Application of Invariant Embedding to Reactor Physics

PrefacePart A: Reflection and Transmission of Gamma Rays by Slabs Chapter One Introduction 1.1 Statement of the Problem 1.2 The Interaction of Gamma Rays with Matter 1.3 Classical Approach 1.4 Invariant Embedding Approach 1.5 Differences between Boltzmann Approach and Invariant Embedding Approach Chapter Two Formulation of the Problem Based on the Invariant Embedding Principle 2.1 Derivation of Basic Equations 2.2 Reflection Function for a Semi-Infinite Medium and the Modified Transmission Functions Chapter Three Solutions of Equations for Simplified Models 3.1 One Group Approximation 3.2 Reflection and Transmission of Monoenergetic Photons by an Isotropically Scattering Medium Chapter Four Method of Numerical Solutions 4.1 Derivation of Equations for Numerical Solutions 4.2 Method for Solution of Numerical Equations 4.3 Accuracy of Numerical Solutions Chapter Five Reflection and Transmission of Gamma Rays 5.1 Reflection by Semi-Infinite Media 5.2 Transmission through Homogeneous Slabs 5.3 Transmission through Multilayer Slabs ReferencesPart Β: Application to Criticality Calculations Chapter Six Introduction 6.1 Introduction to Criticality Calculations 6.2 Classical Approach 6.3 Invariant Embedding Approach Chapter Seven One-dimensional Problem 7.1 Direct Application of Invariant Embedding to Criticality Calculations 7.2 Modification of Invariant Embedding Method 7.3 Calculation of Response Matrices 7.4 Criticality Calculation 7.5 Examples of Criticality Calculations Chapter Eight Two-dimensional Problem 8.1 Introduction 8.2 Definitions of Two-dimensional Response Matrices 8.3 Calculation of Response Matrices 8.4 Criticality Calculation 8.5 Examples of Criticality Calculations 8.6 Application to the Burnup CalculationAppendix A Time-Dependent Problem A.1 Time-Dependent Response Matrices A.2 Law of Synthesis A.3 Periods of a Slab A.4 Periods of a Reactor A.5 Rigorous Treatment of a Noncritical Reactor A.6 Approximate Relation between λ and ω A.7 Calculation of R̄(s) and T̄(s)Appendix Β R̄ and Τ̄ Using Two-Group Diffusion Approximation B.1 The Case k∞ ≥ 1 B.2 The Case 0 < k∞ < 1 B.3 The Case k∞ = 0ReferencesAuthor IndexSubject Index