Tony WeidbergNuclear Physics Lectures1 Applications of Nuclear Physics Fusion –(How the sun works...

Tony Weidberg Nuclear Physics Lectures 1

Applications of Nuclear Physics

• Fusion– (How the sun works covered in Astro

lectures)– Fusion reactor

• Radioactive dating– C dating– Rb/Sr age of the Earth


Physics of Nuclear Fusion

• All reactions at low energy are suppressed by Coulomb barrier (cf decay).

• Reaction rate: convolution of MB distribution and barrier penetration.

222 1 2

0

(0)( ) ~ exp( )

24

G

G

S EE

E E

Z Z eE mc

c

Tk2

mvexpv

Tk

m2)v(P

B

22

2/3

B

2/1


Low Energy Fusion Cross Sections

• Breit-Wigner (no-spin)

• cf decay theory, allow for QM tunnelling through Coulomb barrier

•

4/)EE(k)E(

220

i2

4/)EE(

)/(

mE2)E(

220

i3

)4(c

eZZmc2E;

E

Eexp)E(p

0

2212

GG


Cross Sections (Continued)

• Predicts cross section

• Low energy approximation

0i

)]E(Gexp[/

E

EE

exp

4/)EE(m2)E(

G

2200

3

E

Eexp)0(S

E

1)E( G


Example C

Theory explains rapid rise at very low energy

Ignores multiple resonances!


Fusion Rates

• Consider reaction a+bX (a different from b)– Volume number density a b

– Cross section ab

• Reaction rate/volume )v(vR abba

0

)()()( dvvPvvvv abab

mvdvdEmvE 2

2

1


E/EexpE

)0(S

Tk

Eexp

m2

E

Tk

m2dEv G

B2

2/3

B

2/1

0ab

3/ 21/ 2

0

8 1(0) exp[ ( )]

( ) / /

abB

B G

v S dE Em k T

E E k T E E

Maximum rate minimum for

0E

E

2

1

Tk

1

dE

d2/3

0

G

B


Fusion Rates

Look at exp[-(E)] Function sharply peaked at E=E0

3/2B

2/1G0 )Tk()E(E

pp reaction

E (KeV)10

6ex

p[-

E)]


Fusion Rates

• Most favourable rates for d-t reactions.

• Peak at kBT~ 20 keV

• Why? <v

(v)>

m3s-1

kBT (keV)


Fusion Reactors

• Use deuterium + tritium:

– Large energy release– Large cross-section at low energy– Deuterium abundant (0.015% of H).– Breed Tritium in Lithium blanket– .

MeV62.17nHeHH 42

31

21

MeV8.4HeHLin

nHeHMeV46.2Lin42

31

63

42

31

73


Fusion Reactors

• Energy out > Energy in

• Lawson criteria (assume kBT=20 keV).– number density D ions : – Cross-section: – Confinement time for plasma: tc

– Energy released per fusion: Efusion

cfusion2

out tEvE

TkE Bin c1319

inout t)sm10(~E/E


Magnetic Confinement

• Confine plasma with magnetic fields.– Toroidal field: ions spiral around field

lines.– Poloidal fields: focus ions away from

walls.

• Heating:– RF power accelerates electrons– Current pulse causes further heating.


Jet


MAST

Fusion Progress–Huge strides in physics,

engineering, technology–JET: 16 MW of fusion

power ~ equal to heating power. 21 MJ of fusion energy in one pulse

–Ready to build ITER - the next generation, GigaWatt-scale

–Scaling laws that fit data from existing tokamaks give confidence that ITER/power plants will achieve desired performance

Temperature / 106 K

Fu

sio

n p

rod

uct

p t

(at

m.

sec)


AUG JET

ITER

JET

Cross section of present EU D-shape tokamaks compared to the ITER project

Prediction of ITER performancePrediction of ITER performance


High Energy neutrons

• Use n to make 3H in Li blanket

• n damage to surrounding support structures ~ 10 dpa/yr

• 2H +7Li n + 2 4He


Inertial Confinement Fusion

Very Big Laser

Mirrors

D-T Pellet


Inertial Confinement Fusion


Radioactive Dating

• C14/C12 for organic matter age of dead trees etc.

• Rb/Sr in rocks age of earth.


Carbon Dating• C14 produced by Cosmic rays (mainly

neutrons) at the top of the atmosphere.– n N14 p C14

• C14 mixes in atmosphere and absorbed by plants/trees constant ratio C14 / C12 . Ratio decreases when plant dies. t1/2=5700 years.

• Either– Rate of C14 radioactive decays– Count C14 atoms in sample by Accelerator Mass

Spectrometer.

• Which is better?• Why won’t this work in the future?


Carbon Dating Calibration


How Old Is The Earth?

• Rb87 Sr87: decay t1/2=4.8 1010 yr

• Assume no initial daughter nuclei get age from ratio of daughter/parent now.

)t(N)t(N)t(N 0p1P1D

)tt(exp()t(N)t(N 010p1P

)t(N

)t(Nln1

t1p

0p

)t(N

)t(N1ln

1t

1p

1D


Improved Calculation• Allow for initial daughters to be present.• Need another isotope of the daughter D’ which is stable

and not a product of a radioactive decay chain. • Plot vs straight line fit age and initial ratio.

)t(N)t(N)t(N)t(N 0p0D1P1D

)t(N

)t(N

1D

1D

)t(N

)t(N

1D

1P

)t(N

)t(N)t(N

)t(N

)t(N)t(N

0D

0p0D

1D

1P1D

)t(N

)t(N]1)t[exp(

)t(N

)t(N

)t(N

)t(N

0D

0D

1D

1P

1D

1D


Age of Earth

• Rb/Sr method• Stable isotope of

daughter is Sr86

• Fit gives age of earth=4.53 109 years. S

r87/

Sr8

6

Rb87/Sr86

1.0 4.0

Tony WeidbergNuclear Physics Lectures1 Applications of Nuclear Physics Fusion –(How the sun works...

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