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

The Fusion Process
Neutron proton
Two nuclei combine into one nucleus plus a nucleon is called nuclear fusion , a nuclear reaction.
The picture here illustrates the fusion of
2 D + 3 T

4 He + n that releases a lot of energy.
Fusion
Collision
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.

Estimate the fusion energy for D + T

4 He + n
Estimate the fusion energy Q
The mass excess (MeV) are given below every species.
D + T  4 He + 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

Common fusion reactions and their Q values
D + D

4 He + n +
23.85 MeV
H + H

D +

+ + n
+ 1.44 MeV
D + T

4 He + n + 17.6 MeV
D + 3 He

4 He + p + 18.4 MeV
D + D

3 He + n + 3.3 MeV
D + D

3 T + 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
D + T  4 He + n
100
D + D  3 T + p
10
D + D  3 He + n
1.
0.1
10 20 30 40
D + 3 He  4 He + p
50 60 60 keV
Cross sections data from reactions studied using particles from cyclotron
7 Li (p, n) 7 Be
3 T (p, n) 3 He
1 H (t, n) 3 He
2 D (d, n) 3 He
2 D (t, n) 4 He
3 T (d, n) 4 He

Chapter 5. Thermonuclear Fusion
1.Introduction
2.Thermonuclear Reactions and Energy Production
4.Progress Towards Fusion Power
5.Stellar Burning

Fraction
0.003
Maxwell-Boltzmann Distribution is the probability that the speed lies between v and v + dv
The kinetic energy corresponding to the most probable speed is kT
0.002
0.001
4 amu 50 K
4 amu 500 K
Kinetic energies of particles in plasma follow the Maxwell-
Boltzmann distribution
1000 2000
Speed (m/s)
At room temperature, kT is about 0.025 eV
3000

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.

Consider a mixture of two gases consisting, respectively, of n l and n
2 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 : n l particles have the same speed and that the n particles of the second gas are stationary
2
Reality: Maxwell- Boltzmann distribution

Qualitative plots showing the variation with speed of the Maxwell-Boltzmann probability distribution p(v) and the fusion reaction rate v σ(v). Their product
R(v) (shown dashed), which has a maximum at v m
, corresponding to an effective thermal energy E m
.

Is D-T reaction favourable?

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.

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

n t
20
3

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)

( 惯性约束聚变 )

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

~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

real NIF target
DT capsule
Schematic

11.6微米



 Lawson Criterion: must be achieved
Temperature must be around T = 6 ... 15 eV
Two ways to fulfil Lawson criterion:
(1)
(2)

First solution (magnetically confined plasmas): increase confinement time
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

The Sun derives energy from fusion of protons. There are many possibilities, but two detailed cycles were proposed.
The hydrogen cycle:
3
2
H + H  2 D (+e – ) +  + + n
D + H  3 He + 
He + 3 He  4 He + 2 H
These steps take place in the deep interior of the stars net
4 H = 4 He (+ 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

fusion of four hydrogen atoms to form a 4 He nuclide could be accomplished with the help of the 12 C nuclide. The 12 C undergoes a cycle of reactions:
The carbon cycle:
12 C + H  13 N + 
13 N  13 C (+ e – ) +  + + n
13 C + H  14 N + 
14 N + H  15 O + 
15 O  15 N (+ e – ) +  + + n
15 N + H  12 C + 4 He +  net
4 H = 4 He (+ 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, 12 C is considered a catalyst in the fusion reaction.
34

Nuclear fusion reactions
The hydrogen cycle
The carbon cycle
When temperatures at the center of the mass increase to
Others reactions
3 He + 4 He  7 Be 4 + 
7 Be + H  8 B 5 + 
8 B  8 Be +  +
8 Be  2 4 He +  (major)
8 Be + 4 He  12 C (minor)
10,000,000 (ten million) K,
Fusion energy causes the surface to heat up, and eventually, energy escapes from the mass as radiation the hydrogen fusion cycle begins.
Additional reactions
12 C + 4 He  16 O + 2.425 MeV
16 O + 4 He  20 Ne + 4.73 Me
4 He + 20 Ne  24 Mg + 9.31 MeV
(heat and light). When energy released from fusion equals the energy lost by radiation, the steady state is a star .
Fusion 35

E = mc 2
1 H, 2 D
3 T, 4 He
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.
Energy stored in plants sustains animal lives, ours included.
Fusion 36

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

10 26 watts, ~ 8 kwatt/cm 2 , 0.14 watt/cm 2 reach the earth atmosphere ( solar constant ).
Fusion 37

Core:
Radius = 0.25 R sun
T = 15 Million K
Density = 150 g/cc
Envelope:
Radius = R sun
5800 K
= 700,000 km T =
Density = 10 -7 g
Life of Star: tug-of-war between Gravity &
Pressure
Fusion 38

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
39

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

Mass: m kg
Acceleration: a m s -2
Force: F = m a N (Newton = kg m s -2 )
Distance: s m
Work: W = F • s J (N m or kg m 2 s -2 )
Potential energy W p
= m g h unites?
Kinetic energy W k
= ½ m v 2 work out unites
Think and deal with quantity of energy
Energy & Nuclear Science
0.1 kg
1 N
41

