1. Nuclear Fission elementary principles
BNEN Intro
William D’haeseleer

2. Mass defect & Binding energy
ΔE = Δm c2

3. Nuclear Fission Heavy elements may tend to split/fission
But need activation energy to surmount potential barrier
Absorption of n sufficient in
233U 235U 239Pu … fissile nuclei
Fission energy released ~ 200 MeV
Energetic fission fragments
2 à 3 prompt neutrons released upon fission

4. Nuclear fission

5. Nuclear Fission + products
Ref: Duderstadt & Hamilton

6. Practical Fission Fuels
Ref: Lamarsh NRT
fissile
U-233
fissile
U-235
fissile
Pu-239
BNEN NRT
William D’haeseleer

7. Practical Fission Fuels
From these, only appears in nature (0.71%)
The other fissile isotopes must be “bred”
out of Th-232 (for U-233)
out of U-238 (for Pu-239)

8. Practical Fission Fuels
Fertile nuclei
Nuclei that are not easily “fissile” (see further)
but that produce fissile isotopes
after absorption of a neutron

9. Practical Fission Fuels
* Thorium-uranium
β (22 min)
β (27 d)
- not much used so far
- but large reserves of Th-232
- new interest because of ADS (cf. Rubbia)
Fissile by slow (thermal) neutron

10. Practical Fission Fuels
* Uranium-Plutonium
β (23 min)
β (2.3 d)
- up till now mostly used for weapons
- is implicitly present in U-reactors
- now also used as MOX fuels
- the basic scheme for “breeder reactors”
Fissile by slow (thermal) neutron

11. Practical Fission Fuels
Fissionable nuclei
Th-232 and U-238 fissionable with threshold energy
U-233, U-235 & Pu 239 easily fissionable = “fissile”
-- see Table

12. Practical Fission Fuels
Eth=1.4 MeV
fissionable
Th-232
U-238
fissionable
Eth=0.6MeV
BNEN NRT
William D’haeseleer

13. Fission Chain Reaction
235 U

14. Fission Chain Reaction
k= multiplication factor
k= (# neutrons in generation i) /
(# neutrons in generation i-1)
k=1  critical reactor
k>1  supercritical
k<1 subcritical

15. Critical mass
Critical mass is amount of mass of fissile material, such that
Neutron gain due to fission =
Neutron losses due to leakage & absorption
Critical mass
= minimal mass for stationary fission regime

16. Probability for fission
Logarithmic scale !
Comparison fission cross section U-235 and U-238 [Ref Krane]
BNEN NRT
William D’haeseleer

17. Cross Section of Fissionable Nuclei
Thermal cross section
Important for “fissile” nuclei, is the so-called
thermal cross section
-- See Table

18. Cross Section of Fissionable Nuclei

19. Cross Section of Fissionable Nuclei
Absorption without fission
σγ for these nuclei ~ other nuclei
 behaves like 1/v for small v
at low En, inelastic scattering non existing
 only competition between -fission
-radiative capture

20. Cross Section of Fissionable Nuclei
Define

21. Cross Section of Fissionable Nuclei
α > 1 more chance for radiative capture
U-235
α < 1 more chance for fission

22. Cross Section of Fissionable Nuclei
Note

23. Cross Section of Fissionable Nuclei
Then with
Relative probability fission =
Relative probability rad. capture =

24. Thermal reactors Belgian fission reactors are “thermal reactors”
Neutrons, born with <E>=2MeV to be slowed down to ~ eV
By means of moderator:
Light material: hydrogen, deuterium, water
graphite

25. Fission products / fragments

26. Fission products / fragments

27. Fission products / fragments

28. Fission products / fragments

29. Fission products / fragments
Fission products generally radioactive
Dominantly neutron rich
Mostly β- decay

30. The products of fission: neutrons
→ Besides fission also absorption
Recall
Therefore:
See table 3.2
η=number of n ejected per n absorbed in the “fuel”

31. The products of fission: neutrons

32. The products of fission: neutrons
η(E) for
U-233, U-235, Pu-239 & Pu-241
BNEN NRT
William D’haeseleer
Ref: Duderstadt & Hamilton

33. The products of fission: neutrons
To be compared with curve for α (cfr before)
Ref: Duderstadt & Hamilton

34. The products of fission: neutrons
η usually also defined for mixture U-235 and U-238

35. Enrichment Natural U consist of 99.3% 238U & 0.7% 235U
NU alone cannot sustain chain reaction
NU in heavy water moderator D2O can be critical (CANDU reactors)
Light water (H2O) moderated reactors need enrichment of fissile isotope 235U
Typically in thermal reactors 3-5% 235U enrichment
For bombs need > 90% enrichment

36. Production of transurans
Evolution
of 235U content
and Pu isotopes
in typical LWR

37. Production of transurans

38. Reactor power & burn up ● Fission Rate = # fissions per second
given: a reactor producing P MW
fission rate

39. Reactor power & burn up ● Burn up
= amount of mass fissioned per unit time
 Burn up = fission rate * mass of 1 atom
Burn up =
for A = 235 ; ER = 200 MeV … Burn Up = 1P gram/day
! For a reactor of 1 MW, 1 gram/day U-235 will be fissioned !

40. Reactor power & burn up Hence, burn up But fuel consumption is larger
→ because of radiative capture
Amount of fuel fissioned

41. Reactor power & burn up ~ 50 to 60 x 103 MWD/ton consumption rate
Energy “production” per fissioned amount of fuel:
also often called Burn Up: MWD/ton
- assume pure U-235, and assume that all U-235 is fissioned;
- then: energy “production” 1MWD/g = 106 MWD/ton
- but also radiative capture only 8 x 105 MWD/ton
- but also U-238 in “fuel”  in practice ~ 20 to 30 x 10³ MWD/ton
(however, recently more)
~ 50 to 60 x 103 MWD/ton

42. Actinide Buildup [Ref: CLEFS CEA Nr 53]
Total U
Total Pu

43. Composition of spent fuel
Typical for LWR:

44. Fission Products [Ref: CLEFS CEA Nr 53]
TOTAL , ,1 61,4

45. Fission Products [Ref: CLEFS CEA Nr 53]
Category UOX 33 GWa/tUi UOX 45 GWa/tUi UOX 60 GWa/tUi
Enr 3.5% Enr: 3.7% Enr: 4,5%
Amount kg/tUi Amount kg/tUi Amount kg/tUi
Uranium
Plutonium FP
TOTAL
Remainder converted to energy via E=∆m c2

46. Delayed neutrons
Recall 2 à 3 prompt neutrons, released after ~10-14 sec
Thermalized after ~1 μsec
Absorption after ~200 μs ~ 10-4 s
Difficult to control
Nature has foreseen solution! Delayed Neutrons
Recall β decay from some fission products

47. Neutron emission after β decay
After β decay, if energy excited state daughter larger than “virtual energy” (binding energy weakest bound neutron) in neighbor:
Then n emission rather than γ emission
Called “delayed neutrons”

48. Delayed neutrons
Small amount of delayed neutrons suffices (fraction ~0.0065) to allow appropriate control of reactor
Easy to deal with perturbations