Nuclear Reactor Physics

This text is intended as a first course in the physics of nuclear
reactors. It is designed to be appropriate as an introduction to reactor
theory within an undergraduate nuclear engineering curriculum, as
well as for a stand-alone course that can be taken by undergraduates
in mechanical, electrical, or other fields of engineering who have not
had a previous background in nuclear energy. Likewise, it is planned
to be useful to practicing engineers from a variety of disciplines
whose professional responsibilities call for familiarity with the physics of nuclear reactors.
Why a new book on reactor physics when a number of legacy
texts are still in print? The better of these are well written, and since
the fundamentals of the subject were already worked out at the time
of their publication, they remain useful today. My conviction, however, is that for today’s undergraduates and practicing engineers an
introduction to reactor physics is better presented through both reorganizing and refocusing the material of earlier texts, and in doing that
emphasizing the characteristics of modern power reactors.
Earlier textbooks most commonly have begun with the relevant
nuclear physics and neutron interactions, and then presented a
detailed treatment of neutron slowing down and diffusion in homogeneous mixtures of materials. Only in the latter parts of such texts
does the analysis of the all-important time-dependent behavior of
fissionable systems appear, and the dependence of criticality on lattice structures of reactor cores typically is late in receiving attention.
To some extent such a progression is necessary for the logical development of the subject. However, both in teaching undergraduates and
in offering continuing education instruction for practicing engineers,
I have found it advantageous to present a quantitative but more
general overview early in the text, while deferring where possible
more detailed analysis, and also the more advanced mathematics that
accompanies it, to later. Thus I have moved the treatment of reactor
kinetics forward, attempting to inculcate an understanding of the
time-dependent behavior of chain reactions, before undertaking the
detailed treatment of spatial power distributions, reflector saving,
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and other topics dependent on the solution of the neutron diffusion
equation. Likewise, the compositions of power reactor cores are
incorporated into the discussion early on, emphasizing the interdisciplinary nature of neutronic and thermal design.
My intent in this text is to emphasize physical phenomena,
rather than the techniques necessary to obtain highly accurate
results through advanced numerical simulation. At the time the
legacy texts appeared, computers were emerging as powerful tools
for reactor analysis. As a result, the pedagogy in teaching reactor
theory often emphasized the programming of finite differencing techniques, matrix solution algorithms, and other numerical methods in
parallel with the analysis of the physical behavior of reactors, and
thus extended the range of solutions beyond what could be obtained
with paper and pencil. Now, however, high level programming languages, such as Mathcad or MATLAB, allow students to solve
transcendental or linear systems of equations, to integrate differential equations, and to perform other operations needed to solve the
preponderance of problems encountered in an introductory course
without programming the algorithms themselves. Concomitantly,
the numerical simulation of reactor behavior has become a highly
sophisticated enterprise; one to which I have devoted much of my
career. But I believe that the numerical techniques are better left to
more advanced courses, after a basic understanding of the physical
behavior of reactors has been gained. Otherwise the attempt to incorporate the numerical approaches employed in reactor design dilutes
the emphasis on the physical phenomena that must first be
understood.
By reorganizing and refocusing the materials along these lines,
I hope to have broadened the audience for whom the text may be
useful, in particular those advancing their professional development,
even while they may not be taking a formal reactor physics course in
a university setting. My goal is that the book may be read and
physical insight gained, even though for lack of time or background
some of the more mathematical sections are read and the results
accepted without following each step of the development in detail.
With this in mind, many of the results are presented in graphical as
well as analytical form, and where possible I have included representative parameters for the major classes of power reactors in order to
provide the student with some feel for the numbers.
Examples are integrated into the text’s narrative, and a selection
of problems is provided at the end of each chapter. The problems both
enforce the concepts that have been covered and in some cases
expand the scope of the material. The majority of the problems can
be solved analytically, or with the use of a pocket calculator. In some
cases, where multiple solutions or graphical results are called for, use
of the formula menu of a spreadsheet program, such as ExcelTM
removes any drudgery that might otherwise be entailed. Selected
problems require the use of one of the earlier mentioned high level
computing languages for the solution of transcendental or differential
equations. These are marked with an asterisk.
The preparation of this text would have been immensely more
difficult if not impossible without the help and encouragement of
many friends, colleagues, and students. Advice and assistance from
the staff of the Nuclear Engineering Division of Argonne National
Laboratory have been invaluable in the text’s preparation. Won Sik
Yang, in particular, has provided advice, reactor parameters, graphical
illustrations, and more as well—taking the time to proofread the draft
manuscript in its entirety. Roger N. Blomquist, Taek K. Kim, Chang-ho
Lee, Giuseppe Palmiotti, Micheal A. Smith, Temitope Taiwo, and
several others have also pitched in. Bruce M. Bingman and his colleagues at the Naval Reactors Program have also provided much appreciated help. Finally the feedback of Northwestern University students
has been most helpful in evolving a set of class notes into this text.
Most of all, Ann, my wife, has endured yet another book with grace
and encouragement, while covering for me in carrying much more
than her share of our family’s responsibilities