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TID-25951 1973 Reactor Shielding for Nuclear Engineers - OCR.1973
Prepared for
Division of Reactor Development and Technology U. S. Atomic Energy Commission
Reprinted by the Technical Information Center, Office of Public Affairs, Energy Research and Development Administration
Published by U. S. ATOMIC ENERGY COMMISSION Office of Information Services
IiIfRODUCED BY NATIONAL TECHNICAL INFORMATION SERVICE
u.s. DlfARTME~T Of COMMERCE Sl'RI"Gf HO. VA ?7i61
L?@@~~@c? c!1D=D D@~@ DCfU®
(P@C?
1973
Prepared for
Division of Reactor Development and Technology U. S. Atomic Energy Commission
Reprinted by the Technical Information Center, Office of Public Affairs, Energy Research and Development Administration
Published by U. S. ATOMIC ENERGY COMMISSION Office of Information Services
IiIfRODUCED BY NATIONAL TECHNICAL INFORMATION SERVICE
u.s. DlfARTME~T Of COMMERCE Sl'RI"Gf HO. VA ?7i61
Available as TlD-25951 for from
National Technical Information Service U_ S. Department of Commerce Springfield, Virginia 22161
International Standard Book Number 0-87079-004-8 Library of Congress Catalog Card Number 73-600001' AEC Distribution Category UC-80
Printed in the United States of America
May 1973; latest printing, April 1976
Available as TlD-25951 for from
National Technical Information Service U_ S. Department of Commerce Springfield, Virginia 22161
International Standard Book Number 0-87079-004-8 Library of Congress Catalog Card Number 73-600001' AEC Distribution Category UC-80
Printed in the United States of America
May 1973; latest printing, April 1976
Preface
As the number of nuclear power plants on order continues [0 grow (currently more than thirty per year in the United States alone). the demand for nuclear engineers should also increase, and a new text on reactor shielding is overdue. Shielding technology has matured considerably in the last decade, and shield physics must routinely be translated into shield design. Since the publication in 1959 of Fundamental Aspects of Reactor Shielding, by Herbert Goldstein, new generations of computers have become available to exploit techniques heretofore considered too costly. and new measurement techniques have been devised. The energy and angular distributions of neutrons and gamma rays can be followed. both in theory and in practice, throughout their transport histories. Such powerful rools have brought correspondingly large dividends to the shielding community.
These advances and their underlying fundamentals are recorded in this volume. which is intended as a text for a two-semester course in reactor shielding directed at an advanced undergraduate or graduate level. The reader is assumed to have some familiarity with calculus through partial differential equations and with nuclear physics through particle interaction theory, although pertinent aspects of the latter are reviewed in Chap. 3. The material is arranged to cover fundamental transport considerations in the first semester; portions of Chap. 4 could be reserved for the second semester. The second semester could then consist of special copies, such as Monte Carlo techniques, albedos. ducts. shield-analysis projects, seminars on experime ntal shielding, and shield design. Instructors will doubtless follow plans of their own choosing. Chapters 2 through 6 have problems appended. with solutions given at the back of the book. Metric units have been used exclusively. Citations of classified literature have been avoided, and technical reports have been referenced only whe.re no journal articles could be given.
Although tided Reactor Shielding. this text should be applicable in related areas where neutron and gamma-ray attenuation are important, as in nuclear
Preceding page blank iii
Preface
As the number of nuclear power plants on order continues [0 grow (currently more than thirty per year in the United States alone). the demand for nuclear engineers should also increase, and a new text on reactor shielding is overdue. Shielding technology has matured considerably in the last decade, and shield physics must routinely be translated into shield design. Since the publication in 1959 of Fundamental Aspects of Reactor Shielding, by Herbert Goldstein, new generations of computers have become available to exploit techniques heretofore considered too costly. and new measurement techniques have been devised. The energy and angular distributions of neutrons and gamma rays can be followed. both in theory and in practice, throughout their transport histories. Such powerful rools have brought correspondingly large dividends to the shielding community.
These advances and their underlying fundamentals are recorded in this volume. which is intended as a text for a two-semester course in reactor shielding directed at an advanced undergraduate or graduate level. The reader is assumed to have some familiarity with calculus through partial differential equations and with nuclear physics through particle interaction theory, although pertinent aspects of the latter are reviewed in Chap. 3. The material is arranged to cover fundamental transport considerations in the first semester; portions of Chap. 4 could be reserved for the second semester. The second semester could then consist of special copies, such as Monte Carlo techniques, albedos. ducts. shield-analysis projects, seminars on experime ntal shielding, and shield design. Instructors will doubtless follow plans of their own choosing. Chapters 2 through 6 have problems appended. with solutions given at the back of the book. Metric units have been used exclusively. Citations of classified literature have been avoided, and technical reports have been referenced only whe.re no journal articles could be given.
Although tided Reactor Shielding. this text should be applicable in related areas where neutron and gamma-ray attenuation are important, as in nuclear
Preceding page blank iii
weapons shielding and in isotope source applications. The study of space radiation and high-energy-accelerator shielding, although closely related to the present subject, has been considered outside the scope of this book.
Dr. Samuel Glasstone originally conceived the idea for this text; he concluded that the book was needed and originally proposed to prepare it. In the preliminary planning of the project. the U. S. Atomic Energy Commission asked me to collaborate with Dr. Glasstone. Notwithstanding many plans and discussions for this collaboration, Dr. Glasstone had to relinquish his role in order to carry out a number of other projects. It is a pleasure to acknowledge his efforts in the planning of this book and his useful critiques of early drafts. I sincerely regret' that our proposed association could not be continued.
