Catalog Description: Particle transport, theories of diffusion, numerical analysis of diffusion, transient core analysis. Pr.: NE 630

Instructor: J. K. Shultis, Office WD-125, (913) 532-5626; e-mail jks@ksu.edu

Textbook: J.J. Duderstadt and L.J. Hamilton, Nuclear Reactor Analysis, Wiley, New York, 1976.

Prerequisites: Knowledge of (1) neutron-particle interactions, (2) basic nuclear science, (3) the one-speed diffusion equation and its analytic solutions in simple geometries, (4) Fermi-age slowing down theory, (5) six-factor formula for keff, (6) a programming language.

Course Goals: Understanding of the rigorous development of neutron transport and the diffusion approximation. Understanding of the different numerical techniques used in the modern analysis of large reactor cores.

Topics:

1. Introduction:   Review of radioactivity, cross sections, neutron kinematics, and the neutron cycle (if necessary) Overview of basic approaches to quantify the neutron field Limitations and advantages of different neutron transport methods

2. Monte Carlo Approach:   Uniformly distributed random numbers and their generation Picking random numbers with a specified distribution Estimating keff for a slab reactor by Monte Carlo Statistical analysis of Monte Carlo results

3. Deterministic Transport Theory:   Assumptions and definitions Derivation of the linearized Boltzmann equation Integral form of the transport equation Numerical solution of the one-speed integral transport equation Fixed-source and criticality problems Exact results for critical slab reactor using one-speed model

4. Origins of Diffusion Theory:   Derivation of diffusion equation from transport equation Generalized Fick's Law Fick's law for special cases Boundary conditions for the diffusion approximation

5. One-Speed Diffusion Model:   Analytical Approaches Review of analytical solutions in basic geometries Analytical methods for the fixed-source problem Reciprocity theorem

6. One-Speed Diffusion Model:   Numerical Approaches Overview of fixed-source and critical problems Finite difference approximation in 1-D Finite difference approximation in multi-dimensions Tri-diagonal algorithm for 1-D fixed-source problems Iterative algorithms for multi-D fixed-source problems Criticality problems and the power method Perturbation techniques for reactivity changes

7. Multigroup Diffusion Theory:   Derivation of multigroup diffusion equation Generation of multigroup cross sections and related parameters Infinite medium diffusion theory - fine group calculations Finite medium calculations: few group theory and numerical approaches Adjoint multigroup analysis and multigroup perturbation theory Flux synthesis method

8. Slowing Down Calculations:   Infinite-medium slowing down spectra and resonance interactions Finite-medium calculations based on E-dependent diffusion theory Greuling-Goertzel, Consistent P1, and Fermi-age approximations Solution of slowing down equations; MUFT-GAM algorithm.

Evaluations:

Besides participation in class discussions, your grade will be based primarily on how well you complete the roughly biweekly problem assignments. Each assignment requires an individual formal writeup. An assignment grade will be based not only on the correctness of the results, but also on the completeness of the writeup and the discussion of the results. I expect to see originality in your work with your writeups including results and analyses of issues not specifically requested. Finally, you are expected to treat your assignments with a professional attitude by meeting the time deadlines assigned. There will be no examinations in this class.