AdvANCES iN

NucLEAR SCiENCE ANd TECItNOLoGY VOLUME 19

Festschrift in Honor of Eugene P. Wigner

AdvANCES iN

NucLEAR SCiENCE ANd TECItNOLoGY Series Editors

Jeffery Lewins Fellow of Magdalene College Cambridge University, Cambridge, England

Martin Becker Rensselaer Polytechnic Institute, Troy, New York

Editorial Board

Eugene P. Wigner, Honorary President R. W. Albrecht F. R. Farmer Ernest J. Henley Norman Hilberry John D. McKean K. Oshima A. Sesonske H. B. Smets Karl Wirtz C. P. L. Zaleski

A Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volume immediately upon publication. Volumes are billed only upon actual shipment. For further information please contact the publisher.

AdvANCES iN

NucLEAR SCiENCE ANd TECItNOLoGY VOLUME 19

Festschrift in Honor of Eugene P. Wigner

Edited by

Jeffery Lewins Fellow of Magdalene College Cambridge University Cambridge, England

and

Martin Becker Rensselaer Polytechnic Institute Troy, New York

PLENUM PRESS, NEW YORK AND LONDON

The Library of Congress has cataloged this title as follows:

Advances in nuclear science and technology. v. 1- 1962-

New York, Plenum Press [etc.] v. ill., diagrs. 24 cm.

Annual. Editors: 1962-66 E. J. Henley and H. Kouts; 1968- E. J. Henley and others. ISSN 0065-2989 = Advances in nuclear science and technology. 1. Nuclear engineering-Yearbooks. 2. Nuclear physics-Yearbooks. I. Henley, Ernest

J., ed. II. Kouts, Herbert, 1919- ed. [DNlM: W1 AD685] TK9001.A3 621.48058 62-13039

Library of Congress [8412]

ISBN-13: 978-1-4684-5301-0 e-ISBN-13: 978-1-4684-5299-0 001: 10.1007/978-1-4684-5299-0

© 1987 Plenum Press, New York Softcover reprint of the hardcover 1st edition 1987 A Division of Plenum Publishing Corporation 233 Spring Street, New York, N.Y. 10013

All rights reserved

MARC-S

No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher

Frontispiece: Eugene P. Wigner

PREFACE

Our volume in the annual review series on this occasion represents a departure from our usual practice in that it serves as a Festschrift for Eugene Wigner. Dr. Wigner has won many honours in his long, wide ranging and distinguished career spanning so many upheavals in civilized life. The editors and the authors, indeed the whole nuclear engineering community, will wish to join in a modest but further acknowledgement of the contributions he has made to nuclear engineering, not least to the morality and professionalism of nuclear engineering in a year that has raised such international concerns over safety.

It suffices to make a bald statement of Eugene Wigner's life and times here, for the first article of the volume is a loving appreciation by his long-time colleague, Alvin Weinberg, an evaluation of his contribution historically during and after the Second World War but equally an account of the philosophy which Wigner provided to the burgeoning profession.

Eugene Wigner was born 17th November, 1902 in Budapest, Hungary and his early schooling is described by Dr. Weinberg. In the upheavals of the 'thirties, he came to the u.S. to start a long association with Princeton, 1930-1971, originally as a part time Professor of Mathematics and with extended periods of leave to further other matters. Thus he was at the Metallurgical Laboratory (Plutonium Project), University of Chicago 1942-45, Director of Research and Development at the Clinton Laboratories, Oak Ridge 1945-46 and returned to Oak Ridge as Director of the Civil Defence Project 1964-65. His honours and distinctions are numerous and the following but a partial list: Franklin Medal, 1950; Fermi Award, 1958; Atoms for Peace Award, 1960; Max Planck Medal, 1961; Nobel Prize for Physics, 1963; U.S. National Medal for Science, 1969; Albert Einstein Award, 1972 and of course the first Wigner Medal, 1978.

vO

viii PREFACE

The balance of our Festschrift is provided by an inter­national authorship who bring us modern accounts of some of the developments initiated by Wigner. One of the curiosities of the linear (neutron) transport theory was the late realisation that it would yield to conventional eigenfunction solution, albeit involving singular integrals and a continuous spectrum of eigenvalues for this integro-differential model. Wigner and Boris Davison had both identified a need to look more closely at the mathematical structure and after the War Wigner found time to work out the details, although these are probably better known now from the devoted work of Case and Zweifel together with their school. In this volume, Professor R. T. Ackroyd and his colleagues in What may be called the English school provides a similar theoretical treatment, using the variational method (another of Wigner's contributions to nuclear engineering) to display the nature of the finite element method as applied today in reactor physics calculations.

