Fission.. 1
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Lesson 2: Fission Characteristics, Nuclear Fuels, Neutron Cross-sections
Historical background
Fission products
Fission neutrons, Fission spectrum
Chain reaction
Delayed neutrons, neutron precursor characteristics
Fission energy, decay (residual) heat
Nuclear fuels, fuel burnup
Neutron cross-sections (low, intermediate, “high” energies)
Fission.. 2
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fission: History - 1
Following the discovery of the neutron • Fermi studied the “activation” of the elements (neutron capture)
ZXA + 0n1→ ZXA+1 → (β--decay) → Z+1YA+1 + γ … artificial radioactivity
– each time, one observed a “transmutation”
– occurred more easily if the neutron was first “slowed down”
With U (Z = 92), one expected to create “transuranics” (Z = 93, 94,…)
• Instead, one (initially) found nuclei of intermediate mass (e.g. Ba, Z = 56)
Fission.. 3
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fission: History - 2
Otto Hahn and Fritz Strassmann provided the explanation (1939)
• The U235 nucleus can be split into 2 fragments (discovery of fission)
92U235 + 0n1→ 2 FP’s + ν. 0n1 + 207 MeV
• The emission of ν(bar), i.e. ∼2.5, neutrons gave the possibility of a chain reaction
(Neutron “excess” ∼ related to shape of the Z-vs.-N curve of the nuclide chart)
Fission.. 4
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fission Products - 1
Asymmetric splitting, more probable
Considering FP’s from 100 fissions
• Yield y(A), with Sum [y(Ai)] = 200
• y(A) vs. A: “double-hump” curve
• Most probable, FPs with Ai ∼ 94, 140
e.g. 92U235 + 0n1→ 38Sr94 + 54Xe140+ 2 0n1
Fission.. 5
Laboratory for Reactor Physics and Systems Behaviour
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Fission Products - 2
The FP’s are unstable (excess of n’s)
• β--radioactivity (increases Z/N), e.g.
54Xe140 →(16s) 55Cs140 →(66s) 56Ba140 →(12.8d) 57La140 →(40h) 58Ce140 (stable)
Radioactivity of FP’s problematic
• Radiation protection (irradiated fuel)
• Residual heat after reactor shutdown
Fission.. 6
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fission Product “Poisoning”
For a power reactor, accumulation of FP’s influences the neutron balance
Special case: Xe135 with (σa)th ∼ 3.106 b! 52Te135→(2min) 53I135 →(6.6h) 54Xe135 →(9.1h) 56Cs135 →(3.106y)
• Yield, y(Te+I) ∼ 6%… quite high due to proximity to hump at A ∼ 140) • Following the start-up of a reactor, there is an equilibrium situation: dNx/dt = 0 = Production - Destruction = [y.(Φ. σa .Nf)] - [(λx Nx + (Φ. σx .Nf )]
⇒ Nx/Nf = [y.σa/σf)] / [1 + (λx/Φ. σx)]
Xe135 poisoning depends strongly on Φ: • Fraction of absorptions negligible for Φ < 1011 … 2 to 4% for Φ > 1014 (n/cm2)
Other FP’s less important (for a thermal reactor)
Fission.. 7
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fission Neutrons
Most are “prompt”, a small fraction are “delayed”
ν neutrons created per fission (number varies between ∼ 0 and 5, per event)
ν always expressed as an average, depends on nuclide and neutron energy ν = ν0 + a.E … a in MeV-1 , e.g.
• ν nearly constant at low energies • For a mixture of nuclides, e.g. 92U235, Pu239… νeff = Sum(νiΣfi) / Sum(Σfi)
Nuclide ν0 a
92U235… for E ≤ 1MeV 2.43 0.065
92U235 … for E > 1MeV 2.35 0.150
94Pu239… for E ≤ 1MeV 2.87 0.148
94Pu239… for E > 1MeV 2.92 0.133
Fission.. 8
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fission Spectrum
Energy of the fission neutrons varies… Spectrum χ(E)
For prompt neutrons (U235):
E for χmax ∼ 0.75 MeV
Eaverage: (value for Pu239 slightly higher)
“Slowing down factor” in a thermal reactor > 107! (∼ 2 MeV to 0.0253 eV) • Moderators needed (light nuclei: H2O, graphite,…)
Fission.. 9
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Chain Reaction
If each absorption were “useful”…
⇒ Reaction strongly divergent
In practice, certain neutron are lost
⇒ Captures, Leakage
For a self-sustaining reaction (static neutron flux)
Productions = Losses = Absorptions + Leakage
(criticality condition)
For a supercritical system, the neutron flux increases exponentially
Fission.. 10
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Delayed Neutrons
Small fraction of the neutrons, not prompt (~ 0.6% for U235) • Produced by disintegration of FP’s, e.g.
Many different “precursors”
• ~ 6 groups (of precursors, i.e. of delayed neutrons)
• yi, Ti ⇒ βi, λi (i = 1,6)
created “with delay” ↓
Fission.. 11
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Delayed Neutron Parameters
(U235)
- Eavg of delayed n’s ~ 0.4MeV
- λi’s relatively constant
- βi’s depend on nuclide, e.g.
