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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 2
Nuclear Fusion
Two nuclei combine into one nucleus plus a nucleon is called nuclear fusion, a nuclear reaction.
The picture here illustrates the fusion of
2D + 3T 4He + n
that releases a lot of energy.
The Fusion Process
Collision
Fusion
Neutron proton
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
4
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 + Q13.136 + 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.
Fusion 5
Nuclear Fusion Energy for Fusion Reactions
Common fusion reactions and their Q values
D + D 4He + 23.85 MeV
H + H D + + + + 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/
Nuclear Fusion Cross Sections
Cross sections data from reactions studied using particles from cyclotron
7Li (p, n) 7Be3T (p, n) 3He1H (t, n) 3He2D (d, n) 3He2D (t, n) 4He3T (d, n) 4He
Effective Cross Section (mb) of Fusion Reactions
0.1
1.
10
100
1000
10000
10 20 30 40 50 60 60
D + T 4He + n
D + D 3T + p
D + D 3He + n
D + 3He 4He + p
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
Maxwell-Boltzmann Distribution
1000 2000 3000
0.001
0.002
0.003
4 amu 50 K
4 amu 500 K
Speed (m/ s)
Fraction
Kinetic energies of particles in plasma follow the Maxwell-Boltzmann distribution
FUSION IN A HOT MEDIUM
The kinetic energy corresponding to the most probable speed is kT
At room temperature, kT is about 0.025 eV
is the probability that the speed lies between v and v + dv
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.
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
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
Qualitative plots showing the variation with speed of the Maxwell-Boltzmannprobability distribution p(v) and the fusion reaction rate vσ(v). Their product R(v) (shown dashed), which has a maximum at vm, corresponding to aneffective 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
fusion energy output
There are n ions and n electrons in the plasma and, in equilibrium, each has to begiven the same initial, average kinetic energy 3/2kT. So, the energy required to create the plasma is
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.
D-T plasma, kT = 20 keV,
D-D plasma, kT = l00 keV
Requirements for Fusion
• High Temperatures
• Adequate Densities
• Adequate Confinement
• Lawson Criterion: n >
1020 s/m3
4. Progress Towards Fusion Power
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 x-axis directing the particle towards the region of lower field
Magnetic Confinement
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
25
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
26
For a significant burnup of f ~ 30%, D-T at 20 keV,
s
n ~
Advantages:
• Well advanced technology
• Good control of energy release
Disadvantages:
• Bad energy conversion
• Very expensive to buildEngineering challeges at NIF
Possible Drivers: Lasers (Best Shot)
~1000 large Optics:
192 beam lines:
Compare Driver to Target Sizes!
real NIF target
Schematic
DT capsule
Micro- PIXEMicro- 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 hydrogen cycle:
H + H 2D (+e–) + + + 2D + H 3He + 3He + 3He 4He + 2 H
The Sun derives energy from fusion of protons. There are many possibilities, but two detailed cycles were proposed.
These steps take place in the deep interior of the stars
net 4 H = 4He (+ 2e–) + 2+ +2 + 2 + 26.7
MeVThe energy released is slowly transmitted to the star surface, from which energy is lost by way of radiation
34
Nuclear Fusion of Protons - carbon cycle
The carbon cycle:12C + H 13N + 13N 13C (+ e–) + + + n13C + H 14N + 14N + H 15O + 15O 15N (+ e–) + + + n15N + H 12C + 4He +
net 4 H = 4He (+ 2e–) + 2+ +4 + 2 n + 26.7 MeV
(similar to the hydrogen 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:
carbon is at both the start and the end of the cycle. Thus, 12C is considered a catalyst in the fusion reaction.
Fusion 35
Nuclear Fusion in StarsNuclear fusion reactions
The hydrogen cycleThe carbon cycle
Others reactions 3He + 4He 7Be4 + 7Be + H 8B5 + 8B 8Be + +
8Be 2 4He + (major) 8Be + 4He 12C (minor)
Additional reactions 12C + 4He 16O + 2.425 MeV 16O + 4He 20Ne + 4.73 Me 4He + 20Ne 24Mg + 9.31 MeV
When temperatures at the center of the mass increase to 10,000,000 (ten million) K, the hydrogen fusion cycle begins. Fusion energy causes the surface to heat up, and eventually, energy escapes from the mass as radiation (heat and light). When energy released from fusion equals the energy lost by radiation, the steady state is a star.
