Table Of ContentAdvANCES 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
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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
MARC-S
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
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 inter
national 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 contain
ment. The obvious further development is for the self
contained 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 1
II. The Pre-Chicago Days 3
III. Chicago Metallurgical Laboratory 5
IV. Clinton Laboratories, 1946-47 . 13
V. Reactor Physics and General Engineering 16
VI. Macroscopic Reactor Theory 17
VII. Temperature Effects: The Wigner-Wilkins
Distribution 20
VIII.Solid State Physics . 21
IX. Nuclea.r physics at Chicago and Clinton 21
X. General Energy policy 22
XI. Civil Defence 23
XII. Wigner and the Founding of ORNL 24
XIII. Eugene Wigner and Nuclear Energy 25
XIV. Annotated Bibliographies 27
References 39
The PIUS Principle and the SECURE Reactor Concepts
KOre Hannerz
I. Introduction 41
II. Design Goals for "Forgiving" LWRs 43
III. The PIUS Design Principle 45
IV. System Modelling 51
V. Design Implementation 54
VI. The Nuclear Power Reactor SECURE-P 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 205
II. GPT Methodology for Linear Systems 208
III. GPT Methodology for Nonlinear Systems 262
IV. Fields of Interest 276
V. Expansion of the Perturbed Field Function 335
VI. Final Remarks 344
Appendix 1:
Frechet Derivatives • 347
Appendix 2:
Second Order GPT Critical Systems Expressions · 352
Appendix 3:
Discretised Systems . • 354
Appendix 4:
The Importance Function in the Enthalpy Field · 356
Appendix 5:
Miscellaneous Arguments Relevant to GPT . · 364
Appendix 6:
Alternative Derivatrion in Temperature Field 373
References 375
