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

Text: Hetrick, D.L., Dynamics of Nuclear Reactors, Univ. of Chicago Press, Chicago, IL 1971. This book is now available from the American Nuclear Society.

Prerequisites: (1) Basic nuclear science including radioactivity, neutron interactions, and reaction kinematics. (2) Mathematical analysis through solutions to ordinary differential equations. (3) Reactor statics and neutron diffusion theory.

Topics:

1. Dynamics of reactors without delayed neutrons (1 hour)

2. Delayed neutrons.  Properties and importance (2 hours)

3. Point reactor kinetics equation without feedback.  Derivation of PRKE; alternate forms of PRKE; inverse method of solution--importance for safety analyses; review of Fourier and Laplace transforms; solution for step input; the inhour equation; reactivity and reactor period (7 hours)

4. Linearized Point Reactor Kinetics Equation.  Linearization of kinetic equations; Laplace transform solution of linearized PRKE; response to sinusoidal, step, and impulse reactivity inputs; transfer function and Bode plots; generalization to any linear system (6 hours)

5. Feedback and subsystem description.  Feedback mechanisms and representation by subsystems subsystem descriptions; combining subsystems in the t-domain and s-domain; importance of transfer functions; reactor feedback and generalized linear functional approach; reactor transfer function with feedback (6 hours)

6. Design and analysis of stable linear systems.  Stability definitions and relation to system transfer function; Routhe-Hurwitz and Routhe analytical stability methods; Pontryagin's analytical stability method; Root locus graphical method; Nyquist graphical method (12 hours)

7. Design of stable nuclear reactors.  One-temperature feedback model; dual temperature feedback models; fission product poison feedback; poison plus temperature feedback; xenon spatial oscillations; large core and coupling coefficients (8 hours)

Homework and Exams: The will be a midterm and a final exam. Homework assignments will be given every two weeks. Although I encourage you to work together on the homework, individual effort is required for homework writeups. A professional homework writeup is expected.