NPRE 455
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Nuclear, Plasma, and Radiological Engineering
NPRE 455
COURSE OUTLINE
Course Number: NPRE 455
Title: Neutron Diffusion and Transport
Catalogue Description: Neutron migration, neutron slowing down and thermalization; neutron continuity equation, multigroup diffusion theory, homogeneous and heterogeneous medium, thermal and fast assemblies; numerical methods for multigroup diffusion equations; reactor dynamics, perturbation theory, reactivity coefficients; introductory transport theory.
| Principle Topics Covered | Hours (Approximate) |
|---|---|
| Neutron Migration, Slowing Down and Thermalization | 2 |
| Applications of One-Speed Diffusion Theory in Multi-Dimensions | 9 |
| Criticality [The Solution to the One-Speed Diffusion Equation, Keff] | |
| k-Calculations | |
| The Higher Spatial Modes: The Time-Dependent Problem | |
| The Higher Spatial Modes: The Subcritical Steady-State Case with a Fixed Source[Solution by Eigenfunction Expansion] | |
| Subcritical and Non-Multiplying Systems | |
Green's Functions |
|
The Diffusion Length Problem |
|
The Measurement of the Diffusion Length L |
|
The Physical Meaning of the Diffusion Length L |
|
Kernel Functions for Subcritical and Non-Multiplying Media |
|
The Point Kernal |
|
The Plane Kernel |
|
The Relationship Between the Point and Plane Kernels |
|
| Multiregion Problems: Two-Region Criticality | |
| Numerical Methods for One-Speed Diffusion Equation | |
| Multigroup Diffusion Theory | 15 |
| Derivation of the Multigroup Diffusion Equations | |
| Review of Solution of Simultaneous Differential Equations | |
| Two-Group Criticality | |
| Two-Group, Two-Region Criticality | |
| Numerical Methods for Multi-Group Diffusion Equations | |
| Introduction to Reactor Dynamics | 7 |
| Perturbation Theory | |
| Elementary Derivation of the Point Reactor Kinetics Equations | |
| The "Inhour Equation" and its Properties | |
| Solution of the Point Reactor Kinetics Equations without Feedback | |
| Reactor Period; Reactivity Units; Reactivity Coefficients | |
| Practical Calculations | 4 |
| Conventional Computational Methods for Neutronics Calculations | |
| Advanced Computational Methods for Neutronics Calculations | |
| Fundamentals of Neutron Transport Theory | 6 |
| Basic Definition of Quantities in the Linear Boltzmann (Transport) Equations | |
Number Density |
|
Angular Number Density |
|
Energy-Dependent Angular Number Density |
|
Scalar Flux (Neutron Flux) |
|
Angular Flux (Directional Flux) |
|
Energy-Dependent Angular Flux |
|
Net Neutron Current |
|
Angular Neutron Current |
|
Energy-Dependent Angular Neutron Current |
|
Units |
|
| The Physical Derivation of the Neutron Transport Equation (Boltzmann Equation) | |
Streaming (Leakage) Term |
|
Death (Absorption Plus Outscatter) Terms |
|
Birth (Inscatter Plus Fission Plus Fixed Source) Terms |
|
| Delayed Neutrons and the Precursor Equations | |
| Transport Theory Boundary Conditions | |
Constraint (Non-Negativity) |
|
Interface Condition (Continuity) |
|
Vacuum Boundary Conditions |
|
| Neutron Thermalization | |
The Detailed Balance Condition for Thermal Neutrons |
|
The Maxwellian Distribution in Thermal Reactors |
|
| Exams | 2 |
| Total | 45 |
Basic Texts:
Required:
- J. Duderstadt and L. Hamilton, "Nuclear Reactor Analysis", 1976.
Recommended:
- Recommended: J. Lamarsh, "Nuclear Reactivity Theory"
- G. Bell and S. Glasstone, "Nuclear Reactor Theory."
Prerequisites: NPRE 247
Purpose of Course:
- Prerequisite for NPRE 348, 358, 441, 455, 460.
- Required for the Nuclear Engineering curriculum.
- Elective for other fields of engineering and science.
- This course serves to introduce the student to the fundamentals of neutron diffusion and transport in honogeneous and heterogeneous media. Applications will range from the k-calculation in a multiplying medicine to flux at a tumor site.
- This course will serve as the most advanced "theory course" in neutron migration leading to applied/design courses such as NPRE 348 and NPRE 358. It fits as the intermediate course in the sequence NPRE 247, 355, 455 and 460. It also serves as a graduate course for students with non-nuclear background.
Instructor: Rizwan Uddin
Credit: 4 Credit Hours
Meeting hours per week: 3
Class registration opacity: 20
Semesters course offered: REFER TO MASTER LISTING
Other notes:
Course last revised: May 2007
© 2009 The Board of Trustees at the University of Illinois