Fission and Fusion 3224 Nuclear and Particle Physics Ruben Saakyan UCL
Induced fission • Recall that for a nucleus with A240, 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.
Fissile materials “Fissile” nuclei “Non-Fissile” nuclei (require an energetic neutron to induce fission)
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.
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 < 1, the process is subcritical (reaction dies out) • If k > 1, the process is supercritical (nuclear bomb)
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 tp=10 ns • After that it will be replaced with ~2.5 neutrons
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
Fission chain reactions • N(t) if nq > 1; N(t) if nq < 1 • For 235U, N(t) if q > 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 (nq=1) is 8.7 cm, critical mass 52 kg
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 ~ 3.210-11 j 1g of 235U could give 1 MW-day. In practice efficiency much lower due to conventional engineering
Fast Breeder Reactor • 20% 239Pu(n3) + 80%238U 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
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: E=kBT T~3×1010 K Fortunately, in practice you do not need that much
pep pp hep 8B 7Be The solar pp chain p+p 2H + e+ + ne p+p+e- 2H + ne + 0.42 MeV (0.23%) (99.77%) 2H+p 3He + g + 5.49 MeV (~10-5%) (84.92%) (15.08%) 3He+3He a+2p 3He+p a+ e+ + ne + 12.86 MeV 3He+a 7Be + g (15.07%) (0.01%) 7Be+e- 7Li + ne 7Be+p 8B + g 7Li +p a+a 8B 2a+ e+ + ne Overall:
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 3×108 K • The main problem is how to contain plasma at such temperatures • Magnetic confinement • Inertial confinement (pulsed laser beams)
Fusion reactors Tokamak Lawson criterion
ITER Construction to start in 2008 First plasma in 2016 20 yr of exploitation after that