Lecture 22
Fusion
Experimental Nuclear Physics PHYS 741
heeger@wisc.edu
References and Figures from:
- Basdevant, “Fundamentals in Nuclear Physics
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Reading for Next Week
Phys. Rev. D 57, 3873 - 3889 (1998)
Unified approach to the classical statistical
analysis of small signals
G. Feldman, R. Cousins
http://link.aps.org/abstract/PRD/v57/p3873
supplementary reading:
- Bevington “Data Reduction and Error Analysis for the Physical Sciences”
- Particle Data Group: statistics and probability reviews
http://pdg.lbl.gov/2008/reviews/probrpp.pdf
http://pdg.lbl.gov/2008/reviews/probrpp.pdf
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Sun: A Natural Fusion Reactor
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First thermonuclear reaction on Earth
XX-11 IVY MIKE, was fired on Enewetak by the United States on October 31, 1952. It was
the first hydrogen bomb, an experimental device not appropriate for use as a weapon
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Binding Energies
at A=120: 8.5 MeV
at A=240: 7.6 MeV
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Fusion Reactions
Terrestrial fusion reactions
Note: 4He reaction particularly exothermic because of large binding energy of that nucleus
Basic fusion reaction in the Sun
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Some Fusion Reactions
used in terrestrial
fusion reactors
PPI- cycle of Sun
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Coulomb Barrier
- Coulomb barrier classically prevents low-energy particles to approach each other.
- nuclear potential is here described as a square well.
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Gamow Peak
most reactions occur
within ~5 KeV of EGamow
Gamow peak
= product of the Maxwell-Boltzmann distribution with the tunneling probability of the nuclei through
their Coulomb barrier.
= energy region where the reaction is more likely to take place: at higher energies, the number of
particles becomes insignificant while at lower energies the tunneling through the Coulomb barrier
makes the reaction improbable.
dimension of the Maxwell-Boltzmann distribution and of the Gamow peak is keV, while the
tunnelling probability is dimensionless.
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Tunnel Effect and S-Factor
σ(E) = 1/E S(E) exp(-2 π η)
S(E)
S- factor, 'astrophysical factor' (or sometimes 'nuclear factor').
smoothly-varying function containing the nuclear information and the
normalization of the cross section.
The exponential represents the dependence of the transition probabilities due
to the tunnel effect.
Nuclear models are not detailed enough for most reactions to be completely
calculated theoretically. S factor contains all the unknowns of the problem and
it must be measured in laboratories with particle accelerators bringing the
nuclei at energies simulating the high temperatures in the stars.
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Some Fusion Reactions
used in terrestrial
fusion reactors
PPI- cycle of Sun
why is there such difference in the S(E)?
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Some Fusion Reactions
used in terrestrial
fusion reactors
PPI- cycle of Sun
tiny S(E) for weak reaction,
unobservable in lab
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LUNA Experiment
- underground accelerator
- located at Gran Sasso Natl. Lab
- measuring cross-sections at stellar energies
3He
+ 3He -> 4He+p+p
silicon ionization
counters that measure
dE/dx and E of protons
3He
3He
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gas target
ion source
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3He-3He
Cross-section measured by LUNA
cross-section (b)
3He
+ 3He -> 4He+p+p
Note: while cross-section varies by
more than 10 orders of magnitudes
between 20 KeV and 1 MeV, S(E)
varies only by a factor of 2
Gamow Peak
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p 7Li -> 8Be γ
p beam on target with 10μg/cm of LiF
on copper backing, NaI scintillators
detect photons from target
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p 7Li -> 8Be γ
p beam on target with 10μg/cm of LiF
on copper backing, NaI scintillators
detect photons from target
photon energy spectrum with peaks
due to 7Li(p,γ)8Be + natural
radioactivity in laboratory walls
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p 7Li -> 8Be γ
p beam on target with 10μg/cm of LiF
on copper backing, NaI scintillators
detect photons from target
photon energy spectrum with peaks
due to 7Li(p,γ)8Be + natural
radioactivity in laboratory walls
S(E) factor deduced from photon
counting -> two resonances due to
excited states of 8Be
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LUNA Measurements
cross-section measurements within the Gamow peak of the Sun:
3
He(3He,2p)4He
d(p,γ)3He
He(3He,2p)4He plays a big role in the proton-proton chain, largely affecting the calculated solar
neutrino luminosity
3
d(p,γ)3He reaction rules the proto-star life during the pre-main sequence phase
additional effect at low energies: the electron screening
- electron cloud surrounding the interacting nuclei acts as a screening potential, thus reducing the height
of the Coulomb barrier and leading to a higher cross-section
- screening effect has to be measured and taken into account in order to derive the bare nuclei crossExperimental
- PHYS741
section,
whichUniv.