For their assistance in the preparation of this manuscript, I am greatly indebted to many people in a number of ways. First. no book on shielding could be readied for publication at this time without acknowledgment of the pervasive influence of one man, the late E. P. Blizard. Not the least of his many contributions to the development of the technology was his encouragement of the efforts of others. including my own effort in preparing this manuscript.
The many services and suggestions provided by the staff of the Radiation Shielding Information Center, Oak Ridge National Laboratory. were extremely helpful, particularly in scanning the current literature. It is a distinct pleasure to acknowledge many useful discussions with others at ORNL: Lorraine Abbott, Clyde Claiborne, Charles Clifford. Paul Stevens. and Dave Trubey, each of whom supplied references and data in addition to
contributions cited elsewhere. My colleagues Mike Wells and Bob French have also contributed in this way and in their forbearance.
lowe thanks for reviews and comments on various portions of the manuscript to Arthur Chilton and his students at the University of Illinois. Don Dudziak of Los Alamos Scientific Laboratory, Charles Eisenhauer of National Bureau of Standards, Cliff Horton - of Rolls Royce, Ltd .. Richard Faw of Kansas State University, Norman Francis. David Mesh, and their associates of General Electric Knolls Atomic Power Laboratory. Gene Hungerford of Purdue University, John Lamarsh of New York Uni versity, Fred Maienschein of Oak Ridge National Laboratory. Ed Profio of University of California at Santa Barbara, and Leigh Secrest of Texas Christian University. I am particularly indebted to Lew Spencer of National Bureau of Standards for his detailed review of the complete manuscript and
lV PREFACE
weapons shielding and in isotope source applications. The study of space radiation and high-energy-accelerator shielding, although closely related to the present subject, has been considered outside the scope of this book.
Dr. Samuel Glasstone originally conceived the idea for this text; he concluded that the book was needed and originally proposed to prepare it. In the preliminary planning of the project. the U. S. Atomic Energy Commission asked me to collaborate with Dr. Glasstone. Notwithstanding many plans and discussions for this collaboration, Dr. Glasstone had to relinquish his role in order to carry out a number of other projects. It is a pleasure to acknowledge his efforts in the planning of this book and his useful critiques of early drafts. I sincerely regret' that our proposed association could not be continued.
For their assistance in the preparation of this manuscript, I am greatly indebted to many people in a number of ways. First. no book on shielding could be readied for publication at this time without acknowledgment of the pervasive influence of one man, the late E. P. Blizard. Not the least of his many contributions to the development of the technology was his encouragement of the efforts of others. including my own effort in preparing this manuscript.
The many services and suggestions provided by the staff of the Radiation Shielding Information Center, Oak Ridge National Laboratory. were extremely helpful, particularly in scanning the current literature. It is a distinct pleasure to acknowledge many useful discussions with others at ORNL: Lorraine Abbott, Clyde Claiborne, Charles Clifford. Paul Stevens. and Dave Trubey, each of whom supplied references and data in addition to
contributions cited elsewhere. My colleagues Mike Wells and Bob French have also contributed in this way and in their forbearance.
lowe thanks for reviews and comments on various portions of the manuscript to Arthur Chilton and his students at the University of Illinois. Don Dudziak of Los Alamos Scientific Laboratory, Charles Eisenhauer of National Bureau of Standards, Cliff Horton - of Rolls Royce, Ltd .. Richard Faw of Kansas State University, Norman Francis. David Mesh, and their associates of General Electric Knolls Atomic Power Laboratory. Gene Hungerford of Purdue University, John Lamarsh of New York Uni versity, Fred Maienschein of Oak Ridge National Laboratory. Ed Profio of University of California at Santa Barbara, and Leigh Secrest of Texas Christian University. I am particularly indebted to Lew Spencer of National Bureau of Standards for his detailed review of the complete manuscript and
PREFACE v
for his many useful suggestions. Most of these reviewers provided recommen dations based on teaching experience in shielding.
The guidance and counsel of J oh n Inglima during the planning stages and of Robert Pigeon during the manuscript drafting, both of th~ u. S. Atomic Energy Commission, is gratefully acknowledged. For technical editing I am grateful to Jean Smith and Marian Fox, also of the U. S. Atomic Energy Commission, and, for typing a difficult manuscript, to Monsita Quave of Radiation Research Associates. Inc. I am especially grateful to Ceil Schaeffer for relieving me of many burdensome proofing tasks and. most of all, for her understanding and encouragement.
N. M. Schaeffer
PREFACE v
for his many useful suggestions. Most of these reviewers provided recommen dations based on teaching experience in shielding.
The guidance and counsel of J oh n Inglima during the planning stages and of Robert Pigeon during the manuscript drafting, both of th~ u. S. Atomic Energy Commission, is gratefully acknowledged. For technical editing I am grateful to Jean Smith and Marian Fox, also of the U. S. Atomic Energy Commission, and, for typing a difficult manuscript, to Monsita Quave of Radiation Research Associates. Inc. I am especially grateful to Ceil Schaeffer for relieving me of many burdensome proofing tasks and. most of all, for her understanding and encouragement.
N. M. Schaeffer
H. C. daiborne Oak Ridge National Laboratory, Oak Ridge, Tennessee
S. T. Friedman Consultant, Los Angeles, California
c. W. Garrett Radiation Research Associates, Inc., Fort Worth, Texas (Now with National Academy of Engineering, Washington, D. C.)
