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Nuclear Fission elementary principles

Nuclear Fission elementary principles. BNEN 2012-2013 Intro William D’haeseleer. Mass defect & Binding energy. Δ E = Δ m c 2. Nuclear Fission. Heavy elements may tend to split/fission But need activation energy to surmount potential barrier Absorption of n sufficient in

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Nuclear Fission elementary principles

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  1. Nuclear Fission elementary principles BNEN 2012-2013 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 →fission Ref: Lamarsh NRT fissile U-233 fissile U-235 fissile Pu-239 BNEN NRT 2009-2010 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 3.1 --

  12. Practical Fission Fuels →fission Eth=1.4 MeV fissionable Th-232 U-238 fissionable Eth=0.6MeV BNEN NRT 2009-2010 William D’haeseleer

  13. Fission Chain Reaction 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 2009-2010 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 3.2 --

  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 ~ 0.025 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 2009-2010 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 consumption rate Energy “production” per fissioned amount of fuel: MWD/tonne - assume pure U-235, and assume that all U-235 is fissioned; - then: energy “production” 1MWD/g = 106 MWD/tonne - but also radiative capture only 8 x 105 MWD/tonne - but also U-238 in “fuel”  in practice ~ 20 to 30 x 10³ MWD/tonne (however, recently more) ~ 50 to 60 x 103 MWD/tonne

  42. Actinide Buildup [Ref: CLEFS CEA Nr 53] Total U 955 746 941 026 923 339 Total Pu 9 737 11 338 13 000

  43. Composition of spent fuel • Typical for LWR:

  44. Fission Products [Ref: CLEFS CEA Nr 53] TOTAL 33,6 46,1 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 955.746 941.026 923.339 Plutonium 9.737 11.338 13.0 FP 33.6 46.1 61.4 TOTAL 999.083 998.464 997.739 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: Thenn emissionrather thanγ 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

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