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Nuclear Fusion
STEREO Images of Extreme UV Radia6on at 1 Million C
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Fusion vs. Fission Fission is • the breaking apart of a nucleus • what occurs during radioac6ve decay • naturally occurring and happens in power plants
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Fusion vs. Fission Fusion is • the combining of two nuclei to form a heavier nucleus • what occurs inside the core of the Sun • the magic bullet for solving human energy problems…
or maybe not
Eddington’s Sun:
(1920s) Sir Arthur Eddington: Puts it all together….
1) Gravitational forces pressurize the center of the Sun.
2) Compression heats the interior (he thought to 40 million K).
3) Thermal collisions strip electrons from their nucleus, creating a plasma.
4) Free protons collide and stick to form helium nuclei.
5) The mass difference between H and He is converted to energy and released as light!
There are problems with this idea: Protons are VERY hard to make fuse! Where does all the extra positive charge go???? 4
Overcoming the Impossible:
p + p è D + e+
There was still a problem though.
The amount of thermal energy, even in the core of the Sun, is NOT enough to overcome repulsion between the two protons.
How does it happen then?
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The beginning of the process requires:
Classical Mechanics vs. Quantum Mechanics
Electron moves towards the barrier.
Electron bounces off of the barrier.
Classical Picture: Think of the electron as a point par6cle.
This is NOT what happens quantum mechanically!!!
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Classical Mechanics vs. Quantum Mechanics
Electron wave moves towards the barrier.
Electron has large probability of not passing through the barrier. But it has a small probability of passing through the barrier
Quantum Picture: Think of the electron as a wave, which describe the probability an electron will be found at a given loca6on.
probability wave
Most of the 6me, the electron does not pass through the barrier.
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Classical Mechanics vs. Quantum Mechanics
Electron wave moves towards the barrier.
Quantum Picture: Think of the electron as a wave, which describe the probability an electron will be found at a given loca6on.
probability wave
Quantum Tunneling: Occasionally the electron passes through the barrier.
Electron has large probability of not passing through the barrier. But it has a small probability of passing through the barrier
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A Numbers Game:
How likely is it for two protons to combine in the core of the Sun?
Your chances of winning the lottery are 40 BILLION times greater.
P + P è D + e+ has ~1 chance in 4 x 1016, each second!
So how does this happen?
• Density in the solar core = 150 g/cm3.
• Mass of a proton = 1.7 x 10-30 g.
• Proton density in core = 8 x 1031 p/cm3.
• Thus there are ~ 1015 reactions/s-cm3.
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Hans Bethe:
• Hans Bethe (~1940): Developed a theory for the ways in which fusion (4H è He) could work in stars.
• What kind of fusion happened depended on how hot and dense the core is and how massive the star is.
• Very massive stars have one kind of fusion, called the CNO cycle (Weizsäcker), that involved `rare` elements (carbon, nitrogen, and oxygen).
• Less massive stars (like the Sun) are neither dense or hot enough for CNO fusion. Instead they fused He directly from H.
He called this the Proton-Proton
(P-P) chain. 10
Solar Fusion: The P-P Chain
e+ + e- ⇒ 2γ
Step 1: p + p ⇒ D + e+ + νe
(neutrino)
Reaction Rate = 1015 reactions/s-cm3; once in every 1.4 x 1010 yr per pair of Ps
(p+n)
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Solar Fusion: The P-P Chain
Step 2: D + p ⇒ 3He + γ (p+n) (2p+n)
Reaction Rate = occurs once every 0.6 s per D and P pair
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Solar Fusion: The P-P Chain
Step 3: 3He + 3He ⇒ 4He + 2P (2P+2n=alpha particle)
Reaction Rate = once every 106 yr per 3He pairs
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The P-‐P Chain in the SUN
Step 1: p + p ⇒ D + e+ + ν e (0.42 MeV)
Step 2: D + p ⇒ 3He + γ (5.49 MeV)
Step 3: 3He + 3He ⇒ 4He + 2p (12.86 MeV)
Net: 4p + 2e- ⇒ 4He + 6γ + 2ν e (~ 26 MeV) (Where 1 MeV = 106 eV = 1.6 x 10-13 J)
e+ + e- ⇒ 2γ (1.02 MeV)
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Need two of Step 1 & 2 to have one of Step 3
(2*0.42MeV) + (2*1.02MeV) + (2*5.49MeV) + (1*12.86MeV) = 26.72 MeV
The P-‐P Chain in the SUN
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Fusion Energy on Earth
2) D + T è He4 (3.5 MeV) + n (14 MeV)
3) D + He3 è He4 (3.7 MeV) + p (14.7 MeV)
The P-P chain is very hard to do on the Earth. Instead we can do:
1) D + D è T (1 MeV) + p (3 MeV)
è He3 (0.8 MeV) + n (2.5 MeV)
split 50% - 50%
These three paths are not equal in usefulness 16
There’s a problem However:
• Paths 1) and 2) produce fast neutrons that irradiate the containment vessel and reduce efficiency.
• Path 3) produces the most energy, is the most efficient, and is cleanest.
Fusion Energy on Earth
3He is not found on Earth! 17
Mining the Moon?
• The Apollo Missions found 3He in the lunar soil. Estimates range up to 106 Tons of it.
• The energy content of 3He is:
Energy (3He)= 2x108 kWh/kg
• The average person uses 250 kWh each month:
1 kg powers 105 people for a YEAR!!
• 1 kWh of Energy “Costs” about $0.10
3He is worth $600,000 an ounce!
106 Tons = 300,000 years of power!!! 18
Fusion Energy on Earth Lawson Criterion • Plasma Density (ni) • Plasma Temperature (Ti) • Energy Confinement Time (TE)
19 hap://www.6nt.or.th/adv/fusion/edu/tripleprod.html
= Fusion Triple Product
ITER: D + T
Plasma and Field Interac6ons
• Magne6c field cause moving charges to perpendicular to the field lines
• Charges are bound to magne6c fields
• Charges can move along field lines
B
Posi6ve ion
Electron
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Plasma is bound to the magne6c field. AND
Magne6c fields are bound to the plasma.
= Magne6c field into the page
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Tokamaks
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Fusion Experiments: Magne6c Confinement
• Uses magne6c fields to confine hot plasmas
• Types of expt – Tokamaks (ITER, NSTX, Alcator…)
– Stellerators – Compact Torus (HIT-‐SI…) – Innova6ve Confinement Concepts
• A lot of work s6ll needs to be done
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Fusion Experiments: Iner6al Confinement
• Uses lasers to crush a full target very rapidly
• Types of facili6es: – Solid State Lasers(NIF, NRL…)
– Gas Laser (NRL, PALS…) • Lots of work here too
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