L. G. Mooney Radiation Research Associates, Inc., Fort Worth, Texas
N. M. Schaeffer Radiation Research Associates, Inc., Fort Worth, Texas
W. E. Selph Radiation Research Associates, Inc., Fort Worth, Texas (Now with Intelcom Radiation Technology, San Diego. California)
P. N. Stevens Oak Ridge National Laboratory, Oak Ridge, Tennessee, and University of Tennessee, Knoxville, Tennessee
D. K. Trubey Oak Ridge National Laboratory, Oak Ridge, Tennessee
vi
Contributors
H. C. daiborne Oak Ridge National Laboratory, Oak Ridge, Tennessee
S. T. Friedman Consultant, Los Angeles, California
c. W. Garrett Radiation Research Associates, Inc., Fort Worth, Texas (Now with National Academy of Engineering, Washington, D. C.)
L. G. Mooney Radiation Research Associates, Inc., Fort Worth, Texas
N. M. Schaeffer Radiation Research Associates, Inc., Fort Worth, Texas
W. E. Selph Radiation Research Associates, Inc., Fort Worth, Texas (Now with Intelcom Radiation Technology, San Diego. California)
P. N. Stevens Oak Ridge National Laboratory, Oak Ridge, Tennessee, and University of Tennessee, Knoxville, Tennessee
D. K. Trubey Oak Ridge National Laboratory, Oak Ridge, Tennessee
vi
PREFACE ...
CONTRIBUTORS
2.1.1 Gamma-Ray Sources . . . . 2.1.2 Neutron Sources .....
2.2 Basic Mathematical and Physical Concepts 2.2.1 Differential Distributions . . . 2.2.2 Average and Most-Probable Values 2.2.3 Solid Angle . . . . . . . 2.2.4 Measures of Radiation Intensity
2.3 Spatial and Directional Characteristics 2.3.1 Spatial Distributions 2.3.2 DiIectional Distributions . . . .
2.4 Energy Distributions ..... . 2.4.1 Energy Distributions of Gamma-Ray Sources 2.4.2 Neutron Spectra from Fission 2.4.3 Effect of Medium on Spectra
References
Exercises
3.1 Cross Sections . . . . . . 3.1.1 Microscopic Cross Section 3.1.2 Macroscopic Cross Section 3.1.3 Radiation Reaction Rates
3.2 Radiation Interactions . 3.2.1 Photon Interactions 3.2.2 Neutron Reactions
3.3 Responses to Radiation 3.3.1 Absorbed Dose 3.3.2 First-Collision Dose and Kerma 3.3.3 Exposure . . . . . . 3.3.4 RBE Dose; Dose Equivalent
vii
Contents
. iii
. vi
11
39 39 42
103 105
2.1.1 Gamma-Ray Sources . . . . 2.1.2 Neutron Sources .....
2.2 Basic Mathematical and Physical Concepts 2.2.1 Differential Distributions . . . 2.2.2 Average and Most-Probable Values 2.2.3 Solid Angle . . . . . . . 2.2.4 Measures of Radiation Intensity
2.3 Spatial and Directional Characteristics 2.3.1 Spatial Distributions 2.3.2 DiIectional Distributions . . . .
2.4 Energy Distributions ..... . 2.4.1 Energy Distributions of Gamma-Ray Sources 2.4.2 Neutron Spectra from Fission 2.4.3 Effect of Medium on Spectra
References
Exercises
3.1 Cross Sections . . . . . . 3.1.1 Microscopic Cross Section 3.1.2 Macroscopic Cross Section 3.1.3 Radiation Reaction Rates
3.2 Radiation Interactions . 3.2.1 Photon Interactions 3.2.2 Neutron Reactions
3.3 Responses to Radiation 3.3.1 Absorbed Dose 3.3.2 First-Collision Dose and Kerma 3.3.3 Exposure . . . . . . 3.3.4 RBE Dose; Dose Equivalent
vii
Contents
. iii
. vi
11
39 39 42
103 105
VlU CONTENTS
3.3.5 Maximum Absorbed Dose; Maximum Dose Equivalent 3.3.6 Multicollision Dose
References
Exercises .
The Boltzmann Transport Equation Spherical Harmonics Method Discrete-Ordinates Sn Method . . 4.4.1 Transport Equation and Phase·Space Geometry 4.4.2 Derivation of Finite-Difference Equation 4.4.3 Numerical Solution of the Discrete·Ordinates Equation 4.4.4 Advantages and Disadvantages
4.5 4.6 4.7 4.8
Moments Method ..... Application of Diffusion Theory Invariant Imbedding Method Kernel Technique 4.8.1 Gamma-Ray Calculations 4.8.2 Neutron Techniques
4.9 Combination Removal-Diffusion Methods 4.9.1 The Spinney Method . . . . 4.9.2 Variations of the Spinney Method 4.9.3 Differences in Current Methods
References
Exercises
.'
5 MONTE CARLO METHODS FOR RADIATION TRANSPORT 5.1 Sampling from Probability Distribution Functions 5.2 The Evaluation of Integrals 5.3 Source Parameters
5.3.1 Selection from an Energy Distribution 5.3.2 Selection of Spatial Point of the Source Particle 5.3.3 Selection of Initial Direction of Source Particle 5.3.4 Source-Biasing Parameters
5.4 Path Length . . . . . . . . . 5.5 Collision Parameters .... 5.6 Particle Parameters After Collision
5.6.1 Neutron Elastic Scattering 5.6.2 Neutron I nelastic Scattering 5.6.3 Compton Scattering 5.6.4 Particle Absorptions 5.6.5 Calculation of Emergent·Direction Cosines
5.7 Particle Scoring ....... . 5.8 Statistical Variance . . . . . . . 5.9 Demonstration Monte Carlo Program 5.10 Programming Suggestions
108 112
160 163
201
204
207
209
216
225
234
247
251
254
3.3.5 Maximum Absorbed Dose; Maximum Dose Equivalent 3.3.6 Multicollision Dose
References
Exercises .
