Lecture 22 Fusion Experimental Nuclear Physics PHYS 741 heeger@wisc.edu References and Figures from: - Basdevant, Fundamentals in Nuclear Physics 1
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 2
Sun: A Natural Fusion Reactor 3
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 4
Binding Energies at A=120: 8.5 MeV at A=240: 7.6 MeV 5
Fusion Reactions Terrestrial fusion reactions Note: 4 He reaction particularly exothermic because of large binding energy of that nucleus Basic fusion reaction in the Sun 6
Some Fusion Reactions used in terrestrial fusion reactors PPI- cycle of Sun 7
Coulomb Barrier - Coulomb barrier classically prevents low-energy particles to approach each other. - nuclear potential is here described as a square well. 8
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. 9
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. 10
Some Fusion Reactions used in terrestrial fusion reactors PPI- cycle of Sun why is there such difference in the S(E)? 11
Some Fusion Reactions used in terrestrial fusion reactors PPI- cycle of Sun tiny S(E) for weak reaction, unobservable in lab 12
LUNA Experiment - underground accelerator - located at Gran Sasso Natl. Lab - measuring cross-sections at stellar energies 3 He + 3 He -> 4 He+p+p silicon ionization counters that measure de/dx and E of protons 3 He gas target 3 He ion source 13
3 He- 3 He Cross-section measured by LUNA 3 He + 3 He -> 4 He+p+p cross-section (b) 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 14
p 7 Li -> 8 Be γ p beam on target with 10μg/cm of LiF on copper backing, NaI scintillators detect photons from target 15
p 7 Li -> 8 Be 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 7 Li(p,γ) 8 Be + natural radioactivity in laboratory walls 16
p 7 Li -> 8 Be 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 7 Li(p,γ) 8 Be + natural radioactivity in laboratory walls S(E) factor deduced from photon counting -> two resonances due to excited states of 8 Be 17
LUNA Measurements cross-section measurements within the Gamow peak of the Sun: 3 He( 3 He,2p) 4 He d(p,γ) 3 He 3 He( 3 He,2p) 4 He plays a big role in the proton-proton chain, largely affecting the calculated solar neutrino luminosity d(p,γ) 3 He 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 crosssection, Karsten Heeger, which Univ. is the Wisconsin input data to the Experimental models of Nuclear stellar Physics nucleo-synthesis - PHYS741 18
LUNA Measurements 14 N(p,γ) 15 O S(E) for transitions to the ground state and the 6.79 MeV excitation in 15 O 14 N(p,γ) 15 O http://www.lngs.infn.it/ - 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. 19
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). 20
Determining the Pair Reaction Rate Boltzman factor barrier penetration probability exp(-e/kt) P(E)=exp(- EB/E) calculated for kt ~ 1eV (center of Sun) and for 3 He + 3 He -> 4 He+p+p most reactions occur within 5 KeV of EG 21
Reaction Rate as a Function of Temperature pair reaction rate 22
Reaction Rate as a Function of Temperature pair reaction rate kt ~ 10 kev is a good temperature for fusion reactor 23
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 24
p 7 Li -> 8 Be γ - Resonant Reaction Rates S(E) factor deduced from photon counting -> two resonances due to excited states of 8 Be 25
d-t Fusion Reactors 26
Heat Extraction in Fusion Reactor 27
Confinement Schemes Parameters of the three fusion confinement schemes: magnetic laser gravitational 28
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. 29
Gravitational Confinement (Astrophysics) 30
Magnetic Confinement 31
Magnetic Confinement of Plasma wall interactions are important 32
Heating the Plasma 33
Performance of Various Tokamaks 34
Laser Induced Fusion d-t sphere interacts with the laser beams and it is vaporized superficially by reaction, the corona compresses the central core 35
National Ignition Facility (NIF) 36
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. 37
National Ignition Facility... Big Toys NIF laser bay 1.8 MJ per pulse of 1 ns NOVA laser bay 100 kj per pulse 38
Magnetic and Inertial Confinement 39
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