# Physics of High-Temperature Reactors

## 1st Edition

**Authors:**Luigi Massimo

**eBook ISBN:**9781483280288

**Imprint:**Pergamon

**Published Date:**1st January 1976

**Page Count:**224

## Description

Physics of High-Temperature Reactors focuses on the physics of high-temperature reactors (HTRs) and covers topics ranging from fuel cycles and refueling strategies to neutron cross-sections, transport and diffusion theory, and resonance absorption. Spectrum calculations and cross-section averaging are also discussed, along with the temperature coefficient and reactor control.

Comprised of 16 chapters, this book begins with a general description of the HTR core as well as its performance limitations. The next chapter deals with general considerations about HTR physics, including quantities to be determined and optimized in the design of nuclear reactors. Potential scattering and resonance reactions between neutrons and atomic nuclei are then considered, together with basic aspects of transport and diffusion theory. Subsequent chapters explore methods for solving the diffusion equation; slowing-down and neutron thermalization in graphite; HTR core design, fuel management, and cost calculations; and core dynamics and accident analysis. The final chapter describes the sequence of reactor design calculations.

This monograph is written primarily for students of HTR physics who are preparing to enter the field as well as technologists of other disciplines who are working on the system.

## Table of Contents

Preface

Foreword

Acknowledgments

List of Symbols

1. General Description of the HTR Core

1.1. Basic Concepts

1.2. Fuel Cycles and Refuelling Strategies

1.3. Reactor Control

1.4. Limitations to the Performance of the HTR Core

References

2. General Considerations About Reactor Physics

3. Neutron Cross-Sections

3.1. Potential Scattering and Resonance Reactions

3.2. Resolved Resonances

3.3. Unresolved Resonances

3.4. Doppler Effect

3.5. Nuclear Data Libraries

References

4. Basic Aspects of Transport and Diffusion Theory

4.1. The Neutron Transport Equation

4.2. Problems Posed by the Solution of the Boltzmann Equation. The Multigroup Method

4.3. Treatment of Angular Dependence in the Boltzmann Equation

4.4. The Sn Method

4.5. The Spherical Harmonics Expansion of the Boltzmann Equation

4.6. The Double Pl Approximation

4.7. The Pl Approximation

4.8. The Energy-Independent Case and the Diffusion Equation

4.9. The Energy-Dependent Diffusion Equation

4.10. The Bn Method

4.11. Integral Form of the Boltzmann Equation

4.12. Monte Carlo Calculations

4.13. Neutron Importance and Perturbation Theory

4.14. The Separation of Energy and Space Dependence of the Neutron Flux and the Definition of Bucklings

References

5. Methods for the Solution of the Diffusion Equation

5.1. Analytical Solutions of the Diffusion Equation

5.2. Finite Difference Approximations of the Diffusion Equation

5.3. Choice of the Mesh

5.4. Special Numerical Methods

5.5. The Boundary Conditions for Diffusion Theory Calculations

5.6. Interface Conditions for the Diffusion Equation

References

6. Slowing-Down and Thermalization in Graphite

6.1. Slowing-Down in Graphite

6.2. Neutron Thermalization in Graphite

6.3. Crystal Model

6.4. Free Gas Model

6.5. Principle of Detailed Balance

6.6. Effects of Chemical Bindings on High-Temperature Reactors

References

7. Resonance Absorption

7.1. General Considerations

7.2. Resonance Absorption in an Infinite Homogeneous Medium

7.3. Narrow Resonance Approximation

7.4. Narrow Resonance Infinite Mass Approximation

7.5. Intermediate Resonance Approximation

7.6. Heterogeneous Assemblies

7.7. Narrow Resonance Approximation for Heterogeneous Assemblies

7.8. Narrow Resonance Infinite Mass Approximation for Heterogeneous Assemblies

