Readership
This introduction to reactor kinetics is targeted to those following a specialized course
of study in nuclear engineering or those interested in the way fission reactors work.
While no knowledge of nuclear physics is necessary for an understanding of the material,
mathematical methods covered in the first years of university are a prerequisite. This
book should allow the reader to understand kinetics sufficiently to predict the behaviour
of a reactor subjected to various perturbations and to perform more detailed calculations.
Reactivity is a reactor-physics concept that allows us to characterize in a simple fashion
the dynamic state of a reactor. Its definition stems from point kinetics, and an effort
was made to introduce it in a general and rigorous way. Since the concept of reactivity is
widely used in practice in reactor simulation and control, nuclear-station operations
personnel will be able to make good use of the presentation. By recalling the fundamental
theory and the more basic methods available, this book can also serve as a reference work
for engineers and analysts engaged in technical-support activities for reactor operation.
Need
The theory presented has a general scope and applies to all reactor types. However, the
material is illustrated with numerical examples characteristic of the behaviour of
heavy-water reactors of the CANDU type, since these are in general neglected in manuals.
Their response is compared to that of light-water reactors.
Subject
The material in this introductory work is centred around point kinetics. We are interested
mostly in the evolution of the total power of a reactor, in response to various
perturbations that may be applied. However, point kinetics allows the estimation of the
change in total power only via perturbations to average reactor properties. Since
perturbations are generally localized (i.e., they have an effect on only part of the
domain), the weighting procedure for determining changes in the average properties is
central to the point-kinetics approach. This weighting must take into account the
diffusion of neutrons and the non-uniform distribution of materials in the core. It is
therefore essential to derive first the point-kinetics equations from the more general
equations of space-time kinetics.
The Author
Over the past 20 years, Daniel Rozon has been teaching graduate courses in reactor physics
and fuel management at the Nuclear Engineering Institute of École Polytechnique,
Montreal, Canada. He holds an M.Sc.A. from École Polytechnique and a Ph.D. from McMaster
University. Since 1988, he has held the Hydro-Québec Chair in Nuclear Engineering. In
1994, he became a Fellow of the Canadian Nuclear Society. He is a member of the Research
and Development Advisory Panel of Atomic Energy of Canada Ltd. and was chairman of that
panel in 1996-97. He is currently chairman of the Engineering Physics and Materials
Engineering Department at École Polytechnique.
CONTENTS
Chapter 1 - Neutron-Nucleus Interactions and Fission
Neutron-Nucleus Interactions
Fission
Production of Neutrons
Delayed-Neutron Groups
Chapter 2 - The Diffusion Equation and the
Steady State
Neutron Balance in a Reactor
Diffusion Equation
Time-Independent Equation and Eigenvalue Problem
Perturbation Theory and Adjoint Flux
Chapter 3 - The Point-Kinetics Equations
General Formulation
Common Formulations of the Point-Kinetics Equations
Point Model and Interpretation of the Kinetics Parameters
Integral Formulation of the Equations
Chapter 4 - Elementary Solutions of the
Kinetics Equations
Initial Steady State and Source Multiplication
Response to Reactivity Step with a Single Group of Delayed Neutrons
Generalization to Several Delayed-Neutron Groups
Response to a Unit Neutron Pulse and to Changes in the External
Source
Chapter 5 - Approximate Solutions: Ramps and
Periodic Variations
Approximations for the Delayed-Neutron Source
Small-Amplitude Approximation (Linearization)
Prompt-Jump Approximation
Reactivity Ramps and Log-Rate Protection
Prompt-Kinetics Approximation
Periodic Variations of Reactivity
Chapter 6 - Temperature and Void Feedback in
CANDU
Thermal Power and Neutronic Power
Feedback Effects
Temperature Reactivity Coefficient
Reactivity Effect of Voiding
Calculation of Fuel Temperature
Chapter 7 - Numerical Solutions with
Temperature Feedback
Numerical Methods for Point-Kinetics Equations
Temperature-Feedback Effects on Power in CANDU
Implications for Control and Safety
Prompt Kinetics with Feedback (Nordheim-Fuchs Model)
Chapter 8 - Space-Time Kinetics
General Problem of Reactor Dynamics
Energy-Space-Time Approaches
Factorization Methods
Modal Synthesis
Neutronic Coupling and Space-Time Effects
Appendix A - Xenon and Samarium Effects in
CANDU
Appendix B - The Chernobyl Accident
Bibliography |
