DANCING WITH THE STARSDANCING WITH THE STARS

QUEST FOR FUSION ENERGYQUEST FOR FUSION ENERGY

AbhayAbhay K. RamK. Ram

PSFC, MIT

IAP

2010

January

20

The sun, with all those planetsrevolving around it, and dependent

on it, can still ripen a bunch of grapesas though it had nothing else in the

universe to do.

Galileo

I deduce that the creation of the world happened in the beginning of the autumn of 710 JP. Using

astronomical tables, I determined the first Sunday after the autumnal equinox for the year 710 JP (4004 BC(4004 BC) which was October 23 of that year.

….. the preceding evening of October 23,marks the first day of creation and the start of time.

Reverend James UssherArchbishop of Armagh, Church of IrelandThe Annals of the WorldThe Annals of the World (London, 1658)

JP – Julian Year starting at January 1, 4713 BC

Newton: born 1643Newton: born 1643KeplerKepler: 1571 : 1571 –– 16301630

THE SUN AS A COAL POWER PLANTTHE SUN AS A COAL POWER PLANT

What is the mass of the Sun ??

What is the power output of the Sun ??

How much energy is released in burning coal ??

THE SUN AS A COAL POWER PLANTTHE SUN AS A COAL POWER PLANT

302 10≈ ×M kg

Power output of the 264 10 = Sun Watts×

2 42 0 /C kgO CO MJ+ → +

Sun's lifet

me

i

6 30

2

11

6

(40 10 / ) (2 1

2 10

0 )4 10 /

.

J kg kg

secJ sec

× ××

×=

=

The Sun would last for about 6300 years.The Sun would last for about 6300 years.

Charles Darwin (1809 Charles Darwin (1809 ---- 1882)1882)ON THE ORIGIN OF SPECIES BY MEANS OF

NATURAL SELECTION (London, 1859)

I am tempted to give one other case, the well-known denudation of the Weald.

Hence, under ordinary circumstances, I should infer that for a cliff 500 feet in height, a denudation of one inch per

century for the whole length would be a sufficient allowance. At this rate, on the above data, the denudation

of the Weald must have required 306,662,400 years; or say three hundred million years. But perhaps it would be safer to allow two or three inches per century, and this would reduce the number of years to one hundred and

fifty or one hundred million years.

Charles Darwin, On The Origin of Species

by Means of Natural SelectionLondon (1859)

Hermann von Helmholtz

Conservation of Energy

Conversion of Mechanical Energy to Heat

William Thomson (Lord Kelvin)

Second Law of Thermodynamics

Absolute Temperature Scale

SUN AS A GRAVITY DRIVEN HEAT ENGINESUN AS A GRAVITY DRIVEN HEAT ENGINE

0 83 7 12 10 , 0≈ ×× ≈M R mkg

Power output of the = Sun 264 10 Watts×

Potential energySolar power out

Supu

n's lifetime t

146 10 .sec= ×=

The Sun would last for about 20 million years.The Sun would last for about 20 million years.

235

Potential Energ y M

GR

=

11 3 1 26.674 10 G m kg s− − −= ×

What then are we to think of such geological estimates as 300,000,000 years for the “denudation of the Weald”? Whether is it more probable that the physical conditions

of the sun’s matter differ 1000 times more than dynamics compel us to suppose they differ from of matter in our laboratories; or that a stormy sea, with possible Channel tides of extreme violence, should

encroach of a chalk cliff 1,000 times more rapidly than Mr. Darwin’s estimate of one inch per century?

Sir William Thomson (Lord Kelvin)On the Age of the Sun’s Heat

Macmillan’s Magazine (March 5, 1862)

It takes a long time to prepare a world for man, such thing is not done in a day. Some of the great scientists,

carefully deciphering the evidences furnished by geology, have arrived at the conviction that our world is

prodigiously old, and they may be right, but Lord Kelvin is not of their opinion. He takes a cautious, conservative

view, in order to be on the safe side, and feels sure it is not so old as they think. As Lord Kelvin is the highest authority in science now living, I think we must yield to

him and accept his view.

Mark TwainWas the World Made for Man

(1903).

“This study of the radiation and internal conditions of a star brings forward very pressingly a problem often debated in this Section: What is the source

of the heat which the Sun and stars are continually squandering?”