is the
input data to the
models ofNuclear
stellarPhysics
nucleo-synthesis
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Karsten Heeger,
Wisconsin
LUNA Measurements 14N(p,γ)15O
S(E) for transitions to the ground state and the 6.79 MeV excitation in 15O
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http://www.lngs.infn.it/
N(p,γ) O
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- slowest reaction of the CNO cycle, the key one to decide its efficiency
- analysis of the 2002 data set has strongly reduced the cross section value with
respect to the one used in the standard solar model
- predicted CNO solar neutrino flux has been decreased by about a factor 2 and the
age of the oldest globular clusters has been increased by 0.7 - 1 Gyr with respect to
the current estimates.
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Fusion Rate (Pair Reaction Rate)
R = NX NY < σ v >
,
• NX and NY are the densities of each nucleus in the star
<σv> is the averaged product of the cross section and the
particles' relative velocity, both depending on the relative
energy.
• This rate must be divided by 2 if X and Y are identical
particles (such as in proton-proton fusion).
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Determining the Pair Reaction Rate
barrier penetration
probability
exp(-E/kT)
P(E)=exp(-√EB/E)
Boltzman factor
calculated for kT ~ 1eV (center of
Sun) and for 3He + 3He -> 4He+p+p
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most reactions occur
within 5 KeV of EG
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Reaction Rate as a Function of Temperature
pair reaction rate
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Reaction Rate as a Function of Temperature
kT ~ 10 keV is a good
temperature for fusion reactor
pair reaction rate
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Reaction Rate as a Function of Temperature
- fusion reaction rate increases rapidly with temperature until it maximizes and
then gradually drops off.
- d-t rate peaks at a lower temperature (about 70 keV, or 800 million kelvins) and
at a higher value than other reactions commonly considered for fusion energy
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p 7Li -> 8Be γ - Resonant Reaction Rates
S(E) factor deduced from photon
counting -> two resonances due to
excited states of 8Be
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d-t Fusion Reactors
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Heat Extraction in Fusion Reactor
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Confinement Schemes
Parameters of the three fusion confinement schemes:
magnetic
laser
gravitational
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d-t Fusion
Challenges
1. substantial amounts of neutrons that result in induced radioactivity within
the reactor structure. about 100 times that of fission reactor.
2. only about 20% of the fusion energy yield appears in the form of charged
particles (the rest neutrons), which limits the extent to which direct energy
conversion techniques might be applied. can neutrons be used?
3. The use of d-t fusion power depends on lithium resources, which are less
abundant than deuterium resources.
4. requires the handling of the radioisotope tritium. Similar to hydrogen,
tritium is difficult to contain and may leak from reactors in some quantity.
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Gravitational Confinement (Astrophysics)
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Magnetic Confinement
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Magnetic Confinement of Plasma
wall interactions are important
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Heating the Plasma
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Performance of Various Tokamaks
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Laser Induced Fusion
d-t sphere interacts with the laser
beams and it is vaporized
superficially
by reaction, the corona
compresses the central core
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National Ignition Facility (NIF)
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National Ignition Facility (NIF)
A tiny gold-plated cylinder
called a hohlraum holds the
deuterium-tritium fuel
energy from 192 lasers is
converted to thermal X-rays.
X-rays heat and ablate the
plastic surface of the ignition
capsule, causing a rocket-like
pressure on the capsule and
forcing it to implode and
ignite.
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National Ignition Facility.... Big Toys
NIF laser bay
1.8 MJ per pulse of 1 ns
NOVA laser bay
100 kJ per pulse
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Magnetic and Inertial Confinement
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