The Boltzmann Transport Equation Spherical Harmonics Method Discrete-Ordinates Sn Method . . 4.4.1 Transport Equation and Phase·Space Geometry 4.4.2 Derivation of Finite-Difference Equation 4.4.3 Numerical Solution of the Discrete·Ordinates Equation 4.4.4 Advantages and Disadvantages
4.5 4.6 4.7 4.8
Moments Method ..... Application of Diffusion Theory Invariant Imbedding Method Kernel Technique 4.8.1 Gamma-Ray Calculations 4.8.2 Neutron Techniques
4.9 Combination Removal-Diffusion Methods 4.9.1 The Spinney Method . . . . 4.9.2 Variations of the Spinney Method 4.9.3 Differences in Current Methods
References
Exercises
.'
5 MONTE CARLO METHODS FOR RADIATION TRANSPORT 5.1 Sampling from Probability Distribution Functions 5.2 The Evaluation of Integrals 5.3 Source Parameters
5.3.1 Selection from an Energy Distribution 5.3.2 Selection of Spatial Point of the Source Particle 5.3.3 Selection of Initial Direction of Source Particle 5.3.4 Source-Biasing Parameters
5.4 Path Length . . . . . . . . . 5.5 Collision Parameters .... 5.6 Particle Parameters After Collision
5.6.1 Neutron Elastic Scattering 5.6.2 Neutron I nelastic Scattering 5.6.3 Compton Scattering 5.6.4 Particle Absorptions 5.6.5 Calculation of Emergent·Direction Cosines
5.7 Particle Scoring ....... . 5.8 Statistical Variance . . . . . . . 5.9 Demonstration Monte Carlo Program 5.10 Programming Suggestions
108 112
160 163
201
204
207
209
216
225
234
247
251
254
CONTENTS
References
Exercises
6 SHIELD AITENUATION CALCULATIONS 6.1 Analysis of the Source . . . . 6.2 Direct Solutions . . . . . . 6.3 Application of Parametric Data
6.3.1 Moments-Method Differential Energy Spectra 6.3.2 Monte Carlo 6.3.3 Measured Data 6.3.4 Fitted·Parameter Data
6.4 Simplified Solutions 6.4.1 Applications of Gamma-Ray Buildup Factors 6.4.2 Applications of Neutron-Removal-Theory Kernels 6.4.3 Other Point-Kernel Applications .•.•.. 6.4.4 Methods for Estimating Low-Energy Neutron-flux Density
6.5 Application of Kernel Technique to Calculations of Secondary Gamma-Ray Dose 6.5.1 Calculation for Slab Shield 6.5.2 Calculation for Semi·lnfinite Shield
References
Exercises
7 ALBEDOS, DUCTS, AND VOIDS 7.1 Introduction to Albedos 7.2 Definitions . . . . .
7.2.1 Differential-Dose Albedos 7.2.2 Total-Dose Albedos 7.2.3 Other Albedos
7.3 Neutron Albedos 7.3.1 Fast·Neutron Albedos 7.3.2 I ntermediate·Neutron Albedos 7.3.3 Thermal-Neutron Albedos. .
7.4 Gamma-Ray Albedos .... 7.5 Secondary-Gamma-Ray Albedos 7.6 Applications of Albedos 7.7 Ducts " . . . . . 7.8 Line-of-Sight Component
7.8.1 Rectangular Ducts 7.8.2 Rectangular Slots 7.8.3 Cylindrical Ducts 7.8.4 Cylindrical Annulus
7.9 Wall-Penetration Component 7.9.1 Application to Cylindrical Ducts 7.9.2 Application to Partially Penetrating Cylindrical Ducts 7.9.3 Comparison with Experiment
7.10 Wall-Scattered Component 7.10.1 Analog Monte Carlo Calculations
lX
257
258
261
261
263
264 265 270 274 277 283 284 286 288 298
301 304 308
375 376
CONTENTS
References
Exercises
6 SHIELD AITENUATION CALCULATIONS 6.1 Analysis of the Source . . . . 6.2 Direct Solutions . . . . . . 6.3 Application of Parametric Data
6.3.1 Moments-Method Differential Energy Spectra 6.3.2 Monte Carlo 6.3.3 Measured Data 6.3.4 Fitted·Parameter Data
6.4 Simplified Solutions 6.4.1 Applications of Gamma-Ray Buildup Factors 6.4.2 Applications of Neutron-Removal-Theory Kernels 6.4.3 Other Point-Kernel Applications .•.•.. 6.4.4 Methods for Estimating Low-Energy Neutron-flux Density
6.5 Application of Kernel Technique to Calculations of Secondary Gamma-Ray Dose 6.5.1 Calculation for Slab Shield 6.5.2 Calculation for Semi·lnfinite Shield
References
Exercises
7 ALBEDOS, DUCTS, AND VOIDS 7.1 Introduction to Albedos 7.2 Definitions . . . . .
7.2.1 Differential-Dose Albedos 7.2.2 Total-Dose Albedos 7.2.3 Other Albedos
7.3 Neutron Albedos 7.3.1 Fast·Neutron Albedos 7.3.2 I ntermediate·Neutron Albedos 7.3.3 Thermal-Neutron Albedos. .
7.4 Gamma-Ray Albedos .... 7.5 Secondary-Gamma-Ray Albedos 7.6 Applications of Albedos 7.7 Ducts " . . . . . 7.8 Line-of-Sight Component
7.8.1 Rectangular Ducts 7.8.2 Rectangular Slots 7.8.3 Cylindrical Ducts 7.8.4 Cylindrical Annulus
7.9 Wall-Penetration Component 7.9.1 Application to Cylindrical Ducts 7.9.2 Application to Partially Penetrating Cylindrical Ducts 7.9.3 Comparison with Experiment
7.10 Wall-Scattered Component 7.10.1 Analog Monte Carlo Calculations
lX
257
258
261
261
263
264 265 270 274…
Prepared for
Division of Reactor Development and Technology U. S. Atomic Energy Commission
Reprinted by the Technical Information Center, Office of Public Affairs, Energy Research and Development Administration
Published by U. S. ATOMIC ENERGY COMMISSION Office of Information Services
IiIfRODUCED BY NATIONAL TECHNICAL INFORMATION SERVICE
u.s. DlfARTME~T Of COMMERCE Sl'RI"Gf HO. VA ?7i61
L?@@~~@c? c!1D=D D@~@ DCfU®
(P@C?
