# Tony WeidbergNuclear Physics Lectures1 Applications of Nuclear Physics Fusion –(How the sun works covered in Astro lectures) –Fusion reactor Radioactive.

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Tony WeidbergNuclear Physics Lectures1 Applications of Nuclear Physics Fusion –(How the sun works covered in Astro lectures) –Fusion reactor Radioactive dating –C dating –Rb/Sr  age of the Earth

Tony WeidbergNuclear Physics Lectures2 Physics of Nuclear Fusion All reactions at low energy are suppressed by Coulomb barrier (cf  decay). Reaction rate: convolution of MB distribution and barrier penetration.

Tony WeidbergNuclear Physics Lectures3 Low Energy Fusion Cross Sections Breit-Wigner (no-spin) cf  decay theory, allow for QM tunnelling through Coulomb barrier

Tony WeidbergNuclear Physics Lectures4 Cross Sections (Continued) Predicts cross section Low energy approximation

Tony WeidbergNuclear Physics Lectures5 Example  C Theory explains rapid rise at very low energy Ignores multiple resonances!

Tony WeidbergNuclear Physics Lectures6 Fusion Rates Consider reaction a+b  X (a different from b) –Volume number density  a  b –Cross section  ab Reaction rate/volume

Tony WeidbergNuclear Physics Lectures7 Maximum rate  minimum for 

Tony WeidbergNuclear Physics Lectures8 Fusion Rates Look at exp[-  (E)] Function sharply peaked at E=E 0 pp reaction E (KeV) 10 6 exp[-  E)]

Tony WeidbergNuclear Physics Lectures9 Fusion Rates Most favourable rates for d-t reactions. Peak at k B T~ 20 keV Why? m 3 s -1 k B T (keV)

Tony WeidbergNuclear Physics Lectures10 Fusion Reactors Use deuterium + tritium: –Large energy release –Large cross-section at low energy –Deuterium abundant (0.015% of H). –Breed Tritium in Lithium blanket –.–.

Tony WeidbergNuclear Physics Lectures11 Fusion Reactors Energy out > Energy in Lawson criteria (assume k B T=20 keV). –number density D ions :  –Cross-section:  –Confinement time for plasma: t c –Energy released per fusion: E fusion

Tony WeidbergNuclear Physics Lectures12 Magnetic Confinement Confine plasma with magnetic fields. –Toroidal field: ions spiral around field lines. –Poloidal fields: focus ions away from walls. Heating: –RF power accelerates electrons –Current pulse causes further heating.

Tony WeidbergNuclear Physics Lectures13 Jet

Tony WeidbergNuclear Physics Lectures14

Tony WeidbergNuclear Physics Lectures15 MAST Fusion Progress –Huge strides in physics, engineering, technology –JET: 16 MW of fusion power ~ equal to heating power. 21 MJ of fusion energy in one pulse –Ready to build ITER - the next generation, GigaWatt-scale –Scaling laws that fit data from existing tokamaks give confidence that ITER/power plants will achieve desired performance Temperature / 10 6 K Fusion product p t (atm. sec)

Tony WeidbergNuclear Physics Lectures16 AUGJET ITER JET Cross section of present EU D- shape tokamaks compared to the ITER project Prediction of ITER performance

Tony WeidbergNuclear Physics Lectures17 High Energy neutrons Use n to make 3 H in Li blanket n damage to surrounding support structures ~ 10 dpa/yr 2 H + 7 Li  n + 2 4 He

Tony WeidbergNuclear Physics Lectures18 Inertial Confinement Fusion Very Big Laser Mirrors D-T Pellet

Tony WeidbergNuclear Physics Lectures19 Inertial Confinement Fusion

Tony WeidbergNuclear Physics Lectures20 Radioactive Dating C 14 /C 12 for organic matter  age of dead trees etc. Rb/Sr in rocks  age of earth.

Tony WeidbergNuclear Physics Lectures21 Carbon Dating C 14 produced by Cosmic rays (mainly neutrons) at the top of the atmosphere. –n N 14  p C 14 C 14 mixes in atmosphere and absorbed by plants/trees  constant ratio C 14 / C 12. Ratio decreases when plant dies. t 1/2 =5700 years. Either –Rate of C 14 radioactive decays –Count C 14 atoms in sample by Accelerator Mass Spectrometer. Which is better? Why won’t this work in the future?

Tony WeidbergNuclear Physics Lectures22 Carbon Dating Calibration

Tony WeidbergNuclear Physics Lectures23 How Old Is The Earth? Rb 87  Sr 87 :  decay t 1/2 =4.8 10 10 yr Assume no initial daughter nuclei  get age from ratio of daughter/parent now.

Tony WeidbergNuclear Physics Lectures24 Improved Calculation Allow for initial daughters to be present. Need another isotope of the daughter D’ which is stable and not a product of a radioactive decay chain. Plot vs straight line fit  age and initial ratio.

Tony WeidbergNuclear Physics Lectures25 Age of Earth Rb/Sr method Stable isotope of daughter is Sr 86 Fit gives age of earth=4.53 10 9 years. Sr87/Sr86 Rb87/Sr86 1.04.0

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