Catalog Description: Theory of diffusion and slowing down of neutrons with application to critical and subcritical nuclear reactors. Pr.: NE 520

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

Textbook: Lamarsh, J.R., Introduction to Nuclear Reactor Theory, Addison-Wesley, Reading, Mass. 1966. This book is now available through the American Nuclear Society.

Prerequisites: (1) Basic nuclear science including radioactivity, neutron interactions, and reaction kinematics. (2) Mathematical analysis through solution of ordinary and simple partial differential equations

Topics:

1. Introduction (3 hours):   Review of ordinary differential equations Review of reaction rates, cross sections and nuclear reactions Review of fission mechanism, cross sections and energetics Neutron chain reactions, criticality and keff

2. Diffusion of One-Speed Neutrons:   Description of neutron field; uncollided flux (1 hour) Derivation of diffusion equation and Fick's law (2 hours) Boundary conditions for the diffusion equation (1 hour) Methods for solving diffusion equation; examples (8 hours) (i) variation of constants (ii) Green's function approach (iii) eigenfunction expansion technique Physical significance and measurement of diffusion length; reciprocity theorem (1 hour)

3. Neutron Slowing Down:   Review of scattering kinematics (2 hours) Moderation in hydrogen without absorption (1 hour) Moderation for A>1 without absorption (2 hours) Fermi-age theory for moderation in finite medium (2 hours) Slowing down with absorption (1 hour)

4. Description of Thermal Neutrons:   Thermal equilibrium and Maxwellian spectrum (1 hour) Reaction rates for thermal neutrons (2 hours) Diffusion of thermal neutrons (1 hour) Neutron lifetimes (1 hour) Measurement of thermal neutron parameters (1 hour)

5. Multiplying Media and Reactor Criticality:   Diffusion and slowing down with multiplication (1 hour) Harmonics and time-dependent solution; buckling (2 hours) Criticality for bare reactors (1 hours) Minimum critical mass, size and composition (1 hour) Effect of reflectors (2 hour) Effect of heterogeneous cores (1 hour)

6. Reactivity Feedback:   Effects Temperature feedback (1 hour) Fuel and fission product poisons (2 hours) Delayed neutrons and reactor kinetics (intro) (1 hour)

Evaluations:

You will be assigned to a small group with which you will participate in (1) completing the bi-weekly homework assignments and (2) completing the exercises assigned in class. Each group will submit a single report for each assignment signed by all members of the group. There will be short (15 minute) in-class quizzes on the days homework assignments are due. These quizzes will generally be on some topic related to the homework or to a recently assigned exercise.

Exams and Quizzes:  In addition to the inclass quizzes, there will be a midterm and a final exam.

Grades will be assigned on the basis of a weighted average of scores from group assignments and individual efforts (exams and quizzes). Typically 50-70% of your grade will be from your individual scores and the remainder from the greater of your group scores or your individual scores.