Chapter 45

1. Chapter 45 Applications of Nuclear Physics

2. Processes of Nuclear Energy • Fission • A nucleus of large mass number splits into two smaller nuclei • Fusion • Two light nuclei fuse to form a heavier nucleus • Large amounts of energy are released in both cases

3. Interactions Involving Neutrons • Because of their charge neutrality, neutrons are not subject to Coulomb forces • As a result, they do not interact electrically with electrons or the nucleus • Neutrons can easily penetrate deep into an atom and collide with the nucleus

4. Fast Neutrons • A fast neutron has energy greater than approximately 1 MeV • During its many collisions when traveling through matter, the neutron gives up some of its kinetic energy to a nucleus • For fast neutrons in some materials, elastic collisions dominate • These materials are called moderators since they moderate the originally energetic neutrons very efficiently

5. Thermal Neutrons • Most neutrons bombarding a moderator will become thermal neutrons • They are in thermal equilibrium with the moderator material • Their average kinetic energy at room temperature is about 0.04 eV • This corresponds to a neutron root-mean-square speed of about 2 800 m/s • Thermal neutrons have a distribution of speeds

6. Neutron Capture • Once the energy of a neutron is sufficiently low, there is a high probability that it will be captured by a nucleus • The neutron capture equation can be written as • The excited state lasts for a very short time • The product nucleus is generally radioactive and decays by beta emission

7. Nuclear Fission • A heavy nucleus splits into two smaller nuclei • Fission is initiated when a heavy nucleus captures a thermal neutron • The total mass of the daughter nuclei is less than the original mass of the parent nucleus • This difference in mass is called the mass defect

8. Short History of Fission • First observed in 1938 by Otto Hahn and Fritz Strassman following basic studies by Fermi • Bombarding uranium with neutrons produced barium and lanthanum • Lise Meitner and Otto Frisch soon explained what had happened • After absorbing a neutron, the uranium nucleus had split into two nearly equal fragments • About 200 MeV of energy was released

9. Fission Equation: 235U • Fission of 235U by a thermal neutron • 236U* is an intermediate, excited state that exists for about 10-12 s before splitting • X and Y are called fission fragments • Many combinations of X and Y satisfy the requirements of conservation of energy and charge

10. Fission Example: 235U • A typical fission reaction for uranium is

11. Distribution of Fission Products • The most probable products have mass numbers A  140 and A  95 • There are also an average of 2.5 neutrons released per event

12. Energy in a Fission Process • Binding energy for heavy nuclei is about 7.2 MeV per nucleon • Binding energy for intermediate nuclei is about 8.2 MeV per nucleon • Therefore, the fission fragments have less mass than the nucleons in the original nuclei • This decrease in mass per nucleon appears as released energy in the fission event

13. Energy, cont. • An estimate of the energy released • Releases about 1 MeV per nucleon • 8.2 MeV – 7.2 MeV • Assume a total of 235 nucleons • Total energy released is about 235 MeV • This is the disintegration energy, Q • This is very large compared to the amount of energy released in chemical processes

14. Chain Reaction • Neutrons are emitted when 235U undergoes fission • An average of 2.5 neutrons • These neutrons are then available to trigger fission in other nuclei • This process is called a chain reaction • If uncontrolled, a violent explosion can occur • When controlled, the energy can be put to constructive use

15. Chain Reaction – Diagram

16. Active Figure 45.3 • Use the active figure to observe the chain reaction PLAY ACTIVE FIGURE

17. Enrico Fermi • 1901 – 1954 • Italian physicist • Nobel Prize in 1938 for producing transuranic elements by neutron irradiation • Other contributions include theory of beta decay, free-electron theory of metal, development of world’s first fission reactor (1942)

18. Moderator • The moderator slows the neutrons • The slower neutrons are more likely to react with 235U than 238U • The probability of neutron capture by 238U is high when the neutrons have high kinetic energies • Conversely, the probability of capture is low when the neutrons have low kinetic energies • The slowing of the neutrons by the moderator makes them available for reactions with 235U while decreasing their chances of being captured by 238U

