus7.1.1Breit-Wigner Resonance Reaction Cross Sections7.1.2Resonance and Neutron Cross Section7.2Doppler Effect and Doppler Broadening of Resonance7.3Doppler Coefficient in Power Reactors7.4Infinite Resonance Integrals and Group Cross Section7.4.1The Flux Calculator Method7.4.2The Bondarenko Method - The Bondarenko Factor7.4.3The CENTRM Method7.5Infinite Resonance Integrals and Group Cross Sections7.6Dilution Cross Section - Dilution Factor7.7Resonance Effects7.8Homogeneous Narrow Resonance Approximation7.9Homogeneous Wide Resonance Approximation7.10Heterogeneous Narrow Resonance Approximation7.11Heterogeneous Wide Resonance Approximation7.12References7.13ProblemsChapter Eight: Heterogeneous Reactors and Wigner Seitz Cells8.0Homogeneous and Heterogeneous Reactors8.1Spectrum Calculation in Heterogeneous Reactors8.2Cross Section Self Shielding and Wigner-Seitz Cells8.3References8.4ProblemsChapter Nine: Thermal Spectra and Thermal Cross Sections<9.0Coupling to Higher Energy Sources9.1Chemical Binding and Scattering Kernels9.1.1Scattering Materials9.1.2Thermal Cross Section Average9.2Derivation of the Maxwell-Boltzmann Spectrum9.3References9.4ProblemsChapter Ten: Perturbation Theory for Reactor Neutronics10.0Perturbation Theory10.1Zero Dimensional Methods10.2Spatial Method (1 Group)10.3References10.4ProblemsChapter Eleven: Reactor Kinetics and Point Kinetics11.0Time Dependent Diffusion Equation11.1Derivation of Exact Point Kinetics Equations (EPKE)11.2The Point Kinetics Equations11.3Dynamic versus Static Reactivity11.4Calculating the Time Dependent Shape Function11.5Point Kinetics Approximations11.5.1Level of Approximation to the Point Kinetics Equations11.6Adiabatic Approximation11.7Adiabatic Approximation with Pre-Computed Shape Functions11.8Quasi-Static Approximation11.9Zero Dimensional Reactors11.10References11.11ProblemsChapter Twelve: Reactor Dynamics12.0Background on Nuclear Reactor12.1Neutron Multiplication12.2Simple Feedbacks12.3Multiple Time Constant Feedbacks12.4Fuchs-Nordheim models12.5References12.6ProblemsChapter Thirteen: Reactor Stability13.0Frequency Response13.1Nyquist Plots13.2Non-Linear Stability13.3References13.4ProblemsChapter Fourteen: Numerical Modeling for Time Dependent Problems14.0Fast Breeder Reactor History and Status14.1The Concept of Stiffness14.2The Quasi-Static Method14.3Bethe-Tait Models14.4References14.5ProblemsChapter Fifteen: Fission Product Buildup and Decay15.0Background Introduction15.1Nuclear Fission and the Fission Process15.2Radioactivity and Decay of Fission Product15.3Poisons Produced by Fission15.4References15.5ProblemsChapter Sixteen: Fuel Burnup and Fuel Management16.0The World's Energy Resources16.1Today's Global Energy Market16.2Fuel Utilization and Fuel Burnup16.3Fuel Reprocessing16.3.1PUREX Process16.3.2Transuranium Elements16.3.3Vitrification16.4Fuel Management for Nuclear Reactors16.5Nuclear Fuel Cycle16.6Store and Transport High Burnup Fuel16.7Nuclear Reactors for Power Production16.8Future Nuclear Power Plants Systems16.9Next Generation of Nuclear Power Reactors for Power Production16.10References16.11ProblemsAppendix A: Laplace TransformsA-1Definition of Laplace TransformA-2Basic TransformsA-3Fundamental PropertiesA-4Inversion by Complex Variable Residue TheoremAppendix B: Transfer Functions and Bode PlotsB-1Transfer FunctionsB-2Sample TransformsB-3Fourier TransformsB-4Transfer FunctionsB-4Feedback and ControlB-5Graphical Representation (Bode and Nyquist Diagram)B-6Root Locus Construction RulesB-7ReferencesINDEX