Transcript A 1-d Continuum SOC model for heat transport in tokamaks

Hymn to AGNI the God of Fire
P.K. Kaw
Institute for Plasma Research
Bhat, Gandhinagar 382428, INDIA
Ahmedabad 2004
Search for sources of energy
• Has typically ended with an encounter with
Fire – Agni in one of its manifestations –
either fashioning fuels for storage or
consuming them for energy release.
• As we trace this history we stand in awe of
AGNI – hence the title in praise of the Lord
of Fire!
Outline
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Why the search ?
Muscle Power
Combustibles
Renewables
Nuclear Power
Future Options
Epilogue
Why the search ?
• Man does not live by bread alone ! Limited
prowess but unlimited dreams. Needs a slave (
ENERGY) to help fulfill his dreams !
• Energy is also required for normal comfortable
living :- heating, cooling, transporting,
manufacture, cooking etc.
• Quality of life ~ Electricity Consumption
Huge gap.
• Average consumption/person in developed world
= 6000 KWH/year ~ 17 KWH/day
• In India ~ 1 KWH/day.
Units …
• 1 KWH = 1 unit of electricity ~ Rs. 2- 4
This is equivalent to energy used in lifting
2000 bags of 100 Kg rice by 2 meters .
• Energy that would be supplied by 6 slaves
working full time.
• Modern man needs energy equivalent of
100 slaves/person to live in comfort !!!
Muscle Power
• First source used by man. His own as well
as that of slaves and animals. Pyramids,
Galley ships …West upto 19th century . Has
limited utility.
• Source of energy ~ Food
Average intake per person per day ~ 2500
Cals = 3 KWH. Mostly used up for the
business of staying alive – keeping warm,
repair and maintenance, growth etc.
Muscle Power (Contd.)
• We may be able to divert 10 % of energy
during waking hours to do useful work =
0.3/2 = 0.15 KWH/day.
• This explains why we need ~ 100 slaves to
keep 1 modern man in comfort.
• Not acceptable in free democratic world.
How do animals (including man) do work and
generate heat?
Animals are controlled furnaces ‘slowly
burning’ the fuel of food and generating energy:
Sugars , fats etc. + O2
(Food)
CO2 + H2O + energy
Storage and heat
(Respiration)
Energy Storage
Adenosine
diphosphate
(ADP)
Inorganic
+ phosphate
+
energy
Adenosine
triphosphate
(ATP)
ATP is stored in muscles and converted into ADP and
muscular energy (by contraction) + heat when we order
the muscles to do work.
Our first encounter with AGNI.
Living matter is a slow fire (combustion!) converting
energy trapped in food into a usable form.
Also uses the strategy of employing special catalysts
(enzymes) to give decent rates of reaction at near room
temperatures!
Combustibles
• Discovery of Fire (direct encounter with AGNI )
25000 years
 ago.
• Natural fire – learnt to keep alive by adding
combustibles (wood, dry leaves , fat etc.) ;
ignition.
• Heat (warmth) , light (security) , cook (health) ,
work , metals (improved weapons) .
• First put to work in steam engines of 19th century
– led to the industrial revolution and explosive
growth of western civilization.
Combustibles (contd.)
• Thus began the age of Fossil fuels.
• Internal combustion engine and generators
of electricity invented.
• Coal, Oil, Natural gas have become key
commodities in the 20th century.
• Availability and price of the fuels
determines the pace of world economic
development.
Combustibles (contd.)
• Can we depend on them in 21st century and
beyond ?
• Let us look at this question in a fundamental way!
Fossil fuels (like coal, oil, gas) are hydrocarbons produced
from plants and animal remains trapped by geological
upheavals for millions of years under the earth.
Like Food they release energy by combustion.
Hydrocarbons +O2
CO2 + H2O + energy
FIRE!!
In either case (food or fossil fuels) energy is liberated
because electronic linkages binding atoms in fuel are weaker
than those in product molecules.
Energy per
carbon atom
in fuel
Energy per carbon
atom in CO2
Energy released /
carbon atom.
Energy released/mol ~ few eV ~ 10-19 Watt secs.
1 gm. mol has 6 x 1023 mols.