β = Sum (βi) = 0.21% for Pu239
= 0.26% for U233 … other “fissiles”
- β small, but very important for control of the chain reaction ⇒ kinetic behaviour
- Response of a reactor which becomes slightly supercritical, much slower
Gp. Precursors T1/2 (s) λi (s-1) βi (%)
Fission.. 12
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fission Energy
Most, absorbed in the fuel ~ 180 to 190 MeV (FP’s, β-’s, part of γ’s ), in
form of heat (recovered by coolant)
Following reactor shutdown • Component “FP-radioactivity” remains
~ 7% immediately after shutdown • Slow decrease ~ 1% after 1 day
(Very important factor for nuclear safety)
Components Released (MeV)
Recover-able (MeV)
FP’s 168 168
n’s 5 5
Prompt γ’s 7 7
FP-radioactivity (β-) 8 8
FP-radioactivity (γ) 7 7
Neutrinos 12 -
Capture γ’s - 5 to 10
TOTAL ~ 207 200 to 205
Fission.. 13
Laboratory for Reactor Physics and Systems Behaviour
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“Decay Heat"
The released “FP-radioactivity” energy depends on the FP’s accumulated • Short-lived ones are soon in equilibrium • Presence of others depends on duration of reactor operation
Following shutdown, the latter are the ones remaining longer
Energy release rate, P
- P0 (nominal power)
- T (irradiation time)
- t (time after shutdown)
Empirical curves (for different T’s) 1 h 1 d 1mth
Fission.. 14
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Nuclear Fuels
U, Th : the 2 “natural” nuclear fuels
Only U contains fissile material (can be fissioned by slow neutrons) • U235… ~ 0.7 % Unat
Rest of Unat (~ 99.3 %… U238 ), as also Th (100%… Th232 ), are fertile • Give rise, via neutron capture, to the “artificial” fissile istopes: Pu239, U233
92U238 + 0n1 → 92U239 → 93Np239 → 94Pu239
92Th232 + 0n1 → 90Th233 → 91Pa233 → 92U233
Like U235, Pu239 and 233 U have high σf values for slow (thermal) neutrons
They are radioactive (α): T1/2’s ~ 2.4.104y (Pu239), 1.6.105y (U233)
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Fission.. 15
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Fuel Burnup
Fission of 1g of U235 (about the same for 1g of Pu239 or U233)
= [(6.023.1023) / 235] fissions . 200 MeV/fission . (1.6.10-13 J/MeV) = 8.2.1010 J ~ 1 MWd
( >106 x Energy liberated by the burning of 1g of carbon.. )
Unit of combustion for nuclear fuel… burnup : MWd/t (of fuel)
If one could fission all the atoms, burnup ~ 106 MWd/t
Usually, <10% of the mass is “fissile” ⇒ burnup <100,000 MWd/t
In practice, materials effects of irradiation more restrictive • Change of microscopic structure (radiation damage)
Fission.. 16
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Neutron Cross-sections… U235 σf, σt
thermal “resonance” (epithermal) fast
Fission.. 17
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Neutron Cross-sections… σf for fast n’s
Low values for fissile nuclides Non-zero values for fertiles, above nuclide-specific threhold energies
• ~ 1 MeV for U238 , ~ 2 MeV for Th232
Fission.. 18
Laboratory for Reactor Physics and Systems Behaviour
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Cross-sections at Low Energies… σa (σc , σf)
For absorption (capture, fission) σ ~ 1/√E ~ 1/v
Probability of absorption decreases with neutron velocity, e.g.
5B10 + n → 3Li7 + 2He4
Cross-section ~ 1/v till 104eV
σa for B10(n,α) →
Fission.. 19
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Cross-sections at Low Energies… σs (elastic)
For elastic scattering, σ ~ constant • Till ~ 1 MeV for light nuclei (moderators)
Fission.. 20
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Cross-sections at Intermediate (Epithermal) Energies - 1
“Resonance” region • Some absorption reactions have a large resonance at low energy, e.g. Au197(n,γ )
Fission.. 21
Laboratory for Reactor Physics and Systems Behaviour
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Cross-sections at Intermediate (Epithermal) Energies - 2
“Resonance” region for heavy nuclei • Large, narrow resonances after a few eV (resolved region first, unresolved later) • U238 most important (significant fraction of neutron captures, epithermal)
Fission.. 22
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Cross-sections at High Energies - 1
Inelastic scattering • Target nucleus, excited • Neutron must have a certain
minimal energy (“threshold”) • Main mechanism for heavy nuclei
to slow down fast neutrons
Example: U238 →
• σi shown, with individual components (each corresponding to different excitation levels of compound nucleus; values in keV)
Fission.. 23
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Cross-sections at High Energies - 2
Various other threshold reactions • (n,p), (n,α) • (n,2n), (n,3n)… Example: U238 →
Exceptions
• Certain “exoenergetic” (n,α) reactions, e.g. B10(n,α), have large thermal cross-sections
Fast fission in fertile isotopes also threshold reaction • U238(n,f), Th232(n,f)
Fission.. 24
Laboratory for Reactor Physics and Systems Behaviour
Neutronics
Summary, Lesson 2
Fission discovered relatively soon after discovery of neutron Large variety of FP combinations possible (“double-hump curve”) FP’s radioactive (β--decay): decay heat, important safety factor
On average, ν (2 to 3) n’s emitted per fission… chain reaction rendered possible Delayed neutrons: n’s resulting from decay of certain FP’s, crucial for reactor control Most of fission energy deposited in fuel (as heat) Nuclear fuels: U, Th… only U235 fissile; U238, Th232 fertile (yield fissile Pu239, U233) Neutron cross-sections: thermal, intermediate and fast regions of neutron spectrum Absorptions ~ 1/v in thermal range, scattering almost constant Strong peaks (resonances) in epithermal range (e.g. U238); threshold reactions in fast