1. 4/2003 Rev 2 I.4.6 – slide 1 of 63 Session I.4.6 Part I Review of Fundamentals Module 4Sources of Radiation Session 6Basic Reactor Physics Theory IAEA Post Graduate Educational Course Radiation Protection and Safety of Radiation Sources

2. 4/2003 Rev 2 I.4.6 – slide 2 of 63 Overview  In this session we will discuss fission and fusion reactions  We will also discuss criticality

3. 4/2003 Rev 2 I.4.6 – slide 3 of 63 Fission gamma free neutron fission fragment fission fragment free neutron beta alpha energy nucleus free neutron

4. 4/2003 Rev 2 I.4.6 – slide 4 of 63 Fission Sample fission reactions: 235 U + n  141 Ba + 92 Kr + 3n + 170 MeV 235 U + n  94 Zr + 139 La + 3n + 197 MeV

5. 4/2003 Rev 2 I.4.6 – slide 5 of 63 Fission  Follows neutron capture  Thermal neutrons fission 233 U, 235 U, 239 Pu which have odd number of neutrons  For isotopes with even number of neutrons, the incident neutron must have energy above about 1 MeV

6. 4/2003 Rev 2 I.4.6 – slide 6 of 63 Fission

7. 4/2003 Rev 2 I.4.6 – slide 7 of 63 Fission Neutron Name/Title Energy (eV) Cold Neutrons 0 < 0.025 Thermal Neutrons 0.025 Epithermal Neutrons 0.025 < 0.4 Cadmium Neutrons 0.4 < 0.6 Epicadmium Neutrons 0.6 < 1 Slow Neutrons 1 < 10 Resonance Neutrons 10 < 300 Intermediate Neutrons 300 < 1,000,000 Fast Neutrons 1,000,000 < 20,000,000 Relativistic Neutrons >20,000,000

8. 4/2003 Rev 2 I.4.6 – slide 8 of 63 Fission

9. 4/2003 Rev 2 I.4.6 – slide 9 of 63 fission products and transuranics from neutron capture

10. 4/2003 Rev 2 I.4.6 – slide 10 of 63 Fission Source of energy released during fission:  Kinetic energy of fission fragments  Gamma rays  Kinetic energy of neutrons emitted  Prompt  Delayed

11. 4/2003 Rev 2 I.4.6 – slide 11 of 63 Criticality  Neutrons ejected during fission equal neutrons producing more fissions + neutrons absorbed + neutrons lost from system  Criticality is constant if balance exists. Fission rate (power) can be changed by varying the number of neutrons absorbed and/or controlling the number lost

12. 4/2003 Rev 2 I.4.6 – slide 12 of 63 Criticality Multiplication Factor (4 factor formula) K eff = N f+1 NfNfNfNf N f+1 is the number of neutrons produced in the “f+1” generation by the N f neutrons of the previous “f” generation

13. 4/2003 Rev 2 I.4.6 – slide 13 of 63 Criticality  Sub-Critical (k eff < 1) – more neutrons lost by escape from system and/or non-fission absorption by impurities or “poisons” than produced by fission.  Critical (k eff = 1) – one neutron per fission available to produce another fission  Super-Critical (k eff > 1) – rate of fission neutron production exceeds rate of loss

14. 4/2003 Rev 2 I.4.6 – slide 14 of 63 Criticality  K eff depends on the availability of neutrons with the required energy and the availability of fissile atoms  As a result, k eff depends on composition, arrangement and size of fissile material  If assembly is infinitely large, no neutrons are lost and K eff = L x k , where L is the non-leakage probability and K  depends on 4 factors

15. 4/2003 Rev 2 I.4.6 – slide 15 of 63 Criticality  Let’s follow “n” fission neutrons through their life cycle  η is mean number of neutrons emitted per absorption in uranium  if “n” fission neutrons are captured, n x η fission neutrons will be produced

16. 4/2003 Rev 2 I.4.6 – slide 16 of 63 Criticality  ν is the mean number of neutrons emitted per fission which depends on the fuel (2.5 for 235 U and 3 for 239 Pu)  not every uranium absorption results in fission ( 238 U can absorb thermal neutrons without fission)  mean number of fission neutrons per absorption is less than ν

