1. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 1 Reactor Model: One-Group That was for the bare slab reactor. What about more general bare reactor models? For steady state, homogeneous model: BC:  (extrapolated boundary) = 0.

2. R 0, H 0 are the extrapolated dimensions. BC’s: Let Solve the problem and discuss criticality condition. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 2 Reactor Model: One-Group cosBessel HW 26 Reactor R H z x y r 

3. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 3 Reactor Model: One-Group Reactor R H Briefly, we go through HW 26. z x y r 

4. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 4 Reactor Model: One-Group

5. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 5 Reactor Model: One-Group Reactor R H z x y r   Criticality condition? Do it.

6. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 6 Reactor Model: One-Group R0R0 H 0 /2

7. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 7 Reflected Slab: One-Group x a a/2 Core z Reflected Slab Reactor bb Reflector For steady-state, homogeneous, 1-D C  Core R  Reflector Recall:

8. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 8 Verify.  BC  Reflected Slab: One-Group

9. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 9 Criticality condition. For bare slab CC was  / 2. Smaller core for reflected reactor (even with a 0 > a). Save fuel. Reflected Slab: One-Group

10. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 10 Criticality “Calculation” Can we solve “real” reactor problems analytically? computational techniques. The previous discussion provides understanding of the concepts but also indicates the need for computational techniques. Assume: Adjust parameters so that = 0 (Steady-state). What parameters and how to adjust them? 

11. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 11 Criticality “Calculation” Fixed design and geometry  one free variable is k As we did earlier (be guided by HW 20): As we did earlier (be guided by HW 20):

12. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 12 Criticality “Calculation” Build an algorithm. “Guess” (reasonably) initial k fudge and  (or  ) for the zeroth iteration. Calculate the initial source term. Iterate:

13. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 13 Criticality “Calculation” Or: If for example k > 1, take action to reduce source or increase absorption. How? How?

14. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 14 Reactor Kinetics Reactor kinetics refers to the manipulation of parameters that affect k and to the subsequent direct response of the reactor system. Examples are: Absorber rods or shim movements to compensate for fuel burnup. Safety scram rods to rapidly shutdown the chain reaction. Control rods to provide real-time control to keep k = 1 or to maneuver up and down in power. ….. Reactor Dynamics Reactor dynamics refers to the more indirect feedback mechanisms due to power level effects and other overall system effects such as: Temperature feedback. Void Void feedback. Pump speed control (affects water density and temperature). … How to Adjust Criticality reactivity. Negative or positive reactivity.

15. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 15 How to Adjust Criticality Before all: Core Design The transient response of the reactor to the above direct and indirect changes in basic parameters is highly dependent on the design details of the reactor. Sample issues are: Where should the control rods be placed for maximum effectiveness? Will the power go up or down if a void is introduced into the reactor? Will the power go up or down if core temperature goes up? How often should the reactor be refueled? and so on...

16. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 16 Multi-group Model Wide neutron spectrum. One-group, two-group? Should be generalized. Identify the terms, NOW. Fraction of an eV Flux-averaged quantities.

17. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 17 Multi-group Model Total fission Fraction Scattering in Other sources Leakage Scattering out Absorption Fraction of an eV

18. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 18 Multi-group Model 5-group example. Maxwellian 1/E Fission

19. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 19 Multi-group Model Total fission Thermal fission (~ 97%) Fast fission (~ 3%)

20. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 20 Multi-group Model Scattering in Upscattering!!??? Skipping!!???

21. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 21 Multi-group Model Scattering out

22. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 22 Multi-group Model Group 3 Removal cross section

23. Nuclear Reactor Theory, JU, First Semester, 2010-2011 (Saed Dababneh). 23 Multi-group Model Total fission Fraction Scattering in Other sources LeakageRemovalIn-group Scattering Net Scattering in