The basis of the transport operator in a variational principle is a powerful technique we need not elaborate in the Preface. When this is to be associated with a least squares error measure, then the relation to a non-self adjoint operator is for consideration if the stationary condition is to be a minimum condition having the desired Euler-Lagrange equations. We recall a personal experience when one of us gave an early public paper and the figure rising at the back of the Hall proved to be that of Professor Wigner with a question or rather, a comment; no little occasion to try the nerves of a young lecturer. A propos of Ackroyd's treatment of the A*A operator made thus self-adjoint, Eugene Wigner started by saying "It is a well known fact ... " and then paused, until resuming with his unswerving accuracy "It is well known to some people that every operator can be made self-adjoint".

As Weinberg pOints out, a major thrust of Wigner's philosophy was toward an inherently safe reactor. The volume continues with two up to date accounts of how this philosophy is seen to be accomplished, one from Europe and one from the United States. Dr. Hannerz has given us a description of the PIUS system now offered from Sweden with its ingenious use of hydraulic-thermal locks to provide for automatic supply of cooolant in any excursion. The PRISM reactor described by Dr. Pluta puts more emphasis on the modular nature of the system, the opportunity to dissociate the balance of plant from the nuclear island with its more severe safety require-

PREFACE ix

ments and the appealing financial implications of bringing a multiple station on line early before interest rates cripple the project.

Surely there are other techniques to exploit to promote inherent safety. One recollects the advocacy of Teller for the underground reactor. The experience of the Swiss with their experimental reactor accident suggests that much may be gained by guaranteeing containment. With modern drilling techniques, a reactor vault 300 m underground is readily constructed. It may also be argued as economic if it obviates a number of features required in any surface contain­ment. The obvious further development is for the self­contained i.e. fuel manufacturing and reprocessing plant. Here the original interest of the chemical engineer in Wigner may also be reexploited to provide on-line fuel processing rather than the mechanical engineer's route to the nuclear system. There is, by the way, in the U.K., an 8000 MWe generation plant hollowed out within a Welsh mountain, at the Dinorwic pumped storage plant which testifies to the practicability of underground containment of generating plant.

We have already mentioned the introduciton of variational methods or more particularly non-self adjoint perturbation methods in nuclear engineering by Eugene Wigner. It is appropriate therefore to include in this volume of homage a general treatise on the generalised perturbation method that has sprung from the seed Wigner sowed in discussing the Fermi-age equation. Professor Gandini brings to such a review his lifelong interest in the method, showing how it applied to both continuum and discrete models and therefore to a wide range of engineering phenomena. The extension to higher order methods greatly enhances the computational effectiveness of perturbation theory.

Finally the editors wish to acknowledge the benefit the series has had in its Editorial Board of which Eugene Wigner has been a member since the start (in 1962) and of which he is now our Honorary President. Authors and Editors join with Alvin Weinberg in offering this volume in love and gratitude to a physicist, chemist and mathematician, to a distinguished nuclear scientist, engineer and philosopher, Eugene Paul Wigner.