17. 4/2003 Rev 2 I.4.6 – slide 17 of 63 Sample Calculation For 100% enrichment of 235 U,  = 2.1. What is  for natural uranium?  = x  = x ffff aaaa  = macroscopic cross section  = microscopic cross section = average number of neutrons per fission = average number of neutrons per fission N = atoms per cm 3 a = absorption (5 = 235 U) f = fission (8 = 238 U)  f = (N 5 x  f 5 )  a = (N 5 x  a 5 ) + (N 8 x  a 8 )

18. 4/2003 Rev 2 I.4.6 – slide 18 of 63  = x 2.5 = 1.32 for natural U 549 650 + (139 x 2.8)  f 5 = 549 barns  a 5 = 650 barns  a 8 = 2.8 barns = 2.5 for 235 U = 2.5 for 235 U N8N8N8N8 N5N5N5N5 For natural U, = 139 ffff aaaa (N 5 x  f 5 ) (N 5 x  a 5 ) + (N 8 x  a 8 ) (  f 5 ) (  a 5 ) + ( x  a 8 ) N8N8N8N8 N5N5N5N5 == Sample Calculation

19. 4/2003 Rev 2 I.4.6 – slide 19 of 63 Criticality 238 U has a small cross section for fission by fast neutrons (not thermal)  = 0.29 barns Fast fission factor is ε =ε =ε =ε = total number of fission neutrons number of thermal fission neutrons

20. 4/2003 Rev 2 I.4.6 – slide 20 of 63 Criticality  ε depends on 3 factors:  ratio of moderator to fuel  ratio of inelastic scattering cross section to fission cross section  geometrical relationship between fuel and moderator  capture of n thermal neutrons will produce n x  x ε fission neutrons

21. 4/2003 Rev 2 I.4.6 – slide 21 of 63 Criticality  For unmoderated pure U metal, ε = 1.29 which is the maximum value  For homogenous fuel (such as a solution) ε is very close to 1

22. 4/2003 Rev 2 I.4.6 – slide 22 of 63 Criticality  while fast neutrons are being slowed, they may be captured by 238 U without fission  resonance for this capture occurs between 5 and 200 eV  p is the probability that a neutron will escape this resonance capture

23. 4/2003 Rev 2 I.4.6 – slide 23 of 63 Criticality  p = resonance escape probability (fraction of fast, fission produced neutrons that become thermalized)  p depends on ratio of moderator to fuel  for high ratio of moderator to fuel, p  1  for a low ratio of moderator to fuel, p small  for pure unmoderated natural U, p = 0

24. 4/2003 Rev 2 I.4.6 – slide 24 of 63 Criticality  from the original n thermal neutrons we have n x  x ε x p thermal neutrons  some of the thermal neutrons are absorbed by non-fuel atoms  some are absorbed by 235 U without fission (only 84% of thermal neutrons absorbed by 235 U cause fission)

25. 4/2003 Rev 2 I.4.6 – slide 25 of 63 Criticality  f = thermal utilization factor which is the fraction of all the thermal neutrons which are absorbed by the fuel (all of the U)  the total number of new neutrons produced by the original n thermal neutrons is n x  x ε x p x f

26. 4/2003 Rev 2 I.4.6 – slide 26 of 63 Criticality f =  aU  aU +  aM +  ap  aU = macroscopic cross section for U  aM = macroscopic cross section for moderator  ap = macroscopic cross section for other stuff

27. 4/2003 Rev 2 I.4.6 – slide 27 of 63 Criticality K  = = =  εpf N f+1 NfNfNfNf n  εpf n   depends only on the fuel  ε, p and f depend on the composition and arrangement of the fuel  ε varies from 1.29 for unmoderated U to almost 1 for homogeneous dispersion of fuel and moderator  p is about 0.8 to 1 (for pure 235 U, p = 1)

28. 4/2003 Rev 2 I.4.6 – slide 28 of 63  in a nuclear reactor the factors are combined to produce a controlled, sustained chain reaction  excess reactivity (  k) is an increase in the multiplication factor (k) above 1  k = k - 1 Reactivity and Reactor Control

