Fission and Fusion 3224 Nuclear and Particle Physics

Fission and Fusion 3224 Nuclear and Particle Physics Ruben Saakyan UCL

Induced fission • Recall that for a nucleus with A 240, the Coulomb barrier is 5 -6 Me. V • If a neutron with Ek 0 Me. V enters 235 U, it will form 236 U with excitation energy of 6. 5 Me. V which as above fission barrier • To induce fission in 238 U one needs a fast neutron with Ek 1. 2 Me. V since the binding energy of last neutron in 239 U is only 4. 8 Me. V • 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)

238 U and 235 U Natural uranium: 99. 3% 238 U + 0. 7% 235 U 238 U prompt neutrons: n 2. 5. In addition decay products will decay by b-decay (t 13 s) + delayed component. 235 U

Fission chain reaction • In each fission reaction large amount of energy and secondary neutrons produced (n(235 U) 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 235 U. For a 2 Me. V 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 × 3 cm 7 cm 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 235 U corresponds to a sphere of radius ~ 7 cm • 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 235 U, N(t) if q > 1/n 0. 4 In this case since tp = 10 ns explosion will occur in a ~1 ms • For a simple sphere of 235 U the critical radius (nq=1) is 8. 7 cm, critical mass 52 kg

Nuclear Reactors Core To increase fission probability: 1. 235 U enrichment (~3%) 2. Moderator (D 2 O, graphite) Delayed neutron may be a problem To control neutron density, k = 1 retractable rods are used (Cd) Single fission of 235 U ~ 200 Me. V ~ 3. 2 10 -11 j 1 g of 235 U could give 1 MW-day. In practice efficiency much lower due to conventional engineering

Fast Breeder Reactor • 20% 239 Pu(n 3) + 80%238 U used in the core • Fast neutrons are used to induce fission • Pu obtained by chemical separation from spent fuel rods • Produces more 239 Pu than consumes. Much more efficient. • The main problem of nuclear power industry is radioactive waste. – It is possible to convert long-lived isotopes into shortlived 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=k. BT T~3× 1010 K Fortunately, in practice you do not need that much

The solar pp chain pp p+p 2 H + e+ + ne + 0. 42 Me. V (99. 77%) 2 H+p p+p+e- 2 H + ne pep (0. 23%) 3 He + g+ 5. 49 Me. V (~10 -5%) (84. 92%) (15. 08%) 3 He+3 He a+2 p + 12. 86 Me. V 3 He+p 3 He+a 7 Be + g (15. 07%) 7 Be+e 7 Li Overall: hep (0. 01%) 7 Li + ne +p a+a a+ e+ + ne 7 Be+p 8 B 7 Be +g 8 B 8 B 2 a+ e+ + ne

Solar neutrino spectra

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 ke. V 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