nuclear fission elementary principles

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Mass defect & Binding energy ΔE = Δm c2


Nuclear Fission elementary principles
BNEN Intro William Dhaeseleer Mass defect & Binding energy
E = m c2 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 3 prompt neutrons released upon fission Nuclear fission Nuclear Fission + products
Ref: Duderstadt & Hamilton Practical Fission Fuels
Ref: Lamarsh NRT fissile U-233 fissile U-235 fissile Pu-239 BNEN NRT William Dhaeseleer Practical Fission Fuels
From these, onlyappears 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) Practical Fission Fuels
Fertile nuclei Nuclei that are not easily fissile (see further) but that produce fissile isotopes after absorption of a neutron Practical Fission Fuels
* Thorium-uranium (22 min) (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 Practical Fission Fuels
* Uranium-Plutonium (23 min) (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 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 Practical Fission Fuels
Eth=1.4 MeV fissionable Th-232 U-238 fissionable Eth=0.6MeV BNEN NRT William Dhaeseleer Fission Chain Reaction
235 U 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 more chance for radiative capture U-235 < 1 more chance for fission Cross Section of Fissionable Nuclei
Note Cross Section of Fissionable Nuclei
Then with Relative probability fission = Relative probability rad. capture = Thermal reactors Belgian fission reactors are thermal reactors
Neutrons, born with =2MeV to be slowed down to ~ eV By means of moderator: Light material: hydrogen, deuterium, water graphite Fission products / fragments Fission products / fragments Fission products / fragments Fission products / fragments Fission products / fragments
Fission products generally radioactive Dominantly neutron rich Mostly - decay The products of fission: neutrons
Besides fission also absorption Recall Therefore: See table 3.2 =number of n ejected per n absorbed in the fuel The products of fission: neutrons The products of fission: neutrons
(E) for U-233, U-235, Pu-239 & Pu-241 BNEN NRT William Dhaeseleer Ref: Duderstadt & Hamilton The products of fission: neutrons
To be compared with curve for (cfr before) Ref: Duderstadt & Hamilton The products of fission: neutrons
usually also defined for mixture U-235 and U-238 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 Production of transurans
Evolution of 235U content and Pu isotopes in typical LWR Production of transurans Reactor power & burn up Fission Rate = # fissions per second
given: a reactor producing P MW fission rate 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 ! Reactor power & burn up Hence, burn up But fuel consumption is larger
because of radiative capture Amount of fuel fissioned 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 only8 x 105 MWD/ton - but also U-238 in fuel in practice ~20 to 30 x 10 MWD/ton (however, recently more) ~ 50 to 60 x 103 MWD/ton Actinide Buildup [Ref: CLEFS CEA Nr 53]
Total U Total Pu Composition of spent fuel
Typical for LWR: Fission Products [Ref: CLEFS CEA Nr 53]
TOTAL , ,161,4 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 Delayed neutrons Recall 2 3 prompt neutrons, released after ~10-14 sec Thermalized after ~1 sec Absorption after ~200 s ~ 10-4 s Difficult to control Nature has foreseen solution! Delayed Neutrons Recall decay from some fission products Neutron emission after decay
After decay, if energy excited state daughter larger than virtual energy (binding energy weakest bound neutron) in neighbor: Then n emission rather than emission Called delayed neutrons 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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