1973
Prepared for
Division of Reactor Development and Technology U. S. Atomic Energy Commission
Reprinted by the Technical Information Center, Office of Public Affairs, Energy Research and Development Administration
Published by U. S. ATOMIC ENERGY COMMISSION Office of Information Services
IiIfRODUCED BY NATIONAL TECHNICAL INFORMATION SERVICE
u.s. DlfARTME~T Of COMMERCE Sl'RI"Gf HO. VA ?7i61
Available as TlD-25951 for from
National Technical Information Service U_ S. Department of Commerce Springfield, Virginia 22161
International Standard Book Number 0-87079-004-8 Library of Congress Catalog Card Number 73-600001' AEC Distribution Category UC-80
Printed in the United States of America
May 1973; latest printing, April 1976
Available as TlD-25951 for from
National Technical Information Service U_ S. Department of Commerce Springfield, Virginia 22161
International Standard Book Number 0-87079-004-8 Library of Congress Catalog Card Number 73-600001' AEC Distribution Category UC-80
Printed in the United States of America
May 1973; latest printing, April 1976
Preface
As the number of nuclear power plants on order continues [0 grow (currently more than thirty per year in the United States alone). the demand for nuclear engineers should also increase, and a new text on reactor shielding is overdue. Shielding technology has matured considerably in the last decade, and shield physics must routinely be translated into shield design. Since the publication in 1959 of Fundamental Aspects of Reactor Shielding, by Herbert Goldstein, new generations of computers have become available to exploit techniques heretofore considered too costly. and new measurement techniques have been devised. The energy and angular distributions of neutrons and gamma rays can be followed. both in theory and in practice, throughout their transport histories. Such powerful rools have brought correspondingly large dividends to the shielding community.
These advances and their underlying fundamentals are recorded in this volume. which is intended as a text for a two-semester course in reactor shielding directed at an advanced undergraduate or graduate level. The reader is assumed to have some familiarity with calculus through partial differential equations and with nuclear physics through particle interaction theory, although pertinent aspects of the latter are reviewed in Chap. 3. The material is arranged to cover fundamental transport considerations in the first semester; portions of Chap. 4 could be reserved for the second semester. The second semester could then consist of special copies, such as Monte Carlo techniques, albedos. ducts. shield-analysis projects, seminars on experime ntal shielding, and shield design. Instructors will doubtless follow plans of their own choosing. Chapters 2 through 6 have problems appended. with solutions given at the back of the book. Metric units have been used exclusively. Citations of classified literature have been avoided, and technical reports have been referenced only whe.re no journal articles could be given.
Although tided Reactor Shielding. this text should be applicable in related areas where neutron and gamma-ray attenuation are important, as in nuclear
Preceding page blank iii
Preface
As the number of nuclear power plants on order continues [0 grow (currently more than thirty per year in the United States alone). the demand for nuclear engineers should also increase, and a new text on reactor shielding is overdue. Shielding technology has matured considerably in the last decade, and shield physics must routinely be translated into shield design. Since the publication in 1959 of Fundamental Aspects of Reactor Shielding, by Herbert Goldstein, new generations of computers have become available to exploit techniques heretofore considered too costly. and new measurement techniques have been devised. The energy and angular distributions of neutrons and gamma rays can be followed. both in theory and in practice, throughout their transport histories. Such powerful rools have brought correspondingly large dividends to the shielding community.
These advances and their underlying fundamentals are recorded in this volume. which is intended as a text for a two-semester course in reactor shielding directed at an advanced undergraduate or graduate level. The reader is assumed to have some familiarity with calculus through partial differential equations and with nuclear physics through particle interaction theory, although pertinent aspects of the latter are reviewed in Chap. 3. The material is arranged to cover fundamental transport considerations in the first semester; portions of Chap. 4 could be reserved for the second semester. The second semester could then consist of special copies, such as Monte Carlo techniques, albedos. ducts. shield-analysis projects, seminars on experime ntal shielding, and shield design. Instructors will doubtless follow plans of their own choosing. Chapters 2 through 6 have problems appended. with solutions given at the back of the book. Metric units have been used exclusively. Citations of classified literature have been avoided, and technical reports have been referenced only whe.re no journal articles could be given.
Although tided Reactor Shielding. this text should be applicable in related areas where neutron and gamma-ray attenuation are important, as in nuclear
Preceding page blank iii
weapons shielding and in isotope source applications. The study of space radiation and high-energy-accelerator shielding, although closely related to the present subject, has been considered outside the scope of this book.
Dr. Samuel Glasstone originally conceived the idea for this text; he concluded that the book was needed and originally proposed to prepare it. In the preliminary planning of the project. the U. S. Atomic Energy Commission asked me to collaborate with Dr. Glasstone. Notwithstanding many plans and discussions for this collaboration, Dr. Glasstone had to relinquish his role in order to carry out a number of other projects. It is a pleasure to acknowledge his efforts in the planning of this book and his useful critiques of early drafts. I sincerely regret' that our proposed association could not be continued.