29. 4/2003 Rev 2 I.4.6 – slide 29 of 63 Reactivity and Reactor Control  For n neutrons in one generation, the number of additional neutrons in the next generation is n  k  If the lifetime of a neutron generation is L sec, the time rate of change of neutrons is dndt nknknknk L =

30. 4/2003 Rev 2 I.4.6 – slide 30 of 63 Reactivity and Reactor Control dndt nknknknk L = when integrated from n o to n we get The reactor period (T) is the time during which the neutrons (power level) increase by factor of “e” n nononono kkkkL = e t

31. 4/2003 Rev 2 I.4.6 – slide 31 of 63 Reactivity and Reactor Control or the reactor period is: The mean lifetime of a neutron (birth to absorption) in pure 235 U is about 0.001 sec kkkk L =1T kkkkL T =

32. 4/2003 Rev 2 I.4.6 – slide 32 of 63 Reactivity and Reactor Control The mean lifetime of a neutron (birth to absorption) in pure 235 U is about 0.001 sec Assume excess reactivity = 0.1% (  k = 0.001) 0.0010.001 T = = 1 sec And the power level would increase by 2.718 each second

33. 4/2003 Rev 2 I.4.6 – slide 33 of 63 Reactivity and Reactor Control 0.0050.001 T = = 0.2 sec If  k is increased to 0.5% The power level increase each second would be t T n nononono = e = e = 150 10.2 This would be hard to control

34. 4/2003 Rev 2 I.4.6 – slide 34 of 63 Reactivity and Reactor Control The actual mean generation time in a reactor is much greater than 0.001 because 0.6407% of fission neutrons are delayed from 0.3 seconds to 80 seconds. This delay permits the reactor to be controlled.

35. 4/2003 Rev 2 I.4.6 – slide 35 of 63 Reactivity and Reactor Control Group n i (%) T i (sec) n i x T i 10.02670.330.009 20.07370.880.065 30.25263.310.836 40.12558.971.125 50.140132.784.592 60.021180.391.688  n i = 0.6407  n i xT i = 8.315 Delayed Neutrons

36. 4/2003 Rev 2 I.4.6 – slide 36 of 63 Reactivity and Reactor Control The mean generation time for all fission neutrons is If  k  0.006407 the reactor is prompt critical – the reaction can be sustained by prompt neutrons alone If  k < 0.006407 the reactor is delayed critical – the delayed neutrons are needed to sustain the reaction T = = = 0.084 sec niTiniTiniTiniTi nininini 8.315 + (99.359 x 0.001) 100 delayedprompt

37. 4/2003 Rev 2 I.4.6 – slide 37 of 63 Sample Calculation What is the reactor period and the increase in power level in 1 second for a generation time of 0.084 sec for excess reactivity (  k) of 0.1% and 0.5% For  k = 0.001 0.0010.084 T = = 84 sec 184 n nononono = e = 1.012 This would be hard to control For  k = 0.005 0.0050.084 T = = 16.8 sec 116.8 n nononono = e = 1.06

38. 4/2003 Rev 2 I.4.6 – slide 38 of 63 Reactivity and Reactor Control  Excess reactivity is measured in units of “dollars” and “cents” (one dollar = 100 cents) and “inhours” (inverse hours)  One “dollar” worth of reactivity will cause the reactor to go prompt critical  One “inhour” is the amount of excess reactivity which results in a reactor period of 1 hour

39. 4/2003 Rev 2 I.4.6 – slide 39 of 63 Fission Control of Fission  Fission typically releases 2-3 neutron (average 2.5)  One is needed to sustain the chain reaction at a steady level of controlled criticality  The other 1.5 leak from the core region or are absorbed in non ‑ fission reactions

40. 4/2003 Rev 2 I.4.6 – slide 40 of 63 Fission Control of Fission  Boron or cadmium control rods absorb neutrons  When slightly withdrawn the number of neutrons available for fission exceeds unity and the power level increases  When the power reaches the desired level, the control rods are returned to the critical position

