lesson 2: fission characteristics, nuclear fuels, neutron ... · components released (mev)...

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)

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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)

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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)

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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

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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

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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)

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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

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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,…)

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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

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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” ↓

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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 (%)

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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

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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

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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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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)

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Neutron Cross-sections… U235 σf, σt

thermal “resonance” (epithermal) fast

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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

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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) →

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Cross-sections at Low Energies… σs (elastic)

For elastic scattering, σ ~ constant • Till ~ 1 MeV for light nuclei (moderators)

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Cross-sections at Intermediate (Epithermal) Energies - 1

“Resonance” region • Some absorption reactions have a large resonance at low energy, e.g. Au197(n,γ )

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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)

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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)

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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)

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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

lesson 2: fission characteristics, nuclear fuels, neutron ... · components released (mev)...

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