lecture 22 fusion experimental nuclear physics phys...

Experimental Nuclear Physics - PHYS741Karsten Heeger, Univ. Wisconsin 1

Lecture 22

Fusion

Experimental Nuclear Physics PHYS 741

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References and Figures from:- Basdevant, “Fundamentals in Nuclear Physics

mailto:[email protected]

mailto:[email protected]

Experimental Nuclear Physics - PHYS741Karsten Heeger, Univ. Wisconsin

Reading for Next Week

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Phys. Rev. D 57, 3873 - 3889 (1998)

Unified approach to the classical statistical analysis of small signalsG. Feldman, R. Cousinshttp://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

http://link.aps.org/abstract/PRD/v57/p3873

http://link.aps.org/abstract/PRD/v57/p3873

http://pdg.lbl.gov/2008/reviews/probrpp.pdf





Sun: A Natural Fusion Reactor

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First thermonuclear reaction on Earth

4

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


Binding Energies

5

at A=120: 8.5 MeV

at A=240: 7.6 MeV


Fusion Reactions

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Basic fusion reaction in the Sun

Terrestrial fusion reactions

Note: 4He reaction particularly exothermic because of large binding energy of that nucleus


Some Fusion Reactions

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used in terrestrial fusion reactors

PPI- cycle of Sun


Coulomb Barrier

8

- Coulomb barrier classically prevents low-energy particles to approach each other.

- nuclear potential is here described as a square well.


Gamow Peak

9

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.

most reactions occur within ~5 KeV of EGamow


Tunnel Effect and S-Factor

10

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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PPI- cycle of Sun

why is there such difference in the S(E)?



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PPI- cycle of Sun

tiny S(E) for weak reaction, unobservable in lab


LUNA Experiment

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3He ion source

3He gas target

silicon ionization counters that measure dE/dx and E of protons

- underground accelerator- located at Gran Sasso Natl. Lab- measuring cross-sections at stellar energies

3He + 3He -> 4He+p+p


3He-3He Cross-section measured by LUNA

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Gamow Peak

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

cros

s-se

ctio

n (b

)


p 7Li -> 8Be γ

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p beam on target with 10μg/cm of LiF on copper backing, NaI scintillators detect photons from target


p 7Li -> 8Be γ

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photon energy spectrum with peaks due to 7Li(p,γ)8Be + natural radioactivity in laboratory walls



p 7Li -> 8Be γ

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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



LUNA Measurements

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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 cross-section, which is the input data to the models of stellar nucleo-synthesis

cross-section measurements within the Gamow peak of the Sun:

3He(3He,2p)4He d(p,γ)3He

3He(3He,2p)4He plays a big role in the proton-proton chain, largely affecting the calculated solar neutrino luminosity

d(p,γ)3He reaction rules the proto-star life during the pre-main sequence phase


LUNA Measurements 14N(p,γ)15O

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14N(p,γ)15O

- 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.

http://www.lngs.infn.it/

S(E) for transitions to the ground state and the 6.79 MeV excitation in 15O

http://www.lngs.infn.it

http://www.lngs.infn.it


Fusion Rate (Pair Reaction Rate)

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,• 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).

R = NX NY < σ v >


Determining the Pair Reaction Rate

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exp(

-E/k

T)

P(E)

=exp

(-√E B

/E)

Boltzman factor barrier penetration probability

calculated for kT ~ 1eV (center of Sun) and for 3He + 3He -> 4He+p+p

most reactions occur within 5 KeV of EG


Reaction Rate as a Function of Temperature

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pair reaction rate



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pair reaction rate

kT ~ 10 keV is a good temperature for fusion reactor



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- 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


p 7Li -> 8Be γ - Resonant Reaction Rates

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S(E) factor deduced from photon counting -> two resonances due to excited states of 8Be


d-t Fusion Reactors

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Heat Extraction in Fusion Reactor

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Confinement Schemes

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Parameters of the three fusion confinement schemes:

magnetic lasergravitational


d-t Fusion

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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.


Gravitational Confinement (Astrophysics)

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Magnetic Confinement

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Magnetic Confinement of Plasma

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wall interactions are important


Heating the Plasma

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Performance of Various Tokamaks

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Laser Induced Fusion

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d-t sphere interacts with the laser beams and it is vaporized superficially

by reaction, the corona compresses the central core


National Ignition Facility (NIF)

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National Ignition Facility (NIF)

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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.


National Ignition Facility.... Big Toys

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NIF laser bay1.8 MJ per pulse of 1 ns

NOVA laser bay100 kJ per pulse


Magnetic and Inertial Confinement

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Experimental Nuclear Physics - PHYS741Karsten Heeger, Univ. Wisconsin 40

lecture 22 fusion experimental nuclear physics phys...

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