For their assistance in the preparation of this manuscript, I am greatly indebted to many people in a number of ways. First. no book on shielding could be readied for publication at this time without acknowledgment of the pervasive influence of one man, the late E. P. Blizard. Not the least of his many contributions to the development of the technology was his encouragement of the efforts of others. including my own effort in preparing this manuscript.
The many services and suggestions provided by the staff of the Radiation Shielding Information Center, Oak Ridge National Laboratory. were extremely helpful, particularly in scanning the current literature. It is a distinct pleasure to acknowledge many useful discussions with others at ORNL: Lorraine Abbott, Clyde Claiborne, Charles Clifford. Paul Stevens. and Dave Trubey, each of whom supplied references and data in addition to
contributions cited elsewhere. My colleagues Mike Wells and Bob French have also contributed in this way and in their forbearance.
lowe thanks for reviews and comments on various portions of the manuscript to Arthur Chilton and his students at the University of Illinois. Don Dudziak of Los Alamos Scientific Laboratory, Charles Eisenhauer of National Bureau of Standards, Cliff Horton - of Rolls Royce, Ltd .. Richard Faw of Kansas State University, Norman Francis. David Mesh, and their associates of General Electric Knolls Atomic Power Laboratory. Gene Hungerford of Purdue University, John Lamarsh of New York Uni versity, Fred Maienschein of Oak Ridge National Laboratory. Ed Profio of University of California at Santa Barbara, and Leigh Secrest of Texas Christian University. I am particularly indebted to Lew Spencer of National Bureau of Standards for his detailed review of the complete manuscript and
lV PREFACE
weapons shielding and in isotope source applications. The study of space radiation and high-energy-accelerator shielding, although closely related to the present subject, has been considered outside the scope of this book.
Dr. Samuel Glasstone originally conceived the idea for this text; he concluded that the book was needed and originally proposed to prepare it. In the preliminary planning of the project. the U. S. Atomic Energy Commission asked me to collaborate with Dr. Glasstone. Notwithstanding many plans and discussions for this collaboration, Dr. Glasstone had to relinquish his role in order to carry out a number of other projects. It is a pleasure to acknowledge his efforts in the planning of this book and his useful critiques of early drafts. I sincerely regret' that our proposed association could not be continued.
For their assistance in the preparation of this manuscript, I am greatly indebted to many people in a number of ways. First. no book on shielding could be readied for publication at this time without acknowledgment of the pervasive influence of one man, the late E. P. Blizard. Not the least of his many contributions to the development of the technology was his encouragement of the efforts of others. including my own effort in preparing this manuscript.
The many services and suggestions provided by the staff of the Radiation Shielding Information Center, Oak Ridge National Laboratory. were extremely helpful, particularly in scanning the current literature. It is a distinct pleasure to acknowledge many useful discussions with others at ORNL: Lorraine Abbott, Clyde Claiborne, Charles Clifford. Paul Stevens. and Dave Trubey, each of whom supplied references and data in addition to
contributions cited elsewhere. My colleagues Mike Wells and Bob French have also contributed in this way and in their forbearance.
lowe thanks for reviews and comments on various portions of the manuscript to Arthur Chilton and his students at the University of Illinois. Don Dudziak of Los Alamos Scientific Laboratory, Charles Eisenhauer of National Bureau of Standards, Cliff Horton - of Rolls Royce, Ltd .. Richard Faw of Kansas State University, Norman Francis. David Mesh, and their associates of General Electric Knolls Atomic Power Laboratory. Gene Hungerford of Purdue University, John Lamarsh of New York Uni versity, Fred Maienschein of Oak Ridge National Laboratory. Ed Profio of University of California at Santa Barbara, and Leigh Secrest of Texas Christian University. I am particularly indebted to Lew Spencer of National Bureau of Standards for his detailed review of the complete manuscript and
PREFACE v
for his many useful suggestions. Most of these reviewers provided recommen dations based on teaching experience in shielding.
The guidance and counsel of J oh n Inglima during the planning stages and of Robert Pigeon during the manuscript drafting, both of th~ u. S. Atomic Energy Commission, is gratefully acknowledged. For technical editing I am grateful to Jean Smith and Marian Fox, also of the U. S. Atomic Energy Commission, and, for typing a difficult manuscript, to Monsita Quave of Radiation Research Associates. Inc. I am especially grateful to Ceil Schaeffer for relieving me of many burdensome proofing tasks and. most of all, for her understanding and encouragement.
N. M. Schaeffer
PREFACE v
for his many useful suggestions. Most of these reviewers provided recommen dations based on teaching experience in shielding.
The guidance and counsel of J oh n Inglima during the planning stages and of Robert Pigeon during the manuscript drafting, both of th~ u. S. Atomic Energy Commission, is gratefully acknowledged. For technical editing I am grateful to Jean Smith and Marian Fox, also of the U. S. Atomic Energy Commission, and, for typing a difficult manuscript, to Monsita Quave of Radiation Research Associates. Inc. I am especially grateful to Ceil Schaeffer for relieving me of many burdensome proofing tasks and. most of all, for her understanding and encouragement.
N. M. Schaeffer
H. C. daiborne Oak Ridge National Laboratory, Oak Ridge, Tennessee
S. T. Friedman Consultant, Los Angeles, California
c. W. Garrett Radiation Research Associates, Inc., Fort Worth, Texas (Now with National Academy of Engineering, Washington, D. C.)
L. G. Mooney Radiation Research Associates, Inc., Fort Worth, Texas
N. M. Schaeffer Radiation Research Associates, Inc., Fort Worth, Texas
W. E. Selph Radiation Research Associates, Inc., Fort Worth, Texas (Now with Intelcom Radiation Technology, San Diego. California)
P. N. Stevens Oak Ridge National Laboratory, Oak Ridge, Tennessee, and University of Tennessee, Knoxville, Tennessee
D. K. Trubey Oak Ridge National Laboratory, Oak Ridge, Tennessee
vi
Contributors
H. C. daiborne Oak Ridge National Laboratory, Oak Ridge, Tennessee
S. T. Friedman Consultant, Los Angeles, California
c. W. Garrett Radiation Research Associates, Inc., Fort Worth, Texas (Now with National Academy of Engineering, Washington, D. C.)
