Transcript nuclear fusion

Chapter 5. Thermonuclear Fusion
1.Introduction
2.Thermonuclear Reactions and Energy Production
3.Fusion in a Hot Medium
4.Progress Towards Fusion Power
5.Stellar Burning
Nuclear Fusion
The Fusion Process
Neutron proton
Two nuclei combine into one
nucleus plus a nucleon is
called nuclear fusion, a
nuclear reaction.
Collision
The picture here illustrates
the fusion of
2D
+ 3T  4He + n
that releases a lot of energy.
Fusion
Fusion
2
Penetration through a rectangular energy barrier (height B) of a particle
beam, of kinetic energy E (< B), incident from the left. The form of the
wave functioni, Ψ is sketched In the upper part of the figure. Inside the
barrier, Ψ is an exponentially decaying function of x.
The Coulomb barrier between two
hydrogen nuclei is about 200 keV
Nuclear Fusion Energy for D-T Fusion
Estimate the fusion energy for
D + T  4He + n
Estimate the fusion energy Q
The mass excess (MeV) are given below every species.
D + T
 4He + n + Q
13.136 + 14.950 = 2.425 + 8.070 + Q
Q = 17.6 MeV/fusion
This amount is 3.5 MeV/amu compared to 0.8 MeV/amu for fission.
Estimating Q is an important skill. Mass and mass excess can be used,
the latter is usually given to unstable nuclides.
4
Nuclear Fusion Energy for Fusion Reactions
Common fusion reactions and their Q values
D + D  4He + n + 23.85 MeV
H + H  D + + + n + 1.44 MeV
D + T  4He + n + 17.6 MeV
D + 3He  4He + p + 18.4 MeV
D + D  3He + n + 3.3 MeV
D + D  3T + p + 4.0 MeV
See Interactive Plasma Physics Education
Experience : http:// ippex.pppl.gov/
Fusion
5
Effective Cross Section (mb) of Fusion Reactions
10000
1000
Nuclear Fusion
Cross Sections
D + T  4He + n
Cross sections data from
reactions studied using
particles from cyclotron
100
D + D  3T + p
10
7Li
(p, n) 7Be
3T (p, n) 3He
1H (t, n) 3He
2D (d, n) 3He
2D (t, n) 4He
3T (d, n) 4He
D + D  3He + n
1.
D + 3He  4He + p
0.1
10
20
30
40
50
60
60
keV
Chapter 5. Thermonuclear Fusion
1.Introduction
2.Thermonuclear Reactions and Energy Production
3.Fusion in a Hot Medium
4.Progress Towards Fusion Power
5.Stellar Burning
FUSION IN A HOT MEDIUM
Maxwell-Boltzmann Distribution
Fraction
0.003
0.002
is the probability
that the speed lies
between v and v + dv
The kinetic energy corresponding to the most probable speed is kT
4 amu 50 K
0.001
4 amu 500 K
1000
2000
Speed (m/s)
At room temperature, kT is about 0.025 eV
3000
Kinetic energies of
particles in plasma
follow the MaxwellBoltzmann distribution
Nuclear Fusion and Plasma
D and T mixtures have to be
heated to 10 million degrees. At
these temperatures, the mixture is
a plasma.
A plasma is a macroscopically
neutral collection of charged
particles.
Ions (bare nuclei) at high
temperature have high kinetic
energy and they approach each
other within 1 fm, a distance
strong force being effective to
cause fusion.
Reaction rate
Consider a mixture of two gases consisting, respectively,
of nl and n2 particles per unit volume.
The probability for a particle in the first gas to react with one
in the second, per unit distance travelled, is
The distance travelled per unit time is the speed v of the particle
The reaction probability per unit time is
total reaction rate per unit volume is
Assume: nl particles have the same speed and that the n2
particles of the second gas are stationary
Reality: Maxwell- Boltzmann distribution
Qualitative plots showing the variation with speed of the Maxwell-Boltzmann
probability distribution p(v) and the fusion reaction rate vσ(v). Their product
R(v) (shown dashed), which has a maximum at vm, corresponding to an
effective thermal energy Em.
