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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
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Tony Weidberg Nuclear Physics Lectures 2
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
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Tony Weidberg Nuclear Physics Lectures 3
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
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Tony Weidberg Nuclear Physics Lectures 4
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
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Tony Weidberg Nuclear Physics Lectures 5
Example C
Theory explains rapid rise at very low energy
Ignores multiple resonances!
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Tony Weidberg Nuclear Physics Lectures 6
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
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Tony Weidberg Nuclear Physics Lectures 7
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
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Tony Weidberg Nuclear Physics Lectures 8
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)]
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Tony Weidberg Nuclear Physics Lectures 9
Fusion Rates
• Most favourable rates for d-t reactions.
• Peak at kBT~ 20 keV
• Why? <v
(v)>
m3s-1
kBT (keV)
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Tony Weidberg Nuclear Physics Lectures 10
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
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Tony Weidberg Nuclear Physics Lectures 11
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
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Tony Weidberg Nuclear Physics Lectures 12
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.
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Tony Weidberg Nuclear Physics Lectures 13
Jet
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Tony Weidberg Nuclear Physics Lectures 14
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Tony Weidberg Nuclear Physics Lectures 15
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)
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Tony Weidberg Nuclear Physics Lectures 16
AUG JET
ITER
JET
Cross section of present EU D-shape tokamaks compared to the ITER project
Prediction of ITER performancePrediction of ITER performance
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Tony Weidberg Nuclear Physics Lectures 17
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
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Tony Weidberg Nuclear Physics Lectures 18
Inertial Confinement Fusion
Very Big Laser
Mirrors
D-T Pellet
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Tony Weidberg Nuclear Physics Lectures 19
Inertial Confinement Fusion
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Tony Weidberg Nuclear Physics Lectures 20
Radioactive Dating
• C14/C12 for organic matter age of dead trees etc.
• Rb/Sr in rocks age of earth.
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Tony Weidberg Nuclear Physics Lectures 21
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?
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Tony Weidberg Nuclear Physics Lectures 22
Carbon Dating Calibration
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Tony Weidberg Nuclear Physics Lectures 23
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
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Tony Weidberg Nuclear Physics Lectures 24
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
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Tony Weidberg Nuclear Physics Lectures 25
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