nuclear fission elementary principles
DESCRIPTION
Mass defect & Binding energy ΔE = Δm c2TRANSCRIPT
Nuclear Fission elementary principles
BNEN 2015-2016 IntroWilliam D’haeseleer
Mass defect & Binding energy
ΔΔE = E = ΔΔm cm c22
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
Nuclear fission
Nuclear Fission + products
Ref: Duderstadt & Hamilton
BNEN NRT 2009-2010William D’haeseleer
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Practical Fission Fuels
1 10
A Az zn X X → fission
fissile
fissile
fissile
U-233U-235
Pu-239
Ref: Lamarsh NRT
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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)
23592 U
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Practical Fission Fuels
Fertile nuclei
Nuclei that are not easily “fissile” (see further)but that produce fissile isotopesafter absorption of a neutron
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Practical Fission Fuels
* Thorium-uranium
1 232 2330 90 90Th + Thn
23391Pa
β (22 min)
β (27 d)
23392 U
Fissile by slow (thermal) neutron
- not much used so far
- but large reserves of Th-232
- new interest because of ADS (cf. Rubbia)
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Practical Fission Fuels
* Uranium-Plutonium
1 238 2390 92 92U + Un
23993 Np
23994 Pu
β (23 min)
β (2.3 d)
Fissile by slow (thermal) neutron
- 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”
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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 --
BNEN NRT 2009-2010William D’haeseleer
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Practical Fission Fuels
1 10
A Az zn X X → fission
fissionable
fissionable
Th-232
U-238
Eth=0.6MeV
Eth=1.4 MeV
Fission Chain Reaction
Chain reaction235 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 subcritical
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
BNEN NRT 2009-2010William D’haeseleer
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Probability for fission
Comparison fission cross section U-235 and U-238 [Ref Krane]
Logarithmic scale !
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Cross Section of Fissionable Nuclei
• Thermal cross sectionImportant for “fissile” nuclei, is the so-called
thermal cross section
-- See Table 3.2 --
at 0.025 eVthf
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Cross Section of Fissionable Nuclei
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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
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Cross Section of Fissionable Nuclei
Define
capture to fission ratiof
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Cross Section of Fissionable Nuclei
U-235
α > 1 more chance for radiative capture
α < 1 more chance for fission
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Cross Section of Fissionable Nuclei
f
a f Note
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Cross Section of Fissionable Nuclei
Then with
Relative probability fission =
Relative probability rad. capture =
f
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f
f
1f
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
Fission products / fragments
Fission products / fragments
Fission products / fragments
Fission products / fragments
Fission products / fragments
Fission products generally radioactive
Dominantly neutron rich
Mostly β- decay
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The products of fission: neutrons
→ Besides fission also absorptionRecall
Therefore:
In U-235: 15% for low E1 n
1f
a
vv
f
See table 3.2
η=number of n ejected per n absorbed in the “fuel”
capture to fission ratiof
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The products of fission: neutrons
1f
a
vv
BNEN NRT 2009-2010William D’haeseleer
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The products of fission: neutrons
Ref: Duderstadt & Hamilton
1f
a
vv
η(E) for
U-233, U-235, Pu-239 & Pu-241
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The products of fission: neutrons
Ref: Duderstadt & Hamilton
1f
a
vv
To be compared with curve for α (cfr before)
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The products of fission: neutrons
η usually also defined for mixture U-235 and U-238
(25) (25)(25) (28)
f
a a
v
for material
for materialf i fi i
a i ai i
N i
N i
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 rate6
6 19
18 1
23
10 /10 1.6 10
6.25 10
5.4 10 fissions/day
R
R
R
P J sE J
P sE
PE
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/day1P gram/day
23 gram6.02 10A
0.895 gram/day
R
PAE
! For a reactor of 1 MW, 1 gram/day U-235 will be fissioned !! 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
0.895 gram/dayR
PAE
Amount of fuel fissioned
Total absorption rate = fission ratea
f
1 fission rate
Reactor power & burn upconsumption rate
Energy “production” per fissioned amount of fuel:also often called Burn UpBurn Up: MWD/tonMWD/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
0.895 1 gram/dayR
PAE
Actinide Buildup [Ref: CLEFS CEA Nr 53]
Total U 955 746 941 026 923 339
Total Pu 9 737 11 338 13 000
Composition of spent fuel
• Typical for LWR:
Fission Products [Ref: CLEFS CEA Nr 53]
TOTAL 33,6 46,1 61,4
Fission Products [Ref: CLEFS CEA Nr 53]
FP 33.6 46.1 61.4
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
TOTAL 999.083 998.464 997.739
Remainder converted to energy via E=∆m c2
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
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”
Delayed neutrons
• Small amount of delayed neutrons suffices (fraction ~0.0065) to allow appropriate control of reactor
• Easy to deal with perturbations