Arthur Eddington, The Observatory, 1920.(Volume XLIII, No. 557, pp. 311-358)

“Lord Kelvin’s date of the creation of the Sun is treated with no more respect than Archbishop Ussher’s.

………………….

Only the inertia of tradition keeps the contraction hypothesis alive – or rather, not alive, but an unburied

corpse.”

Arthur Eddington, The Observatory, 1920.(Volume XLIII, No. 557, pp. 311-358)

“A star is drawing on some vast reservoir of energy by means unknown to us. This reservoir can scarcely be other than the sub-atomic energy which, it is known,

exists abundantly in all matter……

There is sufficient in the Sun to maintain its output of heat for 15 billion years.”

Arthur Eddington, The Observatory, 1920.(Volume XLIII, No. 557, pp. 311-358)

1905: Einstein (E=mc2).1913: Bohr (model of the atom).1920: Eddington’s speech.1928: Analysis of Fraunhofer lines (1814) show that hydrogen is

the most abundant element in the Sun’s atmosphere.1929: Tonks and Langmuir (plasma oscillations).1932: Chadwick (discovery of the neutron).1933: Joliot-Curie (conversion of energy into mass).1933: Cockcroft and Walton (conversion of mass into energy).1938: Bethe (energy production in the Sun and stars through

thermonuclear fusion).

TIME LINE OF SOME IMPORTANT EVENTS

“If, indeed, the sub-atomic energy in the stars is being freely used to maintain their

great furnaces, it seems to bring a little nearer to fulfilment our dream of controlling this latent power for the well-being of the

human race - or for its suicide.”

Arthur Eddington, The Observatory, 1920.(Volume XLIII, No. 557, pp. 311-358)

1954: USA tests first hydrogen bombin Bikini.

1956: First experiments on a tokamakin Russia.

1958: Declassification of fusion announced in Geneva.

DANCING WITH THE STARS:

QUEST FORFUSION ENERGY

Acknowledgements:

Dr. Jerry Hughes

Mr. Paul Rivenberg

Dr. Charles Kessel

JUST THE FACTS

SOME BASIC DIMENSIONS

SIZE OF AN ATOM ~ 10-10 m = 1 Å

SIZE OF A NUCLEUS ~ few 10-15 m = few fm

SIZE OF A PROTON OR NEUTRON ~ 1 fm

BASIC FORCES IN NATURE

RANGERELATIVESTRENGTH

FORCE

infinite

finite / infinite

~ few fm

~ 0.1% fm

6 x 10-39GRAVITATIONAL

1/137ELECTROMAGNETIC

1STRONG

~10-6WEAK

No exchange of energy.Exchange of energy through

the field.

Important for magneticfusion on Earth.

Important for fusion inthe Sun.

Magnetic fields existessentially everywhere.

Gravitational fields existeverywhere.

Magnetic field of one movingcharge affects the other.

Gravitational field of one mass affects the other.

Between two movingcharged particles.

Between two masses.

MAGNETIC FORCEGRAVITATIONAL FORCE

“It appears that the radical element responsible for the continuing thread of cosmic unrest is

the magnetic field.”

Eugene N. Parker (1979).

NUCLEAR FUSION INTERACTIONS

If (MA + MB) > (MC +MD) then energy is generated

[E = Mc2]

FUSION REACTIONS ARE QUANTUM PHENOMENA

Need to overcome the mutual repulsion of ions.

NUCLEI OF INTEREST IN FUSION ENERGY

1 eV = 1.6022x10-19 Joule1 eV = 1.16x104 ≈ 12,000 K

0 °C = 32 °F = 273.15 Kenergy required to ionize a hydrogenatom = 13.6 eV ≈ 163,200 K100 Watt bulb lit for one second uses 100 Joules of energy(equivalently, 6.24 x 1020 eV)

1 keV = 1000 eV = 103 eV1 MeV = 1,000,000 eV = 106 eV

FUSION REACTIONS IN THE SUNFUSION REACTIONS IN THE SUN

FUSION REACTIONS IN THE SUNFUSION REACTIONS IN THE SUN

FUSION REACTIONS IN THE SUNEach proton in the solar core leads to 6.55 MeVof electromagnetic energy from the Sun.

The observed solar luminosity requires that3.7x1038 H are converted into 4He per second.

The Sun’s composition and mass shows that itstarted with about 9x1056 hydrogen atoms.