L. G. Mooney Radiation Research Associates, Inc., Fort Worth, Texas
N. M. Schaeffer Radiation Research Associates, Inc., Fort Worth, Texas
W. E. Selph Radiation Research Associates, Inc., Fort Worth, Texas (Now with Intelcom Radiation Technology, San Diego. California)
P. N. Stevens Oak Ridge National Laboratory, Oak Ridge, Tennessee, and University of Tennessee, Knoxville, Tennessee
D. K. Trubey Oak Ridge National Laboratory, Oak Ridge, Tennessee
vi
PREFACE ...
CONTRIBUTORS
2.1.1 Gamma-Ray Sources . . . . 2.1.2 Neutron Sources .....
2.2 Basic Mathematical and Physical Concepts 2.2.1 Differential Distributions . . . 2.2.2 Average and Most-Probable Values 2.2.3 Solid Angle . . . . . . . 2.2.4 Measures of Radiation Intensity
2.3 Spatial and Directional Characteristics 2.3.1 Spatial Distributions 2.3.2 DiIectional Distributions . . . .
2.4 Energy Distributions ..... . 2.4.1 Energy Distributions of Gamma-Ray Sources 2.4.2 Neutron Spectra from Fission 2.4.3 Effect of Medium on Spectra
References
Exercises
3.1 Cross Sections . . . . . . 3.1.1 Microscopic Cross Section 3.1.2 Macroscopic Cross Section 3.1.3 Radiation Reaction Rates
3.2 Radiation Interactions . 3.2.1 Photon Interactions 3.2.2 Neutron Reactions
3.3 Responses to Radiation 3.3.1 Absorbed Dose 3.3.2 First-Collision Dose and Kerma 3.3.3 Exposure . . . . . . 3.3.4 RBE Dose; Dose Equivalent
vii
Contents
. iii
. vi
11
39 39 42
103 105
2.1.1 Gamma-Ray Sources . . . . 2.1.2 Neutron Sources .....
2.2 Basic Mathematical and Physical Concepts 2.2.1 Differential Distributions . . . 2.2.2 Average and Most-Probable Values 2.2.3 Solid Angle . . . . . . . 2.2.4 Measures of Radiation Intensity
2.3 Spatial and Directional Characteristics 2.3.1 Spatial Distributions 2.3.2 DiIectional Distributions . . . .
2.4 Energy Distributions ..... . 2.4.1 Energy Distributions of Gamma-Ray Sources 2.4.2 Neutron Spectra from Fission 2.4.3 Effect of Medium on Spectra
References
Exercises
3.1 Cross Sections . . . . . . 3.1.1 Microscopic Cross Section 3.1.2 Macroscopic Cross Section 3.1.3 Radiation Reaction Rates
3.2 Radiation Interactions . 3.2.1 Photon Interactions 3.2.2 Neutron Reactions
3.3 Responses to Radiation 3.3.1 Absorbed Dose 3.3.2 First-Collision Dose and Kerma 3.3.3 Exposure . . . . . . 3.3.4 RBE Dose; Dose Equivalent
vii
Contents
. iii
. vi
11
39 39 42
103 105
VlU CONTENTS
3.3.5 Maximum Absorbed Dose; Maximum Dose Equivalent 3.3.6 Multicollision Dose
References
Exercises .
The Boltzmann Transport Equation Spherical Harmonics Method Discrete-Ordinates Sn Method . . 4.4.1 Transport Equation and Phase·Space Geometry 4.4.2 Derivation of Finite-Difference Equation 4.4.3 Numerical Solution of the Discrete·Ordinates Equation 4.4.4 Advantages and Disadvantages
4.5 4.6 4.7 4.8
Moments Method ..... Application of Diffusion Theory Invariant Imbedding Method Kernel Technique 4.8.1 Gamma-Ray Calculations 4.8.2 Neutron Techniques
4.9 Combination Removal-Diffusion Methods 4.9.1 The Spinney Method . . . . 4.9.2 Variations of the Spinney Method 4.9.3 Differences in Current Methods
References
Exercises
.'
5 MONTE CARLO METHODS FOR RADIATION TRANSPORT 5.1 Sampling from Probability Distribution Functions 5.2 The Evaluation of Integrals 5.3 Source Parameters
5.3.1 Selection from an Energy Distribution 5.3.2 Selection of Spatial Point of the Source Particle 5.3.3 Selection of Initial Direction of Source Particle 5.3.4 Source-Biasing Parameters
5.4 Path Length . . . . . . . . . 5.5 Collision Parameters .... 5.6 Particle Parameters After Collision
5.6.1 Neutron Elastic Scattering 5.6.2 Neutron I nelastic Scattering 5.6.3 Compton Scattering 5.6.4 Particle Absorptions 5.6.5 Calculation of Emergent·Direction Cosines
5.7 Particle Scoring ....... . 5.8 Statistical Variance . . . . . . . 5.9 Demonstration Monte Carlo Program 5.10 Programming Suggestions
108 112
160 163
201
204
207
209
216
225
234
247
251
254
3.3.5 Maximum Absorbed Dose; Maximum Dose Equivalent 3.3.6 Multicollision Dose
References
Exercises .