19. Reactor Fuel • Most reactors today use uranium as fuel • Naturally occurring uranium is 99.3% 238U and 0.7% 235U • 238U almost never fissions • It tends to absorb neutrons producing neptunium and plutonium • Fuels are generally enriched to at least a few percent 235U

20. Nuclear Reactor • A nuclear reactor is a system designed to maintain a self-sustained chain reaction • The reproduction constant K is defined as the average number of neutrons from each fission event that will cause another fission event • The average value of K from uranium fission is 2.5 • In practice, K is less than this • A self-sustained reaction has K = 1

21. K Values • When K = 1, the reactor is said to be critical • The chain reaction is self-sustaining • When K < 1, the reactor is said to be subcritical • The reaction dies out • When K > 1, the reactor is said to be supercritical • A run-away chain reaction occurs

22. Pressurized Water Reactor – Diagram

23. Pressurized Water Reactor – Notes • This type of reactor is the most common in use in electric power plants in the US • Fission events in the uranium in the fuel rods raise the temperature of the water contained in the primary loop • The primary system is a closed system • This water is maintained at a high pressure to keep it from boiling • This water is also used as the moderator to slow down the neutrons

24. Pressurized Water Reactor – Notes, cont. • The hot water is pumped through a heat exchanger • The heat is transferred by conduction to the water contained in a secondary system • This water is converted into steam • The steam is used to drive a turbine-generator to create electric power

25. Pressurized Water Reactor – Notes, final • The water in the secondary system is isolated from the water in the primary system • This prevents contamination of the secondary water and steam by the radioactive nuclei in the core • A fraction of the neutrons produced in fission leak out before inducing other fission events • An optimal surface area-to-volume ratio of the fuel elements is a critical design feature

26. Basic Design of a Reactor Core • Fuel elements consist of enriched uranium • The moderator material helps to slow down the neutrons • The control rods absorb neutrons • All of these are surrounded by a radiation shield

27. Control Rods • To control the power level, control rods are inserted into the reactor core • These rods are made of materials that are very efficient in absorbing neutrons • Cadmium is an example • By adjusting the number and position of the control rods in the reactor core, the K value can be varied and any power level can be achieved • The power level must be within the design of the reactor

28. Reactor Safety – Containment • Radiation exposure, and its potential health risks, are controlled by three levels of containment: • Reactor vessel • Contains the fuel and radioactive fission products • Reactor building • Acts as a second containment structure should the reactor vessel rupture • Prevents radioactive material from contaminating the environment • Location • Reactor facilities are in remote locations

29. Reactor Safety – Radioactive Materials • Disposal of waste material • Waste material contains long-lived, highly radioactive isotopes • Must be stored over long periods in ways that protect the environment • At present, the most promising solution seems to be sealing the waste in waterproof containers and burying them in deep geological repositories • Transportation of fuel and wastes • Accidents during transportation could expose the public to harmful levels of radiation • Department of Energy requires crash tests and manufacturers must demonstrate that their containers will not rupture during high speed collisions

30. Nuclear Fusion • Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus • The mass of the final nucleus is less than the masses of the original nuclei • This loss of mass is accompanied by a release of energy

31. Fusion: Proton-Proton Cycle • The proton-proton cycle is a series of three nuclear reactions believed to operate in the Sun • Energy liberated is primarily in the form of gamma rays, positrons and neutrinos

32. Fusion in the Sun • These reactions occur in the core of a star and are responsible for the energy released by the stars • High temperatures are required to drive these reactions • Therefore, they are known as thermonuclear fusion reactions

33. Fusion Reactions, final • All of the reactions in the proton-proton cycle are exothermic • An overview of the cycle is that four protons combine to form an alpha particle and two positrons

34. Advantages of a Fusion Reactor • Inexpensive fuel source • Water is the ultimate fuel source • If deuterium is used as fuel, 0.12 g of it can be extracted from 1 gal of water for about 4 cents • Comparatively few radioactive by-products are formed

