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4.5. Fission, nuclear reactor

Energetics:from the mass formula, fission is possible when Z2/A>17

Additional deformation energyfor an ellipsoid with half-axesa and b (V=4/3 ab2π):

a = R(1+ε), b = R(1+ε)-1/2

Es=asA2/3(1+ 2/5ε2+..)

Ec=acZ2A-1/3(1-1/5ε2+..)

Ed= ε2 (2/5asA2/3-1/5acZ2A-1/3 +..)

becomes negative for Z2/A>49 : fission

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example235U + nth → X + Y + ν nfast

η = number of fission neutrons/number of absorbed neutrons= ν σf / (σf +σr)

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Neutron balance in a reactor

keff=ηεpfk > 1 for a critical reactor

Reactivity R = (keff -1)/keff

controlling:neutron density ρ, average time of

one generation t0,

∆ρ/∆t = (kρ – ρ)/t0

ρ = ρ0 exp{(k-1)t/t0}

delayed neutrons!

capture by Cd and B

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Nuclear reactor

First natural reactor in Oklo, Gabun (e.g. PRL 93 (2004)182302)

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controlling

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Principle of a bomb, breading processes

Fast neutrons – fast breader reactor

Slow neutrons

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AlternativesSpallation neutron source

(spallation reaction at high energies, GeV-proton accelerator)

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Transmutation

Spallation driven 232Th-recator

Small amount of long-lived fission and activated products

Electrical power from Th-fission is fed back (used in part for proton accelerator)

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Simple estimate

example of 800-MeV protons onto uranium, 22 MeV needed per neutron.

A beam current of 1 mA yields 2·1017 n/s

Applications:- Spallation neutron source – pulsed neutron source- Spallation driven reactor (232Th)- Transmutation- breading of fission material