Fusion 36
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.
Energy stored in plants sustains animal lives, ours included.
E = mc21H, 2D3T, 4He
Fusion 37
Nuclear Fusion and the SunThe 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 3.861026 watts, ~ 8 kwatt/cm2, 0.14 watt/cm2 reach the earth atmosphere (solar constant).
Fusion 38
The SunCore: 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
39
Energy – driving force of changeChange 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?Heatelasticitygravityelectromagnetic wave
…
Identify changes and energy in everyday events
40
Recognizing energy
Energy plays an important partAnd 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 energyBelongs to a little brown horse.
A school verse by Richard Feynman Nobel laureate for physics
Photo of Feynman and Murray Gell-Men
Energy & Nuclear Science 41
Mechanical Work
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 m2 s-2)
Potential energy Wp = m g h unites?
Kinetic energy Wk = ½ m v 2 work out unites
0.1 kg
1 N
Think and deal with quantity of energy
42
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
Explain state functions
Energy & Nuclear Science 43
The Temperature ConceptObjective comparison of energy flow potentials – temperature scales.
0th law of thermodynamicsTwo bodies each equal in temperature to a third body are equal in temperature to each other. Maxwell (19th century)
Temperature scales led to the concept of heat
The science of heat - thermodynamics.
N F C K
2 1 2 1 0 0 3 7 3 .1 5
1 2 9 8 3 7 3 1 0
0 3 2 0 2 7 3 .1 5
-4 0 -4 0 2 3 3 .1 5
N ew ton (N ), F a h r en h e it (F ) , C e ls iu s ( C ) , a n dK elv in (K ) tem p er a tu r e sca les .
Energy & Nuclear Science 44
Hot, Cold 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.
What are the differences between hot-cold temperature and heat?
Differentiate temperature from heat
Energy & Nuclear Science 45
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 different from hot
- inter-convertible to mechanical work (same units)
Is heat a fluid like water?
Energy & Nuclear Science 46
The Energy Concept
T h e r m o m e t e r
m g h
Jo u le s e x p e r im e n t d e m o n s t r a t e d t h eg e n e ra t io n o f h e a t b y m e c h a n ic a l m e a n s .
Inter-conversion- discovered unexpectedlyby Ben Thompson (1753-1814) while making cannons.
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)
Inter-conversion of Heat and Work
Joule in his 20s
Energy & Nuclear Science 47
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 48
Forms of EnergyHeatMechanical work Waves (sound etc)
Electromagnetic radiation (waves)Electrical (charge transfer)ChemicalMass (nuclear)
Other driving forces
Benefitchi
determinationencouragement
inspirationlovelaw
motivationresolutionscarcity
What are the properties of energy in these forms and how to evaluate them?
Energy & Nuclear Science 49
Electric Energy
+++++++
-------
Electric fieldElectric field
Gravitational field
Electric energy, E Joule
potential, V Volt
charge, q Coulomb
E = V qE = hg m
1 J = 1 CV = 1 N m etc
Be able to evaluate quantities of electric energy
Energy & Nuclear Science 50
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)
Energy and powerE = P t ( unit kilo-watt-hour)
DC and AC
Electric energy, E Joulepotential, V Voltcharge, q Coulomb
E = V qE = hg m
1 J = 1 CV = 1 N m etc
Energy & Nuclear Science 51
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 arekeV (1000 eV)MeV (1e6 eV)GeV (1e9 eV)
Be able to inter-convert energy quantities in various units
Energy & Nuclear Science 52
What is light?Wave properties? Particle properties?
MasslessInterferenceNewton ringdiffraction
Law of reflection law of refraction
move in straight line??
Energy & Nuclear Science 53
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 )
Light is part of the EM spectrum.