August, 1986 J. D. Lewins M. Becker

CONTENTS

Eugene Wigner and Nuclear Energy

A. M. Weinberg

I. Introduction II. The Pre-Chicago Days III. Chicago Metallurgical Laboratory IV. Clinton Laboratories, 1946-47 . V. Reactor Physics and General Engineering VI. Macroscopic Reactor Theory VII. Temperature Effects: The Wigner-Wilkins

Distribution VIII.Solid State Physics . IX. Nuclea.r physics at Chicago and Clinton X. General Energy policy XI. Civil Defence XII. Wigner and the Founding of ORNL XIII. Eugene Wigner and Nuclear Energy XIV. Annotated Bibliographies

References

The PIUS Principle and the SECURE Reactor Concepts

KOre Hannerz

I. Introduction II. Design Goals for "Forgiving" LWRs III. The PIUS Design Principle IV. System Modelling V. Design Implementation VI. The Nuclear Power Reactor SECURE-P

1 3 5

13 16 17

20 21 21 22 23 24 25 27 39

41 43 45 51 54 55

VII. The Heat Producing Reactor SECURE-H 97 VIII.The Low Temperature Heating Reactor SECURE-LH . 103 IX. Concluding Remarks 104

References 107

xi

xii CONTENTS

PRISM: An Innovative Inherently Safe Modular Sodium Cooled Breeder Reactor

P. R. Pluta, F. E. Tippets, R. E. Murata, C. E. Boardman, C. S. Schatmeir, A. E. Dubberley, D. M. Switick, W. Kwant

I. Introduction 109 II. Overall Plant Description 110 III. Reactor Assembly and Support Structures 133 IV. Heat Transport and Power Generation Systems 161 V. Shutdown Heat Removal Systems 167 VI. PRISM Inherent Safety Characteristics 174 VII. Concept Summary and Implementation Strategy 193

Acknowled0ement 202 References 202

Generalised Perturbation Theory (GPT). A Heuristic Approach

A. Gandini

I. Introduction II. GPT Methodology for Linear Systems III. GPT Methodology for Nonlinear Systems IV. Fields of Interest V. Expansion of the Perturbed Field Function VI. Final Remarks

Appendix 1: Frechet Derivatives

Appendix 2: Second Order GPT Critical Systems Expressions

Appendix 3: Discretised Systems .

Appendix 4: The Importance Function in the Enthalpy Field

Appendix 5: Miscellaneous Arguments Relevant to GPT .

Appendix 6: Alternative Derivatrion in Temperature Field

References

205 208 262 276 335 344

• 347

· 352

• 354

· 356

· 364

373

375

CONTENTS xiii

Some Recent Developments in Finite Element Methods for Neutron Transport Theory,

R. T. Ackroyd, J. K. Fletcher, A. J. H. Goddard, J. Issa, N. Riyait, M. M. R. Williams and J. Wood

I. Introduction II. Forms of the Transport Equation III. Approximate Solution Methods IV. A Unified Treatment. V. Application of the Finite Element VI. Three Design Codes Illustrated VII. Composite Solutions VIII.Future Trends

References

Index

381 386 389 397

Method 417 425 470 473 475

485

CONTENTS OF EARLIER VOLUMES

CONTENTS OF VOLUME 10

Optimal Control Applications in Nuclear Reactor Design and Operations, W. B. Terney and D. C. Wade

Extrapolation Lengths in Pulsed Neutron Diffusion Measure­ments, N. G. Sjostrand

Thermodynamic Developments, R. V. Hesketh

Kinetics of Nuclear System: Solution Methods for the Space­Time Dependent Neutron Diffusion Equation, W. Werner

Review of Existing Codes for Loss-of-Coolant Accident Analysis, Stanislav Fabic

CONTENTS OF VOLUME 11

Nuclear Physics Data for Reactor Kinetics, J. Walker and D. R. Weaver

The analysis of Reactor Noise: Measuring Statistical Fluctuations in Nuclear Systems, N. Pacilio, A. Colombina, R. Mosiello, F. Morelli and V. M. J01'io

On-Line Computers in Nuclear Power Plants - A review, M. W. Jervis

Fuel for the SGHWR, D. o. Pickman, J. H. Gittus and K. M. Rose

The Nuclear Safety Research Reactor (NSRR) in Japan, M. Ishikawa dn T. Inabe

Practical Usage of Plutonium in Power Reactor Systems, K. H. Peuchl

xv

xvi

CONTENTS OF VOLUME 11 (Continued)