Is D-T reaction favourable?
Performance criteria
The plasma will radiate energy to its surroundings at a rate that
depends on its temperature T. The primary mechanism for this
power loss is bremsstrahlung.
Lawson criterion
A preliminary stage on the way to either the break-even or ignition points is to
be able to confine a hot, reacting plasma long enough that the nuclear energy
produced exceeds the energy required to create the plasma.
fusion energy output
There are n ions and n electrons in the
plasma and, in equilibrium, each has to be
given the same initial, average kinetic
energy 3/2kT. So, the energy required to
create the plasma is
Lawson criterion
D-T plasma, kT = 20 keV,
D-D plasma, kT = l00 keV
Requirements for Fusion
• High Temperatures
• Adequate Densities
• Adequate Confinement
• Lawson Criterion: nt >
1020 s/m3
4. Progress Towards Fusion Power
Magnetic Confinement
At P, the magnetic field B is uniform in the x direction and so the magnetic.
force F acts vertically downwards. However, at point Q, B has a vertical
component, which results in the force having a component parallel to the xaxis directing the particle towards the region of lower field
plasma particles constrained in a uniform toroidal
field could circulate endlessly
Tokamak : 环形(toroidal)、真空室(kamera)、
磁(magnit)、线圈(kotushka)
Inertial Confinement Fusion(惯性约束聚变) Concept
The rate of depletion of fuel
atoms dn/dt = -2R
After a time t = Γ, the number
remaining n(Γ)
certain fraction f of the fuel be
consumed in the time Γ
25
For a significant burnup of f ~ 30%, D-T at 20 keV,
s
n ~
26
Possible Drivers: Lasers (Best Shot)
~1000 large Optics:
192 beam lines:
Engineering challeges at NIF
Advantages:
• Well advanced
technology
• Good control of
energy release
Disadvantages:
• Bad energy
conversion
• Very expensive to
build
Compare Driver to Target Sizes!
real NIF target
DT capsule
Schematic
Micro- PIXE
PS(聚苯乙烯)靶内壳材
料中掺入过渡金属元素
Br
11.6微米
Two Different Ways to Fusion

Lawson Criterion:
must be achieved

Temperature must be around T = 6 ... 15 eV

Two ways to fulfil Lawson criterion:
(1)
First solution (magnetically confined plasmas):
increase confinement time
(2)
Other solution (inertial confinement fusion - ICF):
increase density of fusion plasma

Many similarities, but a few decisive differences!
Chapter 5. Thermonuclear Fusion
1.Introduction
2.Thermonuclear Reactions and Energy Production
3.Fusion in a Hot Medium
4.Progress Towards Fusion Power
5.Stellar Burning
Nuclear Fusion of Protons - hydrogen cycle
The Sun derives energy from fusion of protons. There are
many possibilities, but two detailed cycles were proposed.
The hydrogen cycle:
H + H  2D (+e–) + + + n
2D + H  3He + 
3He + 3He  4He + 2 H
These steps take place in the deep interior of the stars
net
4 H = 4He (+ 2e–) + 2+ +2  + 2 n + 26.7 MeV
The energy released is slowly transmitted to the star
surface, from which energy is lost by way of radiation
Nuclear Fusion of Protons - carbon cycle
fusion of four hydrogen atoms to form a 4He nuclide could
be accomplished with the help of the 12C nuclide. The 12C
undergoes a cycle of reactions:
The carbon cycle:
12C + H  13N + 
13N  13C (+ e–) + + + n
13C + H  14N + 
14N + H  15O + 
15O  15N (+ e–) + + + n
15N + H  12C + 4He + 
net
4 H = 4He (+ 2e–) + 2+ +4  + 2 n + 26.7 MeV
(similar to the hydrogen cycle)
carbon is at both
the start and the
end of the cycle.