Total known reserves of fossil fuel ~ 1012 tons.
~ 1016 KWH of energy
Energy required /year for world
~ 5 x 109 x 6000 KWH
= 3 x 1013 KWH
Reserves will last for for 1016/3 x 1013 ~ 300 years.
Detailed estimates show that Oil will finish in 50
years , Gas in 100 years and Coal in 500 years.
Energy in fossil fuels
• Food and fossil fuel have energy stored in them in
the form of weaker electronic linkages of atoms.
Where did this energy come from?
• It came from the SUN – that fierce manifestation
of AGNI – in our skies. HOW?
• Solar radiation was utilized by Chlorophyll (green
colouring matter in plants) to carry out
photosynthesis.
CO2 + H2O + light energy
O2 + sugars, carbohydrates
Estimate of fossil fuel reserves
Sun aims about 1017 Watts at earth.
Of this 0.01 % is trapped by photosynthesis.
About 10-6 of the plant matter is stored as
Fossil fuels.
107 Watts for ~ billion years ~ 1017 KWH of
fuels ~ 1013 tons.
Gives an upper bound to fossil fuel reserve.
Homage toThee, O AGNI in the form of SUN
Problems with fossil fuels
• It has taken almost a billion years to build these
reserves and they can be squandered away in less
than 500 years time. It is a wealth belonging to all
future generations. Should we just burn it ?
• Environment degradation, greenhouse effect, cost
of clean up.
• Uneven distribution (e.g countries with 6% of
world population have 66 % oil wealth) leads to
political tensions, wars!
• Thus fossil fuel cannot be a long term solution .
Fossil fuel era in the few thousand
year history of mankind
Renewables
AGNI as Sun delivers a lot of energy to earth –
albeit in a dilute form.
8 x 1016 W
direct
conversion
to heat.
(Solar)
4 x 1016 W
Evaporation,
Precipitation,
Storage in
water cycle.
(Hydro)
4 x 1014 W
Winds, waves
(Wind)
4 x 1013 W
Photosynthesis
Storage in
plants
(Biomass)
Hydropower
Energy of moving water in rivers used since antiquity
– water mills to grind corn, run irrigation systems, saw
wood, run textile looms…
Modern version is to run dynamos to generate
electricity in hydroelectric power stations.
Non – polluting, low running cost but limited because
of geography.
Potential capacity in India ~ 85 G Watts nearly 10 %
of total requirement in future!
Solar Power
Too dilute and diffuse: Not suitable for centralized
urban industrial complexes.
Problems of storage of heat for night, cloudy days.
Mostly residential use – solar cooker, water heater etc.
Electricity plant ~ 35Mwatts/km sq feasible
Solar photovoltaic – direct conversion of sunlight into
electricity by semiconductor materials – relatively
expensive, high maintenance and inefficient – has
found applications in specialized niche areas like space
vehicle power systems, remote places etc.
Wind Power
Limited applicability in certain areas with high wind
velocity like coastal areas of Tamilnadu & Gujarat
Biomass
Fast growing cash crops used for direct burning or
conversion into alcohols for use as liquid fuels or
conversion into bio gas . Could be integrated with local
rural economics. Not a major player in total energy
scene but Significant social consequences for a
country like India !
Nuclear Energy
Sun has been burning brightly for 5 billion
years. It has spewed out
1017 Watts x 108 x 5 x 109 x 3 x 107 = 1042 Joules.
( 1 KWH = 3.6 Million Joules )
of energy. It has a mass of ~ 1033 gms. Even
if every atom burnt in a chemical fire,
rearranging electronic linkages, we would at
best produce 1038 Joules. AGNI in sun is an
unusual fire ! It is a thermonuclear fire !!
Nuclear Energy
Nuclear energy discovered in 20th century.
Einstein showed that mass and energy are interconvertible.
E  m c2
Energy released
Here c is the
velocity of light.
Mass lost
1042 Joules of energy may be produced by loss of 1028
gms. i.e. 1/100,000 of the Sun’s mass. This mass loss
would not have any other drastic consequence on Sun.
Nuclear Fission and Fusion
Bohr – Rutherford model already showed that the mass
of atom is concentrated in nucleus.