41. 4/2003 Rev 2 I.4.6 – slide 41 of 63 Fission Control of Fission  ability to control the reaction is due to presence of delayed neutrons  without delayed neutrons, change in the critical balance of the chain reaction would lead to a virtually instantaneous and uncontrollable rise or fall in the neutron population  safe design and operation of a reactor sets strict limits on departures from criticality

42. 4/2003 Rev 2 I.4.6 – slide 42 of 63 Fission Control of Fission  fission neutrons initially fast (energy above 1 MeV)  fission in 235 U most readily caused by slow neutrons (energy about 0.02 eV)  moderator slows fast neutrons by elastic collisions  For natural (unenriched) U only graphite and “heavy” water suitable moderators  For enriched uranium “light” water may be used

43. 4/2003 Rev 2 I.4.6 – slide 43 of 63 Fission Control of Fission  commercial power reactors are designed to have negative temperature and void coefficients  if temperature too high or excessive boiling occurs rate of fission, and hence temperature, are reduced  238 U absorbs more neutrons as the temperature rises, pushing neutron balance towards subcritical  steam within water moderator reduces its density which pushes neutron balance towards subcritical

44. 4/2003 Rev 2 I.4.6 – slide 44 of 63 Fission Control of Fission  fuel gradually accumulates fission products and transuranic elements which increases neutron absorption (control system has to compensate)  after about three years, fuel is replaced due to:  build ‑ up in neutron absorption  metallurgical changes as a consequence of the constant neutron bombardment  fuel burn ‑ up is effectively limited to about half of the fissile material

45. 4/2003 Rev 2 I.4.6 – slide 45 of 63 Fission Summary

46. 4/2003 Rev 2 I.4.6 – slide 46 of 63  In 1920 Arthur Eddington suggested that the energy of the sun and stars was a product of the fusion of hydrogen atoms into helium  In the core of the sun at temperatures of 10 ‑ 15 million degrees Celsius, hydrogen is converted to helium  Since the 1950's, great progress has been made in nuclear fusion research: however, the only practical application of fusion technology to date has been the "hydrogen" or thermonuclear bomb Fusion

47. 4/2003 Rev 2 I.4.6 – slide 47 of 63  Fusion has an almost unlimited potential  The hydrogen isotopes in one gallon of water have the fusion energy equivalent of 300 gallons of gasoline  A fusion power plant would have no greenhouse gas emissions and would not generate high level radioactive waste  Experts predict the world is still at least 50 years and billions of dollars away from having fusion generated electricity largely due to the enormous size and complexity of a fusion reactor Fusion

48. 4/2003 Rev 2 I.4.6 – slide 48 of 63  Hydrogen atoms merged to create helium  Helium mass is slightly less (1%) than the original mass with the difference being given off as energy  Rather than using hydrogen atoms, it is easier to promote fusion by using two isotopes of hydrogen, deuterium and tritium  Deuterium is a naturally occurring isotope of hydrogen which has one extra neutron  One hydrogen atom in 6700 occurs as deuterium and can be separated from the rest Fusion

49. 4/2003 Rev 2 I.4.6 – slide 49 of 63 Fusion

50. 4/2003 Rev 2 I.4.6 – slide 50 of 63 Fusion A  56 Fission A  56 Atomic Mass Number 0 25020015010050 0 -2 -4 -6 -8 -10 Energy per Nucleon (MeV) Fusion

51. 4/2003 Rev 2 I.4.6 – slide 51 of 63  Tritium is very rare because it is naturally radioactive and decays quickly  Tritium can be made by bombarding the naturally occurring element lithium with neutrons  Tritium could be created by having a "blanket" made of lithium surrounding a fusion containment vessel (this would result in a breeder reactor)  Fusion can only be accomplished at temperatures typical of the centre of stars, (~100 million degrees Celsius) Fusion

52. 4/2003 Rev 2 I.4.6 – slide 52 of 63  The fusion components exist in the form of a plasma, where atoms are broken down into electrons and nuclei  No known solid material could withstand the temperatures involved in nuclear fusion, so that a powerful confinement system is required to keep the plasma away from the walls of the vessel in which it is contained Fusion