Thus, 12C is
considered a
catalyst in the
fusion reaction.
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Nuclear Fusion in Stars
Nuclear fusion reactions
The hydrogen cycle
The carbon cycle
When temperatures at the
center of the mass increase to
10,000,000 (ten million) K, the
Others reactions
hydrogen fusion cycle begins.
3He + 4He  7Be4 + 
Fusion energy causes the
7Be + H  8B5 + 
surface to heat up, and
8B  8Be + +
eventually, energy escapes
8Be  2 4He +  (major)
from the mass as radiation
8Be + 4He  12C (minor)
(heat and light). When energy
Additional reactions
released from fusion equals
12C + 4He  16O + 2.425 MeV
the energy lost by radiation,
16O + 4He  20Ne + 4.73 Me
the steady state is a star.
4He + 20Ne  24Mg + 9.31 MeV
Fusion
35
Nuclear Fusion in Stars
Stars are giant fusion reactors.
Nuclear fusion reactions provide
energy in the Sun and other stars.
Solar energy drives the weather
and makes plants grow.
E = mc2
1H, 2D
3T, 4He
Energy stored in plants sustains
animal lives, ours included.
Fusion
36
Nuclear Fusion and the Sun
The birth of the 4.5e9 year old Sun
Sun-Earth Distance (149,597,870.7 km or 8.3 light minutes) is an
Astronomical Unit (AU).
Alpha (A+B+proxima, Centauri triple star system nearest to the
sun parallax angle of 0.76-arcsec) is 4.35-4.22 light years from the
Sun.
Sun Mass is 333,000 times that of the Earth.
The sun is a big nuclear fusion reactor, 75% H and 25% He.
Sun radius (695000 km) is 109 times that of the Earth (6.4e3 km).
Sun emits 3.861026 watts, ~ 8 kwatt/cm2, 0.14 watt/cm2 reach the
earth atmosphere (solar constant).
Fusion
37
The Sun
Core:
Radius = 0.25 Rsun
T = 15 Million K
Density = 150 g/cc
Envelope:
Radius = Rsun = 700,000 km T =
5800 K
Density = 10-7 g
Life of Star:
tug-of-war between Gravity &
Pressure
Fusion
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Energy – driving force of change
Change is the only constant in the universe.
Changes: winds, rains, storms, thunders, forest fires, earthquakes,
waves, plant growth, food decay, ocean tides, formation and melting
of ice, combustion, and growing old ... more example please.
What are physical and non-physical changes?
What causes changes?
Heat
elasticity
gravity
electromagnetic wave
…
Identify changes and
energy in everyday events
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Recognizing energy
Energy plays an important part
And it’s used in all this work;
Energy, yest energy with power so great,
A kind that cannot shirk.
If the farmer had not this energy,
He would be at a loss,
But it’s sad to think, this energy
Belongs to a little brown horse.
A school verse by Richard Feynman
Nobel laureate for physics
Photo of Feynman and Murray Gell-Men
40
Mechanical Work
Mass: m kg
Acceleration: a m s-2
Force: F = m a N (Newton = kg m s-2)
0.1 kg
Distance: s m
Work: W = F • s J (N m or kg m2 s-2)
1N
Potential energy Wp = m g h unites?
Kinetic energy Wk = ½ m v 2 work out unites
Think and deal with
quantity of energy
Energy & Nuclear Science
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Properties of PE and KE
PE and KE are state functions – depending on only the final conditions
not on how the conditions were arrived (path).
Changes of PE and KE depend on only the initial and final conditions,
not on the paths.
PE and KE are inter-convertible, but not destroyed.
Do you know any other properties?
Energy in
amusement parks
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Explain state functions
The Temperature Concept
Objective comparison of energy
flow potentials – temperature
scales.