Hence nuclear reactions – as opposed to chemical
reactions could change mass and release energy.
Fission
U + n fission
fragments.
Heavy nuclei
Fusion
D+T He +n
+17.6 MeV.
Light Nuclei
Mass is lost and energy is released
Energy/nucleon
in Uranium
Energy/nucleon in
Fe nucleus. Most
stable nucleus
which is bound
intensely.
Energy/nucleon
in D, T
Nuclear energy released / nucleus ~ 106 times the
chemical release /atom.
Sun releases its energy by thermonuclear fusion of protons:
4 protons
Helium + electrons + energy
Need for high temperatures.
Containment by gravitation on Sun.
Fission and Fusion energy on earth
Atomic and Hydrogen Bombs.
Controlled reactors for Electricity Production.
Fission Reactors Commercially exploited > 50 yrs
France
USA
Japan
Korea
India
75 %
25%
33%
40%
3%
15% by 2020
Radioactive waste problem
Radiation Hazard – 3 mile island, Chernobyll
Fuel
Proliferation
Why Fusion ?
• Fuel is limitless!
D (1 part in 6000 of sea water)
T bred from Lithium (earth’s crust +oceans)
Gives energy security to all nations.
• Waste Products minimal
- reaction products non radio –active
- neutron induced radio – activity in vessel etc.
can be minimized by use of low activation
materials.
- radioactivity can be eliminated in advanced
reactors (p-B, D- He3 etc.).
Why Fusion ?
• Inherently safe system.
no chain reaction, melt down etc.
• No dangers of proliferation
• No Atmospheric pollution (no CO2 , GHG
etc.) Tritium leakage problem minimal since
it is continuously bred.
With so many merits, stakes in the
development of FUSION are Colossal !!
How to achieve Fusion?
D+T
He +n +17.6MeV
• Heat the fuel mixture to 100 million degrees and
get conditions such that
Density x Temp x confinement time > 5.1021m-3 keV secs.
• Ignition of thermonuclear AGNI
• He nuclei keep the fuel hot. Neutrons take energy
out, trapped in blanket like fission reactor.
• Mixture at sub-atmospheric densities (~1020 m-3) to
be held and thermally isolated for seconds.
Fuel is in a Plasma State
Figure 4a Components of a fusion reactor
Confining Plasma …
• Can be held in cages made of non material
magnetic field lines – Magnetic bottles.
Ex: TOKAMAKS
• Plasma heated by currents and microwaves.
• Once the Fire ignites it stays hot and we
simply keep adding more and more fuel.
Figure 5 Progress in the critical
parameters for fusion reactor experiments
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ITER: International thermonuclear
Experimental Reactor
Is the flagship experiment being built at a
cost of 5 billion US dollars
Original parties: US, Russia, Europe, Japan.
Recent Additions: China, Korea, Canada.
Each partner contributing around ½ billion
dollars (Rs. 2500 crores).
Experiment ready by 2012. Will pave the
way for DEMO ~ operational by 2030.
First commercial reactors available in 20352050.
Our National Programme
• Started in mid eighties at the Institute for
Plasma Research, Gandhinagar.
• First indigenously built tokamak ADITYA
started operation in 1989.
• ADITYA routinely makes a few million
degrees hot artificial sun and holds it in
magnetic cages for fractions of a second.
Figure 7
ADITYA , the
indigenously
built tokamak at
Institute for
Plasma Research
, Gandhinagar
Our National Programme (contd.)
• Our second generation experiment: Steady
State superconducting tokamak SST1 will
be ready for experiments in 2004.
• Plasma temperature will be 20 –40 million
degrees. It will be the first experiment in the
world holding a hot tokamak plasma for
1000 seconds and will give a preview of
some features of ITER physics on a small
scale.
Figure 8 SST 1 ,
the superconducting
steady state tokamak
, which will hold a
fusion plasma for a
1000 seconds , being
fabricated and
assembled at
Institute for Plasma
Research ,
Gandhinagar
Summary and Future Options
• Muscle power and fossil fuel are out. Nuclear
energy, specially thermonuclear fusion fire is
definitely in. Renewables like hydro, wind, solar
etc. are in but may play a subsidiary role.
