Fission and Fusion

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Fission and Fusion

• 3224
• Nuclear and Particle Physics
• Ruben Saakyan
• UCL

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Induced fission

• Recall that for a nucleus with A?240, the Coulomb
  barrier is 5-6 MeV
• If a neutron with Ek ? 0 MeV enters 235U, it will
  form 236U with excitation energy of 6.5 MeV which
  as above fission barrier
• To induce fission in 238U one needs a fast
  neutron with Ek ? 1.2 MeV since the binding
  energy of last neutron in 239U is only 4.8 MeV
• The differences in BE(last neutron) in even-A and
  odd-A are given by pairing term in SEMF.

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Fissile materials
Fissile nuclei
Non-Fissile nuclei (require an energetic
neutron to induce fission)
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238U and 235U
Natural uranium 99.3 238U 0.7 235U
238U
235U
235U prompt neutrons n ? 2.5. In addition
decay products will decay by b-decay (t ? 13s)
delayed component.
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Fission chain reaction

• In each fission reaction large amount of energy
  and secondary neutrons produced (n(235U)?2.5)
• Sustained chain reaction is possible
• If k 1, the process is critical (reactor)
• If k lt 1, the process is subcritical (reaction
  dies out)
• If k gt 1, the process is supercritical (nuclear
  bomb)

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Fission chain reactions

• Neutron mean free path
• which neutron travels in 1.5 ns
• Consider 100 enriched 235U. For a 2 MeV neutron
  there is a 18 probability to induce fission.
  Otherwise it will scatter, lose energy and
  Pinteraction ?. On average it will make 6
  collisions before inducing fission and will move
  a net distance of ?6 3cm ?7cm in a time tp10 ns
• After that it will be replaced with 2.5 neutrons

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Fission chain reactions

• From above one can conclude that the critical
  mass of 235U corresponds to a sphere of radius
  7cm
• However not all neutrons induce fission. Some
  escape and some undergo radiative capture
• If the probability that a new neutron induces
  fission is q, than each neutron leads to (nq-1)
  additional neutrons in time tp

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Fission chain reactions

• N(t) ? if nq gt 1 N(t) ? if nq lt 1
• For 235U, N(t) ? if q gt 1/n ? 0.4 In this case
  since tp 10ns explosion will occur in a 1 ms
• For a simple sphere of 235U the critical radius
  (nq1) is ? 8.7 cm, critical mass ? 52 kg

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Nuclear Reactors
Core

• To increase fission probability
• 235U enrichment (3)
• Moderator (D2O, graphite)

Delayed neutron may be a problem To control
neutron density, k 1 retractable rods are used
(Cd)
Single fission of 235U 200 MeV 3.2?10-11 j 1g
of 235U could give 1 MW-day. In practice
efficiency much lower
due to conventional
engineering
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Fast Breeder Reactor

• 20 239Pu(n?3) 80238U used in the core
• Fast neutrons are used to induce fission
• Pu obtained by chemical separation from spent
  fuel rods
• Produces more 239Pu than consumes. Much more
  efficient.
• The main problem of nuclear power industry is
  radioactive waste.
• It is possible to convert long-lived isotopes
  into short-lived or even stable using resonance
  capture of neutrons but at the moment it is too
  expensive

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Nuclear Fusion
Two light nuclei can fuse to produce a heavier
more tightly bound nucleus
Although the energy release is smaller than in
fission, there are far greater abundance of
stable light nuclei
The practical problem
EkBT ? T31010 K Fortunately, in practice you
do not need that much
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The solar pp chain
pp ? 2H e ne
ppe- ? 2H ne
0.42 MeV
(0.23)
(99.77)
2Hp ? 3He g
5.49 MeV
(10-5)
(84.92)
(15.08)
3He3He ?a2p
3Hep ?a e ne
12.86 MeV
3Hea ? 7Be g
(15.07)
(0.01)
7Bep ? 8B g
7Bee- ? 7Li ne
7Li p ? aa
8B ?2a e ne
Overall
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Solar neutrino spectra
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Fusion Reactors
Main reactions
Or even better
More heat Cross-section much larger Drawback
there is no much tritium around

• A reasonable cross-section at 20 keV ? 3108 K
• The main problem is how to contain plasma at such
  temperatures
• Magnetic confinement
• Inertial confinement (pulsed laser beams)

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Fusion reactors
Tokamak
Lawson criterion
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ITER
Construction to start in 2008 First plasma in
2016 20 yr of exploitation after that