0th law of thermodynamics
Two bodies each equal in
temperature to a third body are
equal in temperature to each
other. Maxwell (19th century)
N
F
C
K
212
100
373.15
12
98
37
310
0
32
0
273.15
-40
233.15
-40
Temperature scales led to the
concept of heat
The science of heat thermodynamics.
Newton (N), Fahrenheit (F), Celsius ( C), and
Kelvin (K) temperature scales.
Energy & Nuclear Science
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Hot, Cold and Heat
What are the differences between hot-cold temperature and heat?
Temperatures (hot and cold) indicate
potential for heat flow.
They are intensive properties as are
color, electrical potentials,
concentrations heat capacity,
pressures, etc.
Temperature scales made hot-cold
measurements quantitative, but they
are not quantities to be added or
subtracted.
Heat, transfers from object to
object, elusive. When heat is transferred
between objects, their temperatures change.
Heat is an extensive property as
are electric charge, length,
mechanical work, mass, mole,
time, etc.
Heat is measurable in quantities,
units being btu, cal, kcal, J, kJ,
kwh, etc.
An amount of heat required to raise the
temperature of 1.00 g of water from 288.5 to
289.5 K is defined as 1.00 calorie or 4.184 J.
Energy & Nuclear Science
Differentiate temperature from heat
44
The Concept of Heat
Heat is evidently not passive; it is
an expansive fluid which dilates in
consequence of the repulsion
subsisting among its own particles
Joseph Black (1728-1799)
- is a typical additive quantity
Is heat a fluid like water?
- is different from hot
- inter-convertible to mechanical
work (same units)
Energy & Nuclear Science
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The Energy Concept
Inter-conversion of Heat and Work
Inter-conversion
- discovered unexpectedly
by Ben Thompson (1753-1814)
while making cannons.
Joule in his 20s
Thermometer
Conversion factor was
determined by J. Joule (18181889) 1 cal = 4.184 J
This entity was called effort,
living force, and travail, before
the term energy was coined
by Thomas Young (1773-1829)
mgh
Joules experiment demonstrated the
generation of heat by mechanical means.
Energy & Nuclear Science
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Energy
Heat and work are really energy being transferred.
Energy stored in a body is neither heat nor work.
Kinetic energies of gases are proportional to their temperature. Once
absorbed, the nature of heat has changed.
Motion of gas molecules gave rise to pressure
- Daniel Bernoulli (1700-1782).
Rudolf J.E. Clausius (1822-1888), James Clerk Maxwell (1831-1879), W. Thomson,
and Ludwig E. Boltzmann (1844-1906), studied the relationship between temperature
and energy of molecular motion. Many elegant theories have been developed as a
result.
Energy & Nuclear Science
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Forms of Energy
Other driving forces
Heat
Mechanical work
Waves (sound etc)
Electromagnetic radiation (waves)
Electrical (charge transfer)
Chemical
Mass (nuclear)
Benefit
chi
determination
encouragement
inspiration
love
law
motivation
resolution
scarcity
What are the properties of energy in these forms and how to evaluate them?
Energy & Nuclear Science
48
Electric Energy
Electric energy, E Joule
potential, V Volt
charge, q Coulomb
E=Vq
E = hg m
1 J = 1 CV = 1 N m etc
Be able to evaluate quantities
of electric energy
+
+
+
+
+
+
+
-
Electric field
Gravitational field
Energy & Nuclear Science
49
Simple electric energy calculations
Potential difference, V, current i ( = q / t ) and
resistance R.
V = i R (Ohm’s law)
Power P, (I/o)
P = V q / t = V i ( i = current )
= R i 2 (Joules law)
Electric energy, E Joule
potential, V Volt
charge, q Coulomb
E=Vq
E = hg m
1 J = 1 CV = 1 N m etc
Energy and power
E = P t ( unit kilo-watt-hour)
DC and AC
Energy & Nuclear Science
50
eV – a special energy unit
Electron-volt, eV, is a very special energy unit, although we have not
discussed electricity and electrons yet.