EM radiation has a very wide spectrum ( or ).
Energy & Nuclear Science 54
The EM Spectrum
Long-wave RadioBroadcast radio band
Short wavelength radioInfrared
VISIBLEUltraviolet
X-raysGamma rays
The EM Radiation Spectrum
> 600 m 600 - 200 m200 m - 0.1 mm0.1 - 0.0007 mm0.7 - 0.4 um0.4 um - 1 nm1 nm - 0.1 pm0.1 nm
Remember the order of these regions
Energy & Nuclear Science 55
The EM Wave Spectrum
Energy & Nuclear Science 56
The Visible Spectrum
A color pattern seen in an oil filmDouble rainbow
Energy & Nuclear Science 57
Photons, E = h
Max Planck assumption, E = h , was shown to be true by Einstein’s photoelectric experiment.
Speed of light, c = 3e8 m s-1
wavelength, frequency of light, = c / Planck constant, h = 6.62619e-34 J senergy of a photon E = h .
A photon is a bundle of energy, and it’s like a particle of light.
Use wave to show and .
Max Planck(1858-1947)Nobel Prize (1918)
Energy & Nuclear Science 58
The Photon StoryMax Planck assumption, E = h, was shown to be true by Einstein’s photoelectric experiment.
Frequency
INTENSITY
Wien’s Law
Rayleigh’sPrediction
Experimental curveand Planck’s prediction
Kinetic energyof electron
FrequencyThreshold
Explain the photoelectric effect.
Energy & Nuclear Science 59
Photon EnergyTypical red light, = 4.69e14 s-1 (Hz),
= c / = 3e8 m s-1 / 4.69e14 s-1 = 640 nm
Wave number = 1 / = 1 / 6.40e11 m = 1.56e6 m-1
E = h = 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 60
LaserLight Amplification by Stimulated Emission of Radiation (LASER)
Greenphotons Stimulated decay,
Red laser
Spontaneous decay
Red laser
Green pumping light
Partial mirrorMirror
Energy & Nuclear Science 61
Chemical Energyenthalpy
2H2 + O2
2H2O(g)373K
2H2O(l)273K
2H2O(s)273K12 kJ, energy of fusion
81 kJ, energy ofvaporization
484 kJ, energy ofreaction
2H2O(l)373K15 kJ, heat
4H + 2O
1469 kJ, bond energy
Understand these terms on energy or enthalpy
Bond energyenergy of reactionenergy related to temperatureenergy related to states melting, vaporization, phase transitionmass loss in chemical reactions
Energy & Nuclear Science 62
Relative and Zero Masses
m = m
v
c
o
21 - ( ) Universal speed299,792,458 m/s
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.
Energy & Nuclear Science 63
Mass and EnergyEinstein 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 = 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 64
Power – rate of energy transfer
mgh
Power = m g v,v, pulling velocity
The SI unit for power P is watt named after James Watt, 1 watt = 1 J s–1
Work out by heart 1 kilowatt-hour = __ J = __ cal = __ BTU
Energy & Nuclear Science 65
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.
mgh
Power = m g v,v, pulling velocity
1 amu = (12 kg/k mol)/12
= (1 kg/k mol)/(6.022e26 (k mol)-1)
= 1.661e-27 kg = 931.5 MeV
1 amu = 1/12th of mass of a C12 atom
Some conversion factors1 eV = 1.602 x 10‑19 J1 eV/molecule = 23045 cal/mol1 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
Energy & Nuclear Science 67
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 68
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 69
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 70
Energy crisis and social problems
These issues affect us all, and please apply basics and human natures to solve these problems so your generation will live happily hereafter.
Arbitrary Coordinate
Demand
Cost
Level
Chung, Chieh
sprott.physics.wisc.edu/lectures/plasma.ppt
Dirk O. Gericke,
Advantages of Fusion
• Inexhaustible Supply of Fuel
• Relatively Safe and Clean
• Possibility of Direct Conversion
1. Introduction
Fusion 73
The SunThe sun flare
The corona during an eclipse The aurora
corona during an eclipsecorona during an eclipse