1. More on One-Speed Diffusion
Spherical Bare Reactor (one-speed diffusion)
Cube
Sphere
Minimum leakage  minimum fuel to achieve criticality. 
HW 22 r 
Reactor
Continue! r0
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

2. More on One-Speed Diffusion
HW 23
Infinite planer source in an infinite medium.  
HW 24 ?
Infinite planer source in a finite medium. x
a/2 a
a0/2
Source
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

3. More on One-Speed Diffusion
Infinite planer source in a multi-region medium.
Infinite
Finite
Infinite 
Project 2
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

4. Back to Multiplication Factor
Things to be used later…!
Recall:
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:
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

5. Two-Group Neutron Diffusion
Introductory to multi-group (Hence crude).
All neutrons are either in a fast or in a thermal energy group.
Boundary between two groups is set to ~1 eV.
Thermal neutrons diffuse in a medium and cause fission, are captured, or leak out from the system.
Source for thermal neutrons is provided by the slowing down of fast neutrons (born in fission).
Fast neutrons are lost by slowing down due to elastic scattering in the medium, or leak out from the system, or due to fission or capture.
Source for fast neutrons is thermal and fast neutron fission.
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

6. Two-Group Neutron Diffusion
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

7. Fast Two-Group Neutron Diffusion or Fast diffusion coefficient
Depends on thermal and fast fluxes.
Removal cross section = fission + capture + scattering to group 2 or
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

8. Thermal Two-Group Neutron Diffusion or
Thermal absorption cross section = fission + capture.
Thermal diffusion coefficient
Depends on fast flux. or
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

9. Two-Group Neutron Diffusion
A coupled system of equations; both depend on both fluxes.
Recall also, for a steady state system:
Geometrical
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

10. Two-Group Neutron Diffusion
Homogeneous system  Determinant of coefficients matrix = 0
Review Cramer’s rule!
Do we need it here?
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

11. Two-Group Neutron Diffusion
keff for a critical reactor
For large reactors
Migration Length
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

12. Do it. Two-Group Neutron Diffusion If any  leakage .
Slowing down density.
Fermi model.
Do it.
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

13. Reactor Model: One-Group
Before considering multi-group.
So far we did 1-D.
Back to one-group but extend to 3-D. z 
HW 21|
Reactor
For the homogeneous infinite slab reactor, extend the criticality condition that you found in HW 21. x
a/2 a
a0/2 d d
1-D
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

14. Reactor Model: One-Group
In 3-D   
Critical dimensions (size), for the given material properties, predicted by the model.
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

15. Reactor Model: One-Group
Transient case.
Delayed neutrons!!
Reflectors!!
For homogeneous 1-D:
t !
t !
Moderator, structure, coolant, fuel, …
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

16. Reactor Model: One-Group
HW 25
Separation of variables:
= 0 for steady state.
Show that
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

17. Reactor Model: One-Group
HW 25 (continued)
try
eigenvalues
Solution
Initial condition
Show that ? ?
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

18. Reactor Model: One-Group 
Slowest decaying eigenvalue. 
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).

19. Reactor Model: One-Group
For steady state 
Criticality
Super criticality
LE 
Sub criticality
LE 
Nuclear Reactor Theory, JU, First Semester, (Saed Dababneh).