Charge of an electron = 1.6022e-19 C (one of the fundamental physical constants).
The energy required to increase the electric potential of an electron by 1
V is 1 eV = 1.6022e-19 J (J = C V).
Other units used in nuclear energy are
keV (1000 eV)
MeV (1e6 eV)
GeV (1e9 eV)
Be able to inter-convert energy
quantities in various units
Energy & Nuclear Science
51
What is light?
Wave properties?
Particle properties?
Massless
Interference
Newton ring
diffraction
Law of reflection
law of refraction
move in straight line
??
Energy & Nuclear Science
52
Electromagnetic Radiation
Electromagnetic radiation is
transfer of energy by EM waves
via no medium(?).
EM waves travel in empty space at
constant speed
(c = 2.997925e8 m/s constant).
EM waves are characterized by
wavelength  (or frequency n)
Light is part of the EM spectrum.
EM radiation has a very wide
spectrum ( or n ).
Energy & Nuclear Science
53
The EM Spectrum
The EM Radiation Spectrum
Long-wave Radio
Broadcast radio band
Short wavelength radio
Infrared
VISIBLE
Ultraviolet
X-rays
Gamma rays
Remember the order
of these regions
> 600 m
600 - 200 m
200 m - 0.1 mm
0.1 - 0.0007 mm
0.7 - 0.4 um
0.4 um - 1 nm
1 nm - 0.1 pm
0.1 nm
Energy & Nuclear Science
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The EM Wave Spectrum
Energy & Nuclear Science
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The Visible Spectrum
Double rainbow
A color pattern seen in an oil film
Energy & Nuclear Science
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Photons, E = hn
Max Planck assumption, E = h n, was shown
to be true by Einstein’s photoelectric
experiment.
Speed of light, c = 3e8 m s-1
wavelength, 
frequency of light, n = c / 
Planck constant, h = 6.62619e-34 J s
energy of a photon E = h n.
Max Planck
(1858-1947)
Nobel Prize (1918)
A photon is a bundle of energy, and it’s
like a particle of light.
Use wave to show  and n.
Energy & Nuclear Science
57
The Photon Story
Max Planck assumption, E = hn, was shown to be true by
Einstein’s photoelectric experiment.
I
N
T
E
N
S
I
T
Y
Kinetic energy
of electron
Rayleigh’s
Prediction
Experimental curve
and Planck’s prediction
Wien’s Law
Threshold
Frequency
Frequency
Explain the photoelectric effect.
Energy & Nuclear Science
58
Photon Energy
Typical red light, n = 4.69e14 s-1 (Hz),
=c/n
= 3e8 m s-1 / 4.69e14 s-1 = 640 nm
Wave number = 1 / 
= 1 / 6.40e11 m
= 1.56e6 m-1
E=hn
= 6.62619e-34 J s * 4.69e14 s-1
= 3.1 x 10-19 J (1 eV / 1.6 x 10-19 J)
= 1.9 eV per photon
find wavelength or frequency of a violet
photon and carry out similar evaluations.
Energy & Nuclear Science
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Laser
Light Amplification by Stimulated Emission of Radiation (LASER)
Spontaneous decay
Green
photons
Stimulated decay,
Red laser
Partial mirror
Mirror
Red laser
Green pumping light
Energy & Nuclear Science
60
4H + 2O
1469 kJ, bond energy
Understand these terms on
energy or enthalpy
2H2 + O2
484 kJ, energy of
reaction
2H2O(g)373K
81 kJ, energy of
vaporization
2H2O(l)373K
15 kJ, heat
2H2O(l)273K
2H2O(s)273K
Chemical Energy
enthalpy
Bond energy
energy of reaction
energy related to temperature
energy related to states
melting, vaporization, phase
transition
mass loss in chemical reactions
12 kJ, energy of fusion
Energy & Nuclear Science
61
Relative and Zero Masses
Special theory of relativity (by Einstein) shows that
mass m of a particle with velocity, v
relates to the mass when v = 0, which is called
zero mass, mo.
m =
mo
v 2
1 - ( )
c
Universal speed
299,792,458 m/s
Energy & Nuclear Science
62
Mass and Energy
Einstein further showed that the relativistic mass, m, of a particle
exceeds its rest mass mo (m = m - mo). The increase in kinetic
energy E and increase in mass are related by:
E = m c 2
or
E=mc2
Implication:
Mass and energy are equivalent. Mass can be expressed in energy
unit and vice versa.
