NPRE 555

Engineering at Illinois Engineering at Illinois

Nuclear, Plasma, and Radiological Engineering

NPRE 555

COURSE OUTLINE

Course Number: NPRE 555

Title: Reactor Theory I

Catalogue Description: Advanced development of neutron transport theory; neutron slowing-down and resonance absorption; approximations to the transport equation; direct numerical methods and other techniques of approximation theory applied to the neutron transport equation; advanced topics.

Course Topics and Hours
Principle Topics Covered Hours (Approximate)
Fundamentals of Neutron Transport Theory 9
Neutron Balances in Phase Space
  
The Integro-differential Neutron Transport Equation
  
The Adjoint Equation
  
Probability Balances and Neutron Importance
  
The Integral Transport Equation
  
One-speed Transport Theory (Thermalization, "one-speed" thermal and fast neuts.)
  
Exact solutions in One-speed Transport Equation
  
Green's Functions for the Transport Equation
  
Reciprocity Theorems for the Transport Equation
  
The Multigroup Transport Equations
  
Fundamentals of Neutron Slowing-down Theory 7
Exact Solutions for Slowing-down in an Infinite Medium (Hydrogen, A>1 without absorption, hydrogen with a heavy absorber)
  
Approximate Solutions for Slowing-down in an Infinite Medium with Absorptic (Narrow resonance approximation, narrow resonance, infinite mass approximate slowly varying absorption, the Wigner and Greuling-Goertzel approximations)
  
Approximations to the One-speed, Multigroup and Continous Energy-dependent Transport Equations 6
Polynomial Expansions of the Angular Flux (PN and DPN approximations)
  
Diffusion Theory, Fundamental Mode Diffusion Theory
  
Asymptotic Transport Theory (BN approximation)
  
Direct Numerical Solutions 6
Algorithms for the One-speed and Multigroup Diffusion Equations
  
Algorithms for the Integro-differentia and the Integral Forms of the One-speed and Multigroup Transport Equations
  
Applications of Elementary Approximation Theory Techniques to the Neutron Transport Equation 8
Variational Methods, Linear Vector Space Methods, Weighted Residual Methods, Perturbation Theory
  
Special Cases (Multigroup equations, flux weighting, adjoint weighting, bilinear weighting, PN equations.
  
Combinations of Techniques in Practical Reactor Analysis 2
Multigroup Cross Section Sets
  
Calculations (Infinite medium, fundamental mode diffusion theory, asymptotic reactor theory, diffusion theory, transport
  
Group Collapsing of Cross Sections
  
Criticality Calculations
  
The Quasi-Static Method and Related Approximations
  
Synthesis Methods (Time Synthesis, Space-Time Synthesis)
  
Special methods for the Stiff Partial Differential Equations of Space-Time Kinetics
  
Advanced Topics (to be drawn from the subjects listed above and from current research) 5
Examinations 2
Total 45

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Basic Texts: Basic sources include the research papers published in journals together with ERDA R & D reports and overseas R & D reports from England, Germany, France & Italy.

Reference books:

  • B. Davison, "Neutron Transport Theory", 1958
  • Case and Zweifel, "Linear Transport Theory", 1967
  • Case deHoffman and Placzek, &qout;Introduction to the Theory of Neutron Diffusion", 1953
  • Bell and Glasstone, "Nuclear Reactor Theory", 1970
  • Ferziger and Zweifel, "The Theory of Neutron Slowing Down in Nuclear Reactors", 1966
  • Dresner, "Resonance Absorption in Nuclear Reactors", 1960
  • A. F. Henry, "Nuclear Reactor Analysis", 1975.

Prerequisites: NPRE 560, Reactor Kinetics and Dynamics; or Graduate standing in Physics; or consent of instructor.

Purpose of Course:

  • Prerequisite for NPRE 556, Reactor Theory II
  • Elective for Nuclear Engineering and other fields of engineering and science if the student meets the prerequisites.
  • This course is the first in a series of advanced level reactor physics and theory courses for graduate students who want advanced professional study and research preparation in the field of nuclear reactor analysis.

Instructor: Roy Axford

Credit:

Meeting hours per week: 3

Class registration opacity: 20

Semesters course offered: REFER TO MASTER LISTING

Other notes:

Course last revised:

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