Computer Assisted Learning in Nuclear Engineering, P. R. Smith

Nuclear Energy Centers, M. J. McNelly

CONTENTS OF VOLUME 12

CONTENTS

Characteristic Ray Solutions of the Transport Equation, H. D. Bpough and C. T. Chudley

Heterogeneous Core Designs for Liquid Metal Fast Breeder Reactors, P. W. Dickson and R. A. Doncals

Liner Insulation for Gas-Cooled Reactors, B. N. Fupbep and J. Davidson

Outage Trends in Light water Reactors, E. T. Burns, R. R. Fu llwood and R. C. En:Jman

Synergetic Nuclear Energy Systems Concepts, A. A. Havms

Vapor Explosion Phenomena with Respect to Nuclear Reactor Safety Assessment, A. W. Cponenbepg ~nd .R. Benz

CONTENTS OF VOLUME 13

Radioactive Waste Disposal, Hopst Bohm and Klaus Kuhn

Response Matrix Methods, Sten-OPjan Linkahe and Z. J. Weiss

Finite Approximation to the Even-Parity Transport Equation, E. E. Lewis

Advances in Two-Phase Flow Instrumentation, R. T. Lahey and S. Benepjee

Bayesian Methods in Risk Assessment, Geopge Apostolakis

CONTENTS

CONTENTS OF VOLUME 14

Introduction: Sensitivity and Uncertainty Analysis of Reactor Performance Parameters, C. R . . Weisbin

xvii

Uncertainty in the Nuclear Data used for Reactor Calculations, R. W. Peeb Ze

Calculational Methodology and Associated Uncertainties, E. Kujawski and C. R. Weisbin

Integral Experiment Information for Fast Reactors, P. J. Collins

Sensitivity Functions for Uncertainty Analysis, Ehud Greenspan

Combination of Differential and Integral Data, J. H. Marab le, C. R. Weisbin and G. de Saussure

New Developments in Sensitivity Theory, Ehud Greenspan

CONTENTS OF VOLUME 15

Eigenvalue Problems for the Boltzmann Operator, V. Protopopescu

The Definition and Computation of Average Neutron Lifetimes, Allen F. Henry

Non-Linear Nuclear Stochastic Theory, K. Saito

Fusion Reactor Development: A review, Weston M. Stacey, Jr.

Streaming in Lattices, Ely M. Gelbard

xviii CONTENTS

CONTENTS OF VOLUME 16

Electrical Insulation and Fusion Reactors, H. M. Bamford

Human Factors of CRT Displays for Nuclear Power Plant Control, M. M. Danchak

Nuclear Pumped Lasers, R. T. Schneider and F. Bohl

Fusion-Fission Hybrid Reactors, E. Greenspan

Radiation Protection Standards: their Development and Current Status, G. C. Roberts and G. N. Kelly

CONTENTS OF VOLUME 17

A Methodology for the Design of Plant Analysers, T. B. E. Chambers and M. J. whitmash-Everiss

Models and Simulation in Nuclear Power Station Design and Operation, M. W. Jervis

Psychological Aspects of Simulation Design and Use, R. B. Stammers

The Development of Full-Scope AGR Training Simulators within the C.E.G.B., G. C. Budd

Parallel processing for Nuclear Safety Simulation, A. Y. Allidina, M. G. Singh and B. Daniels

Developments in Full-scope, Real-time Nuclear Plant Simulators J. Wi Us hire

CONTENTS xix

CONTENTS OF VOLUME 18

Realistic Assessment of Postulated Accidents at Light Water Reactor Nuclear Power Plants, E. A. Warman

Radioactive Source Term for Light Water Reactors J. P. Hosemann and K. Hassman

Multidimensional Two-Phase Flow Modeling and Simulation M. Arai and N. Hirata

Fast Breeder Reactors - The Point of View of the French Safety Authories, M. Laverie and M. AVenas

Light Water Reactor Space-Dependent Core Dynamics Computer Programs, D. J. Diamond and M. Todosow

Volumes 1-9 of the series were published by Academic Press