241800 J = 241800/c 2
= 2.7 x 10-12 kg = 3 ng
Energy & Nuclear Science
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Power – rate of energy transfer
The SI unit for power P is
watt named after James
Watt,
1 watt = 1 J s–1
Power = m g v,
v, pulling velocity
mgh
Work out by heart
1 kilowatt-hour = __ J
= __ cal
= __ BTU
Energy & Nuclear Science
64
The law of Conservation of Energy
Energy converts among various forms without any loss or gain.
Energy cannot be created nor destroyed.
Conversions of energy in various forms have definite rates. These
rates never change, and we have energy conversion factors.
1 amu = 1/12th of mass of a C12 atom
1 amu = (12 kg/k mol)/12
= (1 kg/k mol)/(6.022e26 (k mol)-1)
= 1.661e-27 kg = 931.5 MeV
Power = m g v,
v, pulling velocity
mgh
Energy & Nuclear Science
65
Some conversion factors
1 eV = 1.602 x 10-19 J
1 eV/molecule = 23045 cal/mol
1 MeV = 1.602 x 10-13 J
1 amu = 1.66043 x 10-31 J
= 931.4812 MeV
1 cal = 4.184 J
1 atm L = 101.3 J
1 J = 1 coulomb-volt
1 joule = 107 ergs
1 BTU = 252 cal
Transmitting Energy by Sound
Sound intensity (I, watt/m2), level (SIL) is
SIL (dB) = SILo + 10 log (I/Io )
At 1000 Hz, the threshold
SILo = 0 dB,
I0 = 10-12 watt / m2)
When I = 1 watt / m2
SIL = 120 dB (work out)
Comfortable hearing is between 50 and 70 dB,
whereas 10 dB is a bel (after A. G. Bell, 1847-1922).
A shock wave is due to a sharp difference in
pressure from (nuclear) explosions. Shock waves
cause serious injuries to ears, and destroy buildings
and structures.
Energy & Nuclear Science
67
Thermodynamics
Thermodynamics was derived from the Greek words therme (heat)
and dynamis (force), intensely studied in the 19th century motivated by
the need to convert heat into mechanical work.
0th law: if T of A, TA = T B, TB = TC, then TA = TC
1st law: law of conservation of energy, recognizing internal energy
Ein = q – w.
2nd law: not possible for a machine to convert all the heat into work.
3rd law: changes are caused be energy decrease and entropy increase.
These laws govern engineering of energy transfer.
Energy & Nuclear Science
68
Energy Resources and Utilization
What are possible energy resources?
Solar energy
Geothermal energy
Nuclear energy
???
What technologies are available to utilize these resources?
???
How efficient are some of the technologies?
???
Energy & Nuclear Science
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Energy crisis and social problems
Level
Demand
These issues affect us all,
and please apply basics and
human natures to solve
these problems so your
generation will live happily
hereafter.
Cost
Arbitrary Coordinate
Energy & Nuclear Science
70
Chung, Chieh
sprott.physics.wisc.edu/lectures/plasma.ppt
Dirk O. Gericke,
1. Introduction
Advantages of Fusion
• Inexhaustible Supply of
Fuel
• Relatively Safe and Clean
• Possibility of Direct
Conversion
The Sun
The sun flare 
The corona during
an eclipse 
The aurora
corona during an eclipse
Fusion
73