7.9. Computer Methods for Resonance Calculations in Heterogeneous Geometry

7.10. Calculation of Escape Probabilities

7.11. Methods for Rapid Calculations: The Equivalence Relation

7.12. Unresolved Resonances

7.13. Resonance Absorption in Double Heterogeneous Arrangements

7.14. Resonances in Thermal Energy Range

References

8. Spectrum Calculations and Cross-Section Averaging

8.1. The Spectrum Calculations

8.2. Bn and Pl Methods for Spectrum Calculations

8.3. Diffusion Theory Spectrum Calculations

8.4. Spectrum Calculations in Heterogeneous Reactors; Cell Calculations

8.5. Space-Dependent Spectrum Calculations in Heterogeneous Cells

8.6. Cross-Section Averaging for Reflector Regions

8.7. Fine Group Structure of Codes for Spectrum Calculations

8.8. The Production of the Fine Group Libraries

8.9. Choice of Energy Structure for Few Group Reactor Calculations

8.10. The Calculation of the Diffusion Coefficient in Presence of Holes

8.11. Neutron Balance and Four-Factor Formula

8.12. Spectrum Calculations in the Upper Energy Range: Dosimetry of Radiation-Induced Damage

References

9. Burn-Up

9.1. The Depletion Equations and the Methods to Solve Them

9.2. The Burn-Up Codes

9.3. Equilibrium Burn-Up Calculations

9.4. Equilibrium Calculations in Case of Off-Load Refuelling

9.5. Burn-Up Calculations in Pebble-Bed Reactors

9.6. Burn-Up Units

9.7. Burn-Up of Burnable Poisons

References

10. Core Design, Fuel Management and Cost Calculations

10.1. Objectives

10.2. Optimization Procedures

10.3. Power Shaping

10.4. Fuel Management

10.5. Continuous and Discontinuous Refuelling

10.6. Types of Fuel Cycles

10.7. Reprocessing

10.8. Running-In

10.9. Methods for Running-In Calculations

10.10. The Out-of-Core Fuel Cycle

10.11. Economic Calculations: The Present Worth Method

10.12. The Cost of Enriched Uranium and of Other Fissile Isotopes

10.13. Methods for Fuel-Cycle Cost Calculations

10.14. Simplified Calculations for the Equilibrium Cycle

References

11. The Temperature Coefficient

11.1 Definitions

11.2. The Doppler Coefficient

11.3. The Moderator Temperature Coefficient

11.4. General Considerations on Temperature Coefficient

References

12. Core Dynamics and Accident Analysis

12.1. General Considerations About Reactor Dynamics

12.2. The Kinetics Equations

12.3. One Group Space-Independent Kinetics Equation

12.4. Simple Analytical Solutions of the Kinetics Equation

12.5. The General Case Involving Heat Transfer and Control

12.6. The Heat Transfer Dynamic Equations

12.7. The Feedback of the Control System

12.8. The Mean Prompt Neutron Lifetime

12.9. The Delayed Neutrons

12.10. The Xe and Sm Equations

12.11. Peculiarities of HTR Dynamics

12.12. Methods for Space-Dependent Reactor Dynamics

12.13. Comparison of Space-Dependent and Point Model Calculations

12.14. Spatial Reactor Instability

12.15. Analysis of the Possible Types of Accidents

12.16. Power Following

12.17. Reactor Instrumentation

12.18. Procedure in Case of Accident

References

13. Reactor Control

13.1. Control-Rod Requirement

13.2. Control-Rod Classification

13.3. Control-Rod Configuration

13.4. Control-Rod Calculation

13.5. Safety Implications

13.6. Burn-Up and Heat Production in Control Rods

13.7. Additional Independent Shut-Down Systems

Reference

14. The Peculiarities of HTR Physics

References

15. Analysis of Calculational Accuracy

15.1. Comparisons Between Theory and Experiments

15.2. Evaluation of Uncertainties in HTR Calculations Due to Uncertainties in Cross-Section Data and Calculational Methods

References

16. The Sequence of Reactor Design Calculations

References

Index

List of Computer Codes

## Details

- No. of pages:
- 224

- Language:
- English

- Copyright:
- © Pergamon 1976

- Published:
- 1st January 1976

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483280288