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