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eactor hysi s

P. F. weifelUnlveralty Profeuor

VirIlnia Po ytechnlc: l IUtuto nd State Unlvenlty

McQ .w HIH ook ompany

New York St. Louis San Franasco QsseJdorf Johannabul lKuala Lumpur London MexIc o Montreal New DeIbI

Panama Rio de Janeiro inppore SydDe TOI OI to

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eactor hysics opyript .C 1973 by McGraw-Hill Inc. All rightsrcscrvcd Printed in the United States of America op u t of this public:ation D 7 be rcprodlad stored in aretricYal system or transmitted in any form or by anymeans electronic mechanical photocoPYina recordina

.. or otherwise without the prior wrincn permission of the. publisher .

Lfbrary COr/ /reR CatalOfl Card Number 72 174628. . 07-073597-2 2 3 4 5 6 7 8 9 7 9 8 7 6 5 4 3 2This book was le t in T mcI New Roman and printediadlloa d by LDa IT I i e .drawinp were done by F. W. Taylor Company. Theeditors were B. 1 . Clark and M. Eo MaflOlies. Joh1A. Sabella supervised production.

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ont nts

Prcfac:e xl

INTRODUCTORY REMARKS

1.1 Basic COncepts of Reactor Physics 11.2 Physical Description of the Chain e ction 10

2 THE NEUTRON DIFFUSION EQUATION 3

2.1 IntrodllCtion and Definitions 132.2 The Neutron Transport Equation 21 3 The _peed Transport Equation 232.4 Anothcc on n of the Balance Relation 242.6 Pick Rule 252.6 Boundary Conditions 282.7 Valid ity of Diffusion Theory 322.8 The Diffusion Equation in Plane Geometry 332.9 The Diffusion Equation in SphericalGeometry 392.10 The Dift usion Equation in CylindricalGcomctry 432 11 Measurement of Diffusion Paramctel l 48

3 ONESPEED REACTOR 63.1 IntrodllCtion : Basic Equation 513 .2 Bare Slab Reactor :3.3 General Remarks on Practical Calculations S63.4 Critical Mall and Critical Size 583.5 Criticality CaJculatiollS in Other GeomctricI 623 6 Physical Mcanina the Criticality Cond ition 673.7 Power Di lt ri bu tion 69

vU

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vln

3 8 Intepal Equation Approach 70. 3.8 Noahomopoooua Rcactora Reftccton 73

4 nMEDEPENDENT PROBLEMS 78

4.1 IntroduetioD 784 Asymptotic Reactor KiDetics 794.3 Kinetics Equations with Delayed Neutrons 824 4 Multistqe Processes Produc:in Delayed Neutrons 864 6 Specific R.csuIlIfor One Delayed Neutron Group 884 6 Measurement of Reactivity: Stab le Period 90

4.7 Rod drop Experiments 914 8 Pubccl ncutroo Expcrimcnta 934.9 Invcne Multiplication 964.10 The Reactor Transfer Function 984.11 Neutroo Wave ExJ Criiocnts 100

I CALCULATION OF REACTIVITY 104

6.1 IntroduetioD 1046.2 Linear pPcraton 1056.3 Variational PriDciple 1136.4 Perturbation Theory 119 .6 Iterated Fission Probabi ity 1236 8 Supemuiational PriDciple 1266.7 Variational Principles for InbomoIeneous Equations 129

NUMERICAL METHODS 131

8.1 Introduction 1358 Outer Iterations 1368 3 Flux Calculation: One dimensional Case 1398 4 Two and fbreo dimenIio Problems: Inner t ~ o n s 448 6 Proof of Converpnc:e 1498.8 Extrapolation Methods 1518.7 BuddiDa Iteration Flux Synthesis 152

7 REACTOR CONTROL 1

7.1 Introduction 1557.2 Direct Calculation of Ro d Worth 1567.3 The SeIf shieIdiDI Factor 1577 4 Fint ftiaht Elc:ape Probability t 64

. CONTENTS

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ONT NTS

7 9 A Black Ro d In Diffusion Theory: Absorpt ion Area 1687:f Fuel Depletion Ell ech 1737.7 Fission Product Poi sonin; 1777.8 Xenon Poisoning 1797.9 0Ulcr Saturating Fission Produets 186

Ix

8 ENERGY D EPENDENT PROBLEMS: THE M ULT G ROU P METHOD 188

8 .1 Introduction 1888.2 The Multigroup Methods 189

8 .3 Derivation of the Multiaroup Equations 1918 .4 Analytical Solutions of the Multigroup Equations 1978 .5 Numerical Solution of the Multigroup Equations 2038.6 Inwaral Equation Formulat ion 2038.7 Measurement of k , 2

a The rench Intermediate Experimenl 205b ermi ExponentialExperiment 209

8.8 Effective Delayed-Neutron Fraction 213

9 SLOWING D OWN CALCULATIONS 218

9.1 Introduction 2189.2 The Collision Kernel: Elastk: Scauerina 2209.3 The Collision Kernel: Inelastic Scat terina 2269.4 Fermi Age Theory 2309 .6 Infinite-medium Resonance Absorption 2379.8 Resonance Absorption In Lumped Absorbers 2429.7 Temperature Effceh 2479.8 Thermal Group Constants 2529.9 Variational Principles an d Perturbation Theory in the Multigroup o ~ l s m254

1 SELECTED SPECIAL TOPICS 268

10 .1 Introduction 25810.2 Some Problems Encountered in the Design of Light-water Reactors 2 8

a General Remorkl 258b Fast Spectrum 259c Resonance Caplure 261d ThermalSpeclrum 264e Fuel Managemenl 26

10.3 Fast Reac tors 26610 .4 The Thorium Converter 26910.6 Heavy-water R plctors 27010 .6 Graphite Pilca 27210.7 Temperature Cocfficicnh 273

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x

PPENDIX A PPENDIX 8 PPENDIX C PPENDIX D

APPENDIX EAPPENDIX F

atrb 7The Delta Diltribution 28Fourier aDd Laplace TraDsforma 284Spacial Func:tioaa orRcac w PhYli ca 290D I SpbericaJ Coordinatel 290D 1 CyUndricaI CoordiDatei 293Dynamia Elastic clIisioaI 95The Telepapher Equation 300

CONTENTS

I I IUOGft PHY J02

NAME INDEX aot

SU JECT INDEX 311

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