1. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 1 One-speed neutron diffusion in a finite medium Steady State Diffusion Equation A B At the interface What if A or B is a vacuum? Linear extrapolation distance. x

2. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 2 One-speed neutron diffusion in a multiplying medium More realistic multiplying medium The reactor core is a finite multiplying medium. Neutron flux? Reaction rates? Power distribution in the reactor core? Recall: Critical (or steady-state): Number of neutrons produced by fission = number of neutrons lost by: absorption and leakage

3. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 3 More realistic multiplying medium Steady state homogeneous reactor Material buckling For a critical reactor: K eff = 1 K  > 1 Recall: multiplying medium Things to be used later…!

4. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 4 More on One-Speed Diffusion HW 20 critical homogeneous reactor Show that for a critical homogeneous reactor Infinite Bare Slab Reactor (one-speed diffusion) x a a/2 d d a 0 /2  Vacuum beyond. Return current = 0. d = linear extrapolation distance = 0.71 tr (for plane surfaces) = 2.13 D. z Reactor

5. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 5 HW 21 For the infinite slab. Show that the general solution with BC’s Flux is symmetric about the origin.  More on One-Speed Diffusion

6. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 6 HW 21 (continued) Fundamental mode, the only mode significant in critical reactors. For a critical reactor, the geometrical buckling is equal to the material buckling. To achieve criticality More on One-Speed Diffusion

7. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 7 More on One-Speed Diffusion To achieve criticality But criticality at what power level??  0 can not be determined by the geometry alone. Do it.

8. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 8 More realistic multiplying medium The buckling is a measure of extent to which the flux curves or “buckles.” For a slab reactor, the buckling goes to zero as “a” goes to infinity. There would be no buckling or curvature in a reactor of infinite width. Buckling can be used to infer leakage. The greater the curvature, the more leakage would be expected.

9. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 9 Spherical Bare Reactor (one-speed diffusion) Minimum leakage  minimum fuel to achieve criticality. r0r0  HW 22  Continue! Reactor More on One-Speed DiffusionCubeSphere r

10. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 10 HW 23 Infinite planer source in an infinite medium. x a a/2 a 0 /2 Source HW 24   More on One-Speed Diffusion Infinite planer source in a finite medium.

11. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 11 More on One-Speed Diffusion Infinite planer source in a multi-region medium. FiniteInfinite Project 2

12. Nuclear Reactors, BAU, 1st Semester, 2008-2009 (Saed Dababneh). 12 Back to Multiplication Factor k  = fp ,  Fast from thermal, Fast from fast, . Thermal from fast, p. Thermal available for fission Thinking QUIZ For each thermal neutron absorbed, how many fast neutrons are produced? Recall: Things to be used later…!