Neutron Fluctuations: A Treatise on the Physics of Branching Processes
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Table of contents
- Contentsvii
- Prefacexi
- Acknowledgementxiii
- List of most frequently used notationsxv
- Part I. Physics of Branching Processes1
- Chapter 1. Basic Notions3
- 1.1 Definitions3
- 1.2 Equations for the Generating Functions4
- 1.3 Investigation of the Generating Function Equations11
- 1.4 Discrete Time Branching Processes20
- 1.5 Random Tree as a Branching Process23
- 1.6 Illustrative Examples25
- Chapter 2. Generalisation of the Problem36
- 2.1 Joint Distribution of Particle Numbers at Different Time Instants36
- 2.2 Branching Process with Two Particle Types39
- 2.3 Extinction and Survival Probability41
- Chapter 3. Injection of Particles55
- 3.1 Introduction55
- 3.2 Distribution of the Number of Particles57
- 3.3 Limit Probabilities69
- 3.4 Probability of the Particle Number in a Nearly Critical System77
- Chapter 4. Special Probabilities82
- 4.1 Preliminaries82
- 4.2 The Probability of the Number of Absorptions82
- 4.3 Probability of the Number of Detections102
- 4.4 Probability of the Number of Renewals107
- 4.5 Probability of the Number of Multiplications113
- Chapter 5. Other Characteristic Probabilities119
- 5.1 Introduction119
- 5.2 Distribution Function of the Survival Time119
- 5.3 Number of Particles Produced by a Particle and Its Progeny121
- 5.4 Delayed Multiplication of Particles127
- 5.5 Process with Prompt and Delayed Born Particles141
- Chapter 6. Branching Processes in a Randomly Varying Medium149
- 6.1 Characterisation of the Medium150
- 6.2 Description of the Process150
- 6.3 Factorial Moments, Variances154
- 6.4 Random Injection of the Particles165
- Chapter 7. One-Dimensional Branching Process179
- 7.1 Cell Model179
- 7.2 Continuous model191
- Part II. Neutron Fluctuations203
- Chapter 8. Neutron Fluctuations in the Phase Space: The Pál–Bell Equation205
- 8.1 Definitions206
- 8.2 Derivation of the Equation207
- 8.3 Expectation, Variance and Covariance213
- 8.4 Pál–Bell Equation in the Diffusion Approximation217
- Chapter 9. Reactivity Measurement Methods in Traditional Systems231
- 9.1 Preliminaries231
- 9.2 Feynman-Alpha by the Forward Approach234
- 9.3 Feynman-Alpha by the Backward Approach240
- 9.4 Evaluation of the Feynman-Alpha Measurement250
- 9.5 The Rossi-Alpha Method253
- 9.6 Mogilner's Zero Probability Method257
- Chapter 10. Reactivity Measurements in Accelerator Driven Systems259
- 10.1 Steady Spallation Source260
- 10.2 Pulsed Poisson Source with Finite Pulse Width264
- 10.3 Pulsed Compound Poisson Source with Finite Width281
- 10.4 Periodic Instantaneous Pulses283
- Chapter 11. Theory of Multiplicity in Nuclear Safeguards294
- 11.1 Neutron and Gamma Cascades295
- 11.2 Basic Equations298
- 11.3 Neutron Distributions299
- 11.4 Gamma Photon Distributions305
- 11.5 Joint Moments309
- 11.6 Practical Applications: Outlook311
- Appendices313
- A. Elements of the Theory of Generating Functions315
- A.1 Basic Properties315
- A.2 On the Roots of Equation g(x)=x, 0 ≤ x ≤ 1321
- A.3 A Useful Inequality322
- A.4 Abel Theorem for Moments323
- A.5 Series Expansion Theorem325
- A.6 An Important Theorem327
- B. Supplement to the Survival Probability330
- B.1 Asymptotic Form of Survival Probability in Discrete Time Process330
- Bibliography335
- Index339
- A339
- B339
- C339
- D339
- E339
- F339
- G339
- H339
- I339
- J339
- L339
- M339
- N340
- O340
- P340
- Q340
- R340
- S340
- T340
- V340
- Y340
- Z340
The transport of neutrons in a multiplying system is an area of branching processes with a clear formalism. This book presents an account of the mathematical tools used in describing branching processes, which are then used to derive a large number of properties of the neutron distribution in multiplying systems with or without an external source.
In the second part of the book, the theory is applied to the description of the neutron fluctuations in nuclear reactor cores as well as in small samples of fissile material. The question of how to extract information about the system under study is discussed. In particular the measurement of the reactivity of subcritical cores, driven with various Poisson and non-Poisson (pulsed) sources, and the identification of fissile material samples, is illustrated.
The book gives pragmatic information for those planning and executing and evaluating experiments on such systems.
- Gives a complete treatise of the mathematics of branching particle processes, and in particular neutron fluctuations, in a self-contained manner;
- The first monograph containing the theory and application of neutron fluctuations in low power ADS (spallation and pulsed sources);
- Suitable as a tutorial and handbook/reference book for scientists and graduate students;
- One of the authors is the founder of the mathematical theory of neutron fluctuations in zero power systems.
In the second part of the book, the theory is applied to the description of the neutron fluctuations in nuclear reactor cores as well as in small samples of fissile material. The question of how to extract information about the system under study is discussed. In particular the measurement of the reactivity of subcritical cores, driven with various Poisson and non-Poisson (pulsed) sources, and the identification of fissile material samples, is illustrated.
The book gives pragmatic information for those planning and executing and evaluating experiments on such systems.
- Gives a complete treatise of the mathematics of branching particle processes, and in particular neutron fluctuations, in a self-contained manner;
- The first monograph containing the theory and application of neutron fluctuations in low power ADS (spallation and pulsed sources);
- Suitable as a tutorial and handbook/reference book for scientists and graduate students;
- One of the authors is the founder of the mathematical theory of neutron fluctuations in zero power systems.