The Boltzmann Transport Equation Spherical Harmonics Method Discrete-Ordinates Sn Method . . 4.4.1 Transport Equation and Phase·Space Geometry 4.4.2 Derivation of Finite-Difference Equation 4.4.3 Numerical Solution of the Discrete·Ordinates Equation 4.4.4 Advantages and Disadvantages
4.5 4.6 4.7 4.8
Moments Method ..... Application of Diffusion Theory Invariant Imbedding Method Kernel Technique 4.8.1 Gamma-Ray Calculations 4.8.2 Neutron Techniques
4.9 Combination Removal-Diffusion Methods 4.9.1 The Spinney Method . . . . 4.9.2 Variations of the Spinney Method 4.9.3 Differences in Current Methods
References
Exercises
.'
5 MONTE CARLO METHODS FOR RADIATION TRANSPORT 5.1 Sampling from Probability Distribution Functions 5.2 The Evaluation of Integrals 5.3 Source Parameters
5.3.1 Selection from an Energy Distribution 5.3.2 Selection of Spatial Point of the Source Particle 5.3.3 Selection of Initial Direction of Source Particle 5.3.4 Source-Biasing Parameters
5.4 Path Length . . . . . . . . . 5.5 Collision Parameters .... 5.6 Particle Parameters After Collision
5.6.1 Neutron Elastic Scattering 5.6.2 Neutron I nelastic Scattering 5.6.3 Compton Scattering 5.6.4 Particle Absorptions 5.6.5 Calculation of Emergent·Direction Cosines
5.7 Particle Scoring ....... . 5.8 Statistical Variance . . . . . . . 5.9 Demonstration Monte Carlo Program 5.10 Programming Suggestions
108 112
160 163
201
204
207
209
216
225
234
247
251
254
CONTENTS
References
Exercises
6 SHIELD AITENUATION CALCULATIONS 6.1 Analysis of the Source . . . . 6.2 Direct Solutions . . . . . . 6.3 Application of Parametric Data
6.3.1 Moments-Method Differential Energy Spectra 6.3.2 Monte Carlo 6.3.3 Measured Data 6.3.4 Fitted·Parameter Data
6.4 Simplified Solutions 6.4.1 Applications of Gamma-Ray Buildup Factors 6.4.2 Applications of Neutron-Removal-Theory Kernels 6.4.3 Other Point-Kernel Applications .•.•.. 6.4.4 Methods for Estimating Low-Energy Neutron-flux Density
6.5 Application of Kernel Technique to Calculations of Secondary Gamma-Ray Dose 6.5.1 Calculation for Slab Shield 6.5.2 Calculation for Semi·lnfinite Shield
References
Exercises
7 ALBEDOS, DUCTS, AND VOIDS 7.1 Introduction to Albedos 7.2 Definitions . . . . .
7.2.1 Differential-Dose Albedos 7.2.2 Total-Dose Albedos 7.2.3 Other Albedos
7.3 Neutron Albedos 7.3.1 Fast·Neutron Albedos 7.3.2 I ntermediate·Neutron Albedos 7.3.3 Thermal-Neutron Albedos. .
7.4 Gamma-Ray Albedos .... 7.5 Secondary-Gamma-Ray Albedos 7.6 Applications of Albedos 7.7 Ducts " . . . . . 7.8 Line-of-Sight Component
7.8.1 Rectangular Ducts 7.8.2 Rectangular Slots 7.8.3 Cylindrical Ducts 7.8.4 Cylindrical Annulus
7.9 Wall-Penetration Component 7.9.1 Application to Cylindrical Ducts 7.9.2 Application to Partially Penetrating Cylindrical Ducts 7.9.3 Comparison with Experiment
7.10 Wall-Scattered Component 7.10.1 Analog Monte Carlo Calculations
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258
261
261
263
264 265 270 274 277 283 284 286 288 298
301 304 308
375 376
CONTENTS
References
Exercises
6 SHIELD AITENUATION CALCULATIONS 6.1 Analysis of the Source . . . . 6.2 Direct Solutions . . . . . . 6.3 Application of Parametric Data
6.3.1 Moments-Method Differential Energy Spectra 6.3.2 Monte Carlo 6.3.3 Measured Data 6.3.4 Fitted·Parameter Data
6.4 Simplified Solutions 6.4.1 Applications of Gamma-Ray Buildup Factors 6.4.2 Applications of Neutron-Removal-Theory Kernels 6.4.3 Other Point-Kernel Applications .•.•.. 6.4.4 Methods for Estimating Low-Energy Neutron-flux Density
6.5 Application of Kernel Technique to Calculations of Secondary Gamma-Ray Dose 6.5.1 Calculation for Slab Shield 6.5.2 Calculation for Semi·lnfinite Shield
References
Exercises
7 ALBEDOS, DUCTS, AND VOIDS 7.1 Introduction to Albedos 7.2 Definitions . . . . .
7.2.1 Differential-Dose Albedos 7.2.2 Total-Dose Albedos 7.2.3 Other Albedos
7.3 Neutron Albedos 7.3.1 Fast·Neutron Albedos 7.3.2 I ntermediate·Neutron Albedos 7.3.3 Thermal-Neutron Albedos. .
7.4 Gamma-Ray Albedos .... 7.5 Secondary-Gamma-Ray Albedos 7.6 Applications of Albedos 7.7 Ducts " . . . . . 7.8 Line-of-Sight Component
7.8.1 Rectangular Ducts 7.8.2 Rectangular Slots 7.8.3 Cylindrical Ducts 7.8.4 Cylindrical Annulus
7.9 Wall-Penetration Component 7.9.1 Application to Cylindrical Ducts 7.9.2 Application to Partially Penetrating Cylindrical Ducts 7.9.3 Comparison with Experiment
7.10 Wall-Scattered Component 7.10.1 Analog Monte Carlo Calculations
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261
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264 265 270 274…