Chemical, Biological and Environmental Engineering A Few Comments About Fusion.
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Transcript of Chemical, Biological and Environmental Engineering A Few Comments About Fusion.
Chemical, Biological and Environmental Engineering
A Few Comments About Fusion
Advanced Materials and Sustainable Energy LabCBEE
Binding Energy
Energy released when nucleus created from protons and neutrons
Larger binding energy per nucleon means more stable nucleus
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Fusion vs. Fission
Fusion
Fission
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Relevant fusion reactions
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Calculation of energy released Released energy follows from the mass deficit.
Consider the reaction
Masses of products are
The mass deficit (Total mass before minus total mass after) for reaction is
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Energy then follows from Einstein’s formula
Physicist’s unit of energy is electron volt (eV)
(kilo-electron volt, keV; mega-electron volt MeV)
Calculation of released energy
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Energy released by 1kg of D-T mixture
1 kg of a Deuterium/Tritium mixture would allow for a number of fusion reactions N
This would generate
If released over 24h, this is around 4 GW
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Availability of the fuel Natural abundance of D is 0.015% of all H (1 in 6700)
However, at current rate of energy use there is enough H in the ocean for 1011 yearsDeuterium is also very easy to separate (i.e., cheap)
Tritium is unstable with a half age of 12.3 yearsThere is virtually no naturally occuring Tritium
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Availability of the fuel: T Tritium can be bred from Lithium
Note that the neutron released in the D-T fusion reaction can be used for this purpose
Enough Lithium on land for 10k to 30k years at low cost If the oceans included, enough Li for 107 years
Advanced Materials and Sustainable Energy LabCBEE
Why fusion …. A large amount of fuel is available, at a very low cost
The fuel is available in all locations of the earth.
Like fission, fusion is CO2 neutral
Fusion would yield only a small quantity of high level radioactive waste.There is only a small threat to non-proliferation of weapon material
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But... An energy producing working concept is yet to be
demonstrated.
The operation of a fusion reactor is hindered by several difficult (and rather interesting) physics phenomena
Also bear in mind that the cost argument thus far focuses on the fuel only
However, the cost of the energy is largely determined by the cost of the reactor...
Advanced Materials and Sustainable Energy LabCBEE
Distribution of energy over the products
Energy released as kinetic energy of products
Kinetic energy is not equally distributed:
Since both energy and momentum are conserved
You can solve for the energy in He and n
Therefore n has 80% of energy and He has 20%
2 21 1 and 0
2 2fusion He He n n He He n nE m m m m
21 and
2n He
He He He fusion n fusionHe n He n
m mE m E E E
m m m m
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Key problem of fusion
…. Is the Coulomb barrier
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Reaction Cross Section
Cross section is the effective area connected with the occurrence of the reaction
If you are playing billiards, the cross section is pr2
(with r the radius of the ball)
Reaction cross section of relevant fusion reactions as function of energy.
1 barn = 10-28 m2
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Averaged reaction rate Imagine particle B bombarded by many particles A
Number of collisions in Dt is
Bear in mind that s and v both depend on the energy (which is not the same for all particles)
Cross section s
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Averaged reaction rate …..The cross section must be averaged over energies of
the particles. Assuming a Maxwell distribution
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Number of fusion reactions as function of average T
Particle energy for average T (from Maxwell distribution)
The reaction cross section
The product of distribution and cross section(proportional to reaction rate)
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Compare the two
Cross section as a function of energy
Averaged reaction rate as a function of Temperature
Averaged reaction rate has lesser dependence on energy
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Current fusion reactor concepts Based on a mixture of Deuterium and Tritium
Designed to operate at around 10 keV
(10 keV is equivalent to 100,000,000 K)
Matter is in the plasma state (fully ionized)
Both decisions are related to reaction cross section
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Implications from high temperatureTemperature expresses an averaged energy.
You can convert between K and eV
(so 10 keV is 100 million Kelvin)
The average thermal velocity at 10keV can be estimated as
This is 106 m/s for Deuterium nuclei in plasma
In a reactor of 10 m size the particles would be lost in 10 ms...
1eV = 11605 K 1K=8.616x10-5 eV
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Lawson criterion Derives conditions where production of fusion energy is
possible
We derived reaction rate of particle B due to particles A as
In the case of more than one particle B we could get
Remember we derived <su> for a given temperature
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Fusion powerThe total fusion power then is the reaction rate times energy
Using quasi-neutrality (Deuteriums and Tritiums are indistiguishable)
For a 50-50% mixture of Deuterium and Tritium (nD=nT=1/2n)
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Fusion powerAt the relevant temperature range 6-20 keV the average cross
section is
Plugging in, the fusion power can then be expressed as
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To examine power economy if devices, power produced must be compared with power loss from the plasma
For this we introduce the energy confinement time tE
Ratio of energy content and power loss (e.g. Thermal conduction)
Where W is the stored energy density
The power loss
Eheat
WP
13
3heat E heat EW nTV P nT PV
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Fusion Power to Heating Power ratio
Combine this with the fusion power derived earlier
This is called the “n-T-tau product”
We can get two strategies for fusion energy from here:
High n, low tE
Low n, high tE
(remember, temperature is fixed by cross section at 10 keV)
2 27.7fusionP n T V
0.16fusionE
heat
PnT
P
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Break-even and IgnitionThe break-even condition is defined as the state in which the
total fusion power is equal to the heating power
Note that some power could be externally supplied...
Ignition is defined as the state in which the energy produced by the fusion reactions is sufficient to heat the plasma
Remember that neutrons (80% of the energy) escape reactor; energy in He remains for plasma heating (20%)
1 0.16 Break even when 6fusionE E
heat
PnT nT
P
5 0.16 Ignition when 30fusionE E
heat
PnT nT
P
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Inertial Containment Fusion: high n low tE
Rapid compression and heating of a solid fuel (high n) pellet using laser or particle beams.
Fusion occurs for a few mS... (low t)
Idea is to obtain a sufficient amount of fusion reactions (Pfusion) to generate energy (Pheat) before the material flies apart
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Magnetic confinement: low n high tE
In a plasma, all particles are chargedIf strong magnetic field applied, Lorentz force can be used to
trap charged particlesForce causes charged particles to gyrate around the field lines
with a typical radius At 10 keV and 5 Tesla this radius of 4 mm for Deuterium and
0.07 mm for the electrons
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Tokamak / Stellarator
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Large Helical Device (LHD,Japan)
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Stellarator
• Inside the device it looks something like this • Picture from LHD in JAPAN
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Tokamak progress as n-T-tau
Current experiments are close to break-even
The next step ITER is expected to operate above break-even but still below ignition
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ITER: International Thermonuclear Experimental Reactor
1985 partnership between EU, Russia (started by Soviet Union…), USA (left in 1999, returned in 2003), Japan, Canada (left in 2003), RoK (2003), India (2005), PRC (2007)
• Budget about G€10… (as in 10 billion euros)• 50% from host “nation” (EU), remainder shared by others
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ITER GoalsAchieve steady-state plasma with Q > 5 (5x break even)
Momentarily achieve Q > 10 (ten times more thermal energy from fusion heating than is supplied by auxiliary heating
Maintain fusion pulse for up to eight minutes.
Develop technologies needed for fusion power plant
Verify tritium breeding concepts.
Refine neutron shield/heat conversion technology
(most of energy in the D+T fusion reaction is released in the form of fast neutrons)