• New ideas on improved utilization of solar by
genetically engineered accelerated
photosynthesis/dissociation exist, e.g. work is
going on development of algae/bacteria which
would use sunlight and water as inputs and
generate hydrogen as a product.
Some Future Options (contd.)
• Hydrogen is an excellent fuel – gas, readily
transportable by pipes – produces non – polluting
water in combustion. Hydrogen economy will take
over from Carbon economy anyway!
• Another attractive idea is to put solar power
stations on satellites –
- they would see sun all the times
- they would not occupy valuable real estate.
- would not be effected by dust, atmosphere etc.
- would send concentrated energy through
microwave beams to ground power stations.
Fig. 9 The Solar satellite concept
Some Future Options (contd.)
• A dreamer, Freeman Dyson, has asked – Why
should we be satisfied with 10-8 of Sun’s energy,
which it aims at us?
With improved engineering skills – trap all of
Sun’s energy on spherical shell of material from
Saturn at Jupiter’s orbit.
Advanced civilizations may already be doing this.
Figure 10
Our Sun
surrounded by
the Dyson
sphere
collecting all
of sun’s
radiation and
beaming the
energy to
earth.
Epilogue
• Explorations into search for new sources of energy
has led us into interesting alleys of fundamental
science.
• Most sources were traced to nuclear fire inside the
Sun or some day in our reactors.
• Where does energy trapped in nuclear fuels come
from?
• Genesis of elements – nucleosynthesis of light and
heavy nuclei.
• In the beginning there was the BIG BANG! The
primordial FIRE or the earliest AGNI.
Epilogue (contd.)
• It started with a ball of radiation which expanded,
cooled and formed a quark gluon plasma. As the
ball cooled further, the quarks condensed into
protons, neutrons and some of the lightest
elements like He, Li, B … etc.
• Heavier elements like C, N, O … are formed in
the fusion furnaces of young stars. Elements
beyond Fe are formed by neutron capture
processes.
• We see a rich variety of elements because cooking
in the primitive universe and stars is imperfect.
Perfect cooking would have led to Fe everywhere.
What are we ? A deeper look at ourselves
• Made of natural elements H, C, N, O …
• Our atoms are billions of years old !
• Each H nucleus of my body was fashioned from
quarks in that primeval AGNI 14 billion years ago.
• Each C,N, O nucleus has been fashioned in the
fusion furnace of some star, spewed out into space
during its death – throes and picked up by the gas
clouds from which our Sun and its planets have
emerged.
Thus we may verily say to AGNI:
Thou art the Source
And fashioned every limb of mine …
Thou art the sustainer
And provide energy to keep me together …
And when I am ready to Sleep
Into thy bosom will I disappear!
In expressing our deepest yearnings, our sentiments
are no different form our RIGVEDIC ancestors who
sang Hymns to AGNI!!
Figure 6
ITER , the
International
Thermonuclear
Experimental
Reactor
Our National Programme (contd.)
• Our projected plan calls for SST2 expt in 2015-20
time frame. SST2 will be a prototype fusion
breeder which will use neutrons from the fusion
fire to breed fissile material from Thorium.
• If pure fusion makes unqualified progress by then
we will follow that path.
• Otherwise we will continue the path of hybrid
development in which fusion fire will be used to
exploit our enormous deposits of Thorium into
fissile material for use in fission reactors.
Figure 4 b
Magnetic
Bottles ...the
Tokamak
Concept
where the
magnetic cage
is produced by
a combination
of plasma
currents and
external coil
currents
Progress and Outlook
• Early experiments showed that tokamak
plasmas lose heat more rapidly than they
should! Traced to the Collective effects or
mob mentality of matter in Plasma
state!Gives electromagnetic storms which
makes the bottles leaky.
• It has taken 4 decades to learn enough of
plasma science to know how to plug these
leaks.
Phenomenal progress in past
decade
• Temperatures upto 400 million degrees.
• nT within striking distance of ignition.
• Fusion power output ~ 16 Mwatts sustained for
seconds.
• Reactor Size plasmas (millions of Amps of current
and several cubic meters in volume) manipulated
• Next Step Experiments: Will study Burning
plasmas, Steady State devices and Fusion
materials.