Application of Invariant Embedding to Reactor Physics - 1st Edition - ISBN: 9780126401509, 9781483268347

Application of Invariant Embedding to Reactor Physics

1st Edition

Authors: Akinao Shimizu Katsutada Aoki
Editors: V. L. Parsegian
eBook ISBN: 9781483268347
Imprint: Academic Press
Published Date: 1st January 1972
Page Count: 194
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Application of Invariant Embedding to Reactor Physics describes the application of the method of invariant embedding to radiation shielding and to criticality calculations of atomic reactors. The authors intend to show how this method has been applied to realistic problems, together with the results of applications which will be useful to shielding design. The book is organized into two parts. Part A deals with the reflection and transmission of gamma rays by slabs. The chapters in this section cover topics such as the reflection and transmission problem of gamma rays; formulation of the problem based on the invariant embedding principle; solutions of equations for simplified models; and solving the equations for the reflection and transmission functions based on the realistic cross section for gamma rays. Part B discusses applications to criticality calculations, covering one-dimensional and two-dimensional problems.

Table of Contents


Part 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


Part 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 Calculation

Appendix 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∞ = 0


Author Index

Subject Index


No. of pages:
© Academic Press 1972
Academic Press
eBook ISBN:

About the Author

Akinao Shimizu

Katsutada Aoki

About the Editor

V. L. Parsegian

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