About 10% of the hydrogen in the Sun has beenconsumed in the past 4.5 billion years.

FUSION REACTIONS IN THE SUNFUSION REACTIONS IN THE SUN

NUCLEAR REACTION FOR FUSION POWER ON EARTH

TEMPERATURE DEPENDENCE OF “RATES”FOR FUSION REACTIONS

MEAN REACTION TIME FOR D-T FUSION

Assume: temperature T = 20 keVdensity n = 1020 nuclei per cubic meter

Then: <σv> ≈ 4x10-22 m3 / sec

So the mean lifetime before fusion reactions is= ≈ 25 seconds

The speed of a deuteron is about 1,000 km / sec.

>< vσ1

n

NUCLEAR REACTION FOR FUSION POWER ON EARTH

MAGNETIC CONFINEMENT

MOTION IN A MAGNETIC FIELD

Motion along the magnetic field line is unconfined.Alcator routinely operates at 5 Tesla magnetic fields

(100,000 times the Earth’s magnetic field)

MOTION IN A TOROIDAL MAGNETIC FIELD

Electrons and ions drift in opposite directions(ions drift upwards, electrons downwards).

First pointed out by Enrico Fermi.

MOTION IN A TOROIDAL MAGNETIC FIELD

TWISTED MAGNETIC FIELD LINES

Create helical magnetic field lines by introducing a toroidal current.

In Alcator currents of the order of 1 MA are generated.

STARTING THE FUSION ENGINE

STARTUP PHASE LEADING TO THE SUN

Compression of hydrogen molecular cloud(pressure 10-15 torr ≈ 1.4 x 10-18 atmosphere)Collapsing cloud cores (globules) begin to light up as gravitational potential energy is converted to heat.

STARTUP PHASE LEADING TO THE SUN

A globule collapses and continues to heat up.

The temperature in the core rises to about150,000 K ( ≈ 13 eV).

Around 107 K (≈ 1 keV)the p-p reaction starts.

STARTUP PHASE LEADING TO THE SUN

GIANT MOLECULAR CLOUD

Density ≈ 108 particles per cubic meter; temperature ≈ 100 K

Pressure ≈ 10-15 torr ≈ 1.4 x 10-18 atmosphere

BIRTH REGION OF STARSBIRTH REGION OF STARS

HH46-47As observed by SPITZERSPITZER

PROTOSTARSPROTOSTARS

MAIN SEQUENCE STAR

EVOLUTION OF THE SOLAR LUMINOSITY

Luminosity is the total electromagnetic power emitted.

Presently, L⊙ = 3.84 x 1026 Watts (solar constant ≈ 1.4 kW / m2) .

STARTUP OF A LABORATORY FUSION DEVICE

Prior to a discharge create high vacuum (10-6 torr).Hydrogen gas injected into the vacuum vessel (few 10-6 torr).Turn on the toroidal magnetic field coils.Transformer is discharged (the current in the primary is slowly changed).

STARTUP OF A LABORATORY FUSION DEVICE

The induced voltage in the chamber ionizes the gas creating a plasma.The plasma current, density, and temperature increase.

EVOLUTION OF A LABORATORY FUSION PLASMA(Alcator C-Mod)

MAIN SEQUENCE

COMPARING THE SUN WITH A FUSION COMPARING THE SUN WITH A FUSION REACTORREACTOR

SUNSUN ARIES IVARIES IV

J. N. Bachall & R. K. Ulrich, Reviews of Modern Physics (1988).C. Kessel et al., Fusion Engineering and Design (2006);

and private communications,

Solar power output = 3.84 x 1028 Watts

Global power consumption = 1.6 x 1013 Watts

Typical power output of a reactor = 1 - 2 x 109 Watts

ELECTRON DENSITY PROFILESELECTRON DENSITY PROFILESx 1011

n e(1

0 20

) m -3

n e(1

020

) m -3

20 3

19 3

peak density 3.6 10edge density 7.2 0 1

mm

−

−

= ×

= ×

31 3

27 3

peak density 6 10edge density 9 10

mm

−

−

≈ ×

≈ ×

Sun ARIES

R / R⊙ r / a

a = 1.38 mR⊙ = 108 m

TEMPERATURE PROFILESTEMPERATURE PROFILES

Sun ARIES

R / R⊙ r / a

T (k

eV)

T (k

eV)

peak temperature 1.35edge tempera

tur e 0.04

keVkeV

==

peak temperature 25edge temperature

0. 1

keVkeV

==

SOLAR LUMONISITY AND ENERGY OUTPUTSOLAR LUMONISITY AND ENERGY OUTPUTL

/ L⊙

R / R⊙d(

Ener

gy)/(

dR/R

⊙)

Energy Production

Luminosity is the total electromagnetic power emitted.