35. Considerations for a Fusion Reactor • The proton-proton cycle is not feasible for a fusion reactor • The high temperature and density required are not suitable for a fusion reactor • The most promising reactions involve deuterium and tritium

36. Considerations for a Fusion Reactor, cont. • Tritium is radioactive and must be produced artificially • The Coulomb repulsion between two charged nuclei must be overcome before they can fuse • A major problem in obtaining energy from fusion reactions

37. Potential Energy Function • The potential energy is positive in the region r > R, where the Coulomb repulsive force dominates • It is negative where the nuclear force dominates • The problem is to give the nuclei enough kinetic energy to overcome this repulsive force

38. Critical Ignition Temperature • The temperature at which the power generation rate in any fusion reaction exceeds the lost rate is called the critical ignition temperature, Tignit • The intersections of the gen lines with the lost line give the Tignit

39. Requirements for Successful Thermonuclear Reactor • High temperature ~ 108 K • Needed to give nuclei enough energy to overcome Coulomb forces • At these temperatures, the atoms are ionized, forming a plasma • Plasma ion density, n • The number of ions present • Plasma confinement time,  • The time interval during which energy injected into the plasma remains in the plasma

40. Lawson’s Criteria • Lawson’s criteria states that a net power output in a fusion reactor is possible under the following conditions • n≥ 1014 s/cm3 for deuterium-tritium • n≥ 1016 s/cm3 for deuterium-deuterium • These are the minima on the curves

41. Requirements, Summary • The plasma temperature must be very high • To meet Lawson’s criterion, the product nt must be large • For a given value of n, the probability of fusion between two particles increases as t increases • For a given value of t, the collision rate increases as n increases • Confinement is still a problem

42. Confinement Techniques • Magnetic confinement • Uses magnetic fields to confine the plasma • Inertial confinement • Particles’ inertia keeps them confined very close to their initial positions

43. Magnetic Confinement • One magnetic confinement device is called a tokamak • Two magnetic fields confine the plasma inside the donut • A strong magnetic field is produced in the windings • A weak magnetic field is produced by the toroidal current • The field lines are helical, they spiral around the plasma, and prevent it from touching the wall of the vacuum chamber

44. Fusion Reactors Using Magnetic Confinement • TFTR – Tokamak Fusion Test Reactor • Close to values required by Lawson criterion • NSTX – National Spherical Torus Experiment • Produces a spherical plasma with a hole in the center • Is able to confine the plasma with a high pressure • ITER – International Thermonuclear Experimental Reactor • An international collaboration involving four major fusion programs is working on building this reactor • It will address remaining technological and scientific issues concerning the feasibility of fusion power

45. Inertial Confinement • Uses a D-T target that has a very high particle density • Confinement time is very short • Therefore, because of their own inertia, the particles do not have a chance to move from their initial positions • Lawson’s criterion can be satisfied by combining high particle density with a short confinement time

46. Laser Fusion • Laser fusion is the most common form of inertial confinement • A small D-T pellet is struck simultaneously by several focused, high intensity laser beams • This large input energy causes the target surface to evaporate • The third law reaction causes an inward compression shock wave • This increases the temperature

47. Fusion Reactors Using Inertial Confinement • Omega facility • University of Rochester (NY) • Focuses 24 laser beams on the target • National Ignition Facility • Lawrence Livermore National Lab (CA) • Currently under construction • Will include 192 laser beams focused on D-T pellets • Fusion ignition tests are planned for 2010

48. Fusion Reactor Design – Energy • In the D-T reaction, the alpha particle carries 20% of the energy and the neutron carries 80% • The neutrons are about 14 MeV

49. Active Figure 45.12 • Use the active figure to observe different fusion reactions • Measure the energy released PLAY ACTIVE FIGURE

50. Fusion Reactor Design, Particles • The alpha particles are primarily absorbed by the plasma, increasing the plasma’s temperature • The neutrons are absorbed by the surrounding blanket of material where their energy is extracted and used to generate electric power • One scheme is to use molten lithium to capture the neutrons • The lithium goes to a heat-exchange loop and eventually produces steam to drive turbines