Chapter 5. Thermonuclear 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

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


1.Introduction




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!


1.Introduction




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


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 .


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


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?


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

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.


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?


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


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


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


What is light?Wave properties? Particle properties?

MasslessInterferenceNewton ringdiffraction

Law of reflection law of refraction

move in straight line??


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 ).


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


The EM Wave Spectrum


The Visible Spectrum

A color pattern seen in an oil filmDouble rainbow


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)


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.


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.


LaserLight Amplification by Stimulated Emission of Radiation (LASER)

Greenphotons Stimulated decay,

Red laser

Spontaneous decay

Red laser

Green pumping light

Partial mirrorMirror


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


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.


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


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


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


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.


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 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 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

Documents

Chapter 5. Thermonuclear Fusion