Luminosity

Presently, L⊙ = 3.84 x1026 Watts (solar constant ≈ 1.4 kW / m2)

R / R⊙

SOLAR LUMONISITY AND ENERGY OUTPUTSOLAR LUMONISITY AND ENERGY OUTPUTL

/ L⊙

R / R⊙d(

Ener

gy)/(

dR/R

⊙)

Energy Production

Luminosity

R / R⊙

COMPARISON OF PRESSURE PROFILES

ARIES

Sun

Pres

sure

(N /

m2 )

R / R⊙ r / a

Solar pressure normalized to 2.29 x 1016

ARIES pressure normalized to 2.79 x 106

ENERGY CONFINEMENT TIME

ENERGY CONFINEMENT TIME

(Watts) rate heating(Joules)energy stored total

τE (sec) =

The goal in fusion is to reach the required temperaturewith the least amount of heating power.

In the Sun the energy confinement time is a million years.

In magnetic fusion devices it is around a second.

THE PLASMA EDGE

THE SOLAR CORONA

THE SOLAR CORONA

THE SOLAR CORONA

S. J. Zweben: http://www.pppl.gov/~szweben

THE EDGE IN A LABORATORY FUSION DEVICETHE EDGE IN A LABORATORY FUSION DEVICE

THE EDGE IN A LABORATORY FUSION DEVICETHE EDGE IN A LABORATORY FUSION DEVICE

THE EDGE IN A LABORATORY FUSION DEVICE

THE EDGE IN A LABORATORY FUSION DEVICE

THE REACTOR WALLTHE REACTOR WALL

Constraint on a fusion reactor:

No “squandering” of energy

FUSION BIFUSION BI--PRODUCTSPRODUCTS

Sun: 4He γ ν

Fusion reactor: 4He n

For every reaction cycle producing 4He, about 26 MeV is contained in the core as heat and

about 0.8 MeV is carried away by ν’s.

For every reaction cycle, the energy in 4Heis about 3.5 MeV and that in n is 14.1 MeV.

Neutrinos they are very small.They have no charge and have no massAnd do not interact at all.The earth is just a silly ballTo them, through which they simply pass,Like dustmaids down a drafty hallOr photons through a sheet of glass.

John UpdikeCosmic Gall

The neutron releasedblow open some otherswhich release more neutronsand start this all over

Blow open some othersand choirs will crumbleand start this all overwith eyes burned to ashes.

Peter MeinkeAtomic Pantoum

STEADY STATE OPERATION

OPERATION OF A LABORATORY FUSION DEVICE

SOLAR IRRADIANCE OVER “SHORTER” TIME

TOWARD FULFILLING THE QUESTTOWARD FULFILLING THE QUEST

D-T operation

Controlling the edge

Plasma facing materials

Energy extraction

Steady state operation

Breeding of Tritium

SOME TOPICS TO PONDER OVERSOME TOPICS TO PONDER OVER

No problem is so big or so complicatedthat it can't be run away from!

Linus Van Pelt(Peanuts by Charles M. Schulz)

PROGRESS TOWARDS THE FUTURE

INTERNATIONAL THERMONUCLEAR EXPERIMENAL REACTOR

30 m

24 m

INTERNATIONAL THERMONUCLEAR EXPERIMENAL REACTOR

Q =

Demonstrate the scientific and technological feasibility of fusion energyExtended burn of D-T plasmas with steady state operation as a goal.Q > 5Typical fusion power level ~ 500 MW

Plasma current ~ 15 MAToroidal magnetic field of 5.3 TeslaDensity ~ 1020 m-3

inEnergy outEnergy

MEASURING PERFORMANCE – LAWSON CRITERION

MEASURING PERFORMANCE – LAWSON CRITERION

The best way to predict the future is to invent it.

Alan Kay, Computer Scientist (1982).