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
42
Explain state functions

Objective comparison of energy flow potentials – temperature scales.
0 th law of thermodynamics
Two bodies each equal in temperature to a third body are equal in temperature to each
other. Maxwell (19 th century)
Temperature scales led to the concept of heat
The science of heat thermodynamics.
N
12
0
F
212
98
32
-40
C
100
37
0
K
373.15
310
273.15
-40 233.15
Newton (N), Fahrenheit (F), Celsius ( C), and
Kelvin (K) temperature scales.
Energy & Nuclear Science 43

What are the differences between hot-cold temperature and heat?
Temperatures ( hot and potential for heat flow.
cold ) indicate
Heat, transfers from object to object, elusive.
When heat is transferred between objects, their temperatures change.
They are intensive properties as are color, electrical potentials, concentrations heat capacity , pressures, etc.
Heat is an time, etc.
extensive property are electric charge, length, mechanical work, mass, mole, as
Temperature scales made hot-cold measurements quantitative, but they are not quantities to be added or subtracted.
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 44
Differentiate temperature from 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 different from hot
- inter-convertible to mechanical work (same units)
Energy & Nuclear Science 45

Inter-conversion
- discovered unexpectedly by Ben Thompson
(1753-1814) while making cannons.
Joule in his 20s
Thermometer
Conversion factor was determined by J. Joule (1818-
1889) 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 46

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 47

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, E J oule potential, V V olt charge, q C oulomb
E = V q
E = hg m
1 J = 1 CV = 1 N m etc
+
+
+
+
+
+
+
-
-
-
-
-
-
-
Be able to evaluate quantities of electric energy
Gravitational field
Energy & Nuclear Science 49

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)
Energy and power
E = P t ( unit kilo-watt-hour)
DC and AC
Electric energy, E J oule potential, V V olt charge, q C oulomb
E = V q
E = hg m
1 J = 1 CV = 1 N m etc
Energy & Nuclear Science 50

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

Wave properties?
Massless
Interference
Newton ring diffraction
Particle properties?
Law of reflection law of refraction move in straight line
??
Energy & Nuclear Science 52

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

Long-wave Radio
Broadcast radio band
Short wavelength radio
Infrared
VISIBLE
Ultraviolet
X-rays
Gamma rays
> 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
Remember the order of these regions
Energy & Nuclear Science 54

Energy & Nuclear Science 55

Double rainbow
A color pattern seen in an oil film
Energy & Nuclear Science 56

E = h n
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
.
A photon is a bundle of energy, and it’s like a particle of light.
Use wave to show
 and n
.
Energy & Nuclear Science
Max Planck
(1858-1947)
Nobel Prize (1918)
57

I
N
T
E
N
S
I
T
Y
Max Planck assumption,
E = h n
, was shown to be true by
Einstein’s photoelectric experiment.
Kinetic energy of electron
Rayleigh’s
Prediction
Experimental curve and Planck’s prediction
Wien’s Law
Frequency
Threshold
Frequency
Explain the photoelectric effect.
Energy & Nuclear Science 58

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 = h n
= 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 59

Light Amplification by Stimulated Emission of Radiation (LASER)
Spontaneous decay
Green photons Stimulated decay,
Red laser
Mirror
Partial mirror
Green pumping light
Energy & Nuclear Science
Red laser
60

4H + 2O
1469 kJ, bond energy
2H
2
+ O
2
2H
2
O(g)373K
2H
2
O(l)373K
2H
2
O(l)273K
2H
2
O(s)273K
Understand these terms on energy or enthalpy
484 kJ, energy of reaction
81 kJ, energy of vaporization
15 kJ, heat
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

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, m o
.
m = m o v
1 - ( ) c
2 Universal speed
299,792,458 m/s
Energy & Nuclear Science 62

Einstein further showed that the relativistic mass, m, of a particle exceeds its rest mass m o
(  m = m - m o
). The increase in kinetic energy  E and increase in mass are related by:
 E =  m c 2 or E = m c 2
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 63

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

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 /
12 th of mass of a C 12 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

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 = 10 7 ergs
1 BTU = 252 cal

Sound intensity (I, watt/m 2 ), level (SIL) is
SIL (dB) = SIL o
+ 10 log (I/I o
)
At 1000 Hz, the threshold
I
SIL
0 o
= 0 dB,
= 10 -12 watt / m 2 )
When I = 1 watt / m 2
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 was derived from the Greek words therme (heat) and dynamis (force), intensely studied in the 19 th century motivated by the need to convert heat into mechanical work.
0 th law: if T of A, T
A
= T
B
, T
B
= T
C
, then T
A
= T
C
1 st law: law of conservation of energy, recognizing internal energy
E in
= q – w.
2 nd law: not possible for a machine to convert all the heat into work.
3 rd law: changes are caused be energy decrease and entropy increase.
These laws govern engineering of energy transfer.
Energy & Nuclear Science 68

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 69

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,

•
•
•

The sun flare

The corona during an eclipse

The aurora
Fusion 73