fission and fusion 3224 nuclear and particle physics ruben saakyan ucl
TRANSCRIPT
Fission and Fusion
3224Nuclear and Particle Physics
Ruben SaakyanUCL
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
233 235 239 24192 92 94 94, , ,U U Pu Pu
232 238 240 24290 92 94 94, , ,Th U Pu Pu
“Fissile” nuclei
“Non-Fissile” nuclei(require an energetic neutron to induce fission)
238U and 235U
Natural uranium: 99.3% 238U + 0.7% 235U
235U 238U
14~ 1 / 10f f feV s
235U prompt neutrons: n 2.5. In addition decay products will decayby -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)
( 1)
( )
Neutrons nk
Neutrons n
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
235 238 1(1 ) for 2 MeV neutron 3tot tot tot
nucl tot
c c l l cm
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
( 1) /
( ) ( ) 1 ( 1)( / )
( 1)In the limit 0, ( )
( ) (0) p
p
p
nq t t
N t t N t nq t t
dN nqt N t
dt t
N t N e
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 s
• For a simple sphere of 235U the critical radius (nq=1) is 8.7 cm, critical mass 52 kg
Nuclear Reactors
To increase fission probability:1. 235U enrichment (~3%)2. Moderator (D2O, graphite)
Core
Delayed neutron may be a problemTo control neutron density, k = 1retractable rods are used (Cd)
Single fission of 235U ~ 200 MeV ~ 3.210-11 j1g 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 producea heavier more tightly bound nucleus
Although the energy release is smallerthan in fission, there are far greaterabundance of stable light nuclei
The practical problem: 2
0
1 ' For 8, 4
4 'C C
ZZ eV A V MeV
R R
E=kBT T~3×1010 KFortunately, in practice you do not needthat much
The solar pp chain
p+p 2H + e+ + e p+p+e- 2H + e
2H+p 3He +
3He+3He +2p 3He+p + e+ + e
3He+ 7Be +
7Be+p 8B + 7Be+e- 7Li + e
7Li +p + 8B 2e+ + e
(99.77%) (0.23%)
(84.92%) (~10-5%)
(15.08%)
(15.07%) (0.01%)
pp pep
hep
7Be8B
+ 0.42 MeV
+ 5.49 MeV
+ 12.86 MeV
Overall: 1 44 2 2 2 24.68eH He e MeV
Solar neutrino spectra
Fusion ReactorsMain reactions:
2 2 31 1 2
2 2 31 1 1
3.27
4.03
H H He n MeV
H H H p MeV
Or even better: 2 3 41 1 2 17.62H H He n MeV
More heatCross-section much largerDrawback: there is no much tritium around
A reasonable cross-section at ~20 keV 3×108 KThe main problem is how to contain plasma at such temperatures• Magnetic confinement• Inertial confinement (pulsed laser beams)
Fusion reactors
Tokamak
Lawson criterion
219 3 1
21
19 3
(17.6 )(10 )
6
- number density of ions, - prop. to , - plasma confinement time
10
d cd c
d B
d c
d c
t MeVenergy outputL m s t
energy input k T
H t
t m s
4 (3 / 2)d BInput of energy k T
2Reaction rate d
ITERITER
Construction to start in 2008Construction to start in 2008First plasma in 2016First plasma in 201620 yr of exploitation after that20 yr of exploitation after that