53. 4/2003 Rev 2 I.4.6 – slide 53 of 63  Deuterium can be extracted from water (If all the world's electricity were to be provided by fusion, deuterium would last for millions of years)  Tritium does not occur naturally and will be manufactured from lithium within the machine  Lithium, the lightest metal, is plentiful in the earth's crust (if all the world's electricity were to be provided by fusion, known reserves would last for at least 1000 years)  Even though fusion occurs between Deuterium and Tritium, the consumables are Deuterium and Lithium Fusion Fuels

54. 4/2003 Rev 2 I.4.6 – slide 54 of 63  For example, 10 grams of Deuterium which can be extracted from 500 litres of water and 15g of Tritium produced from 30g of Lithium would produce enough fuel for the lifetime electricity needs of an average person in an industrialised country Fusion Fuels

55. 4/2003 Rev 2 I.4.6 – slide 55 of 63  Fusion research was big news in 1989 when it was reported that scientists had achieved fusion at room temperatures with simple equipment  Unfortunately, the scientists involved could not prove their claims and the experiments were not repeatable  Currently, two methods of confining the hot plasma are being studied around the world, "magnetic confinement" and "inertial confinement" Current Fusion Research

56. 4/2003 Rev 2 I.4.6 – slide 56 of 63  Magnetic confinement has the greatest potential and most research is now based on the "TOKOMAK" system (Tokomak is an acronym for the Russian words "torroidal magnetic chamber“)  The tokomak system was developed in the former U.S.S.R. and has been taken to an advanced stage in the ITER project whose construction began in 2007  A torroidal magnetic chamber is a doughnut-shaped steel structure in which the fusion plasma is confined by means of powerful coils of super ‑ conducting material which create a strong magnetic field Current Fusion Research

57. 4/2003 Rev 2 I.4.6 – slide 57 of 63  The other method is inertial confinement (small amounts of a deuterium ‑ tritium mixture are rapidly heated to extremely high temperatures with a high powered laser beam or a beam of charged particles)  Very high-power lasers are needed in the inertial confinement method. Biggest test facility is NIF. Less advanced than magnetic confinement.  To be useful the energy produced must be many times that required to sustain the reaction  Even the most optimistic researchers feel this will not be achieved before second half of the century Current Fusion Research

58. 4/2003 Rev 2 I.4.6 – slide 58 of 63  A fusion reactor capable of generating 1000 MW of electricity would be very large and complex  While fission reactors can be made small enough to be used in submarines or satellites, the minimum size of a fusion reactor would be similar to that of today's largest commercial nuclear plants  The difficult part is creating a sustainable fusion reaction - capturing the energy to generate electricity is very similar to a fission reactor  A 1000 MW fusion generator would consume only 150 kg of deuterium and 400 kg of lithium annually Fusion Power Plants

59. 4/2003 Rev 2 I.4.6 – slide 59 of 63  The fuels required for fusion reactors, deuterium and lithium, are so abundant that the potential for fusion is virtually unlimited  Oil and gas fired power plants as well as nuclear plants relying on uranium will eventually run into fuel shortages as these non ‑ renewable resources are consumed  Unlike fossil plants, fusion reactors have no emission of carbon dioxide (contributor to global warming) or sulphur dioxide (cause of acid rain) Advantages of Fusion

60. 4/2003 Rev 2 I.4.6 – slide 60 of 63  Barriers to the widespread use of nuclear power have been public concern over operational safety, and the disposal of radioactive waste  Accidents such as Chernobyl are virtually impossible with a fusion reactor because only a small amount of fuel is in the reactor at any time  It is also so extremely difficult to sustain a fusion reaction that, should anything go wrong, the reaction would invariably stop Advantages of Fusion

61. 4/2003 Rev 2 I.4.6 – slide 61 of 63  Long lived highly radioactive wastes are generated by conventional nuclear plants  Radioactive wastes generated by a fusion reactor are the walls of the vessel exposed to neutrons  Although the quantity of radioactive waste produced by a fusion reactor might be slightly greater than that from a conventional nuclear plant, the wastes would have low levels of short lived radiation, decaying almost completely within 100 years. Advantages of Fusion

62. 4/2003 Rev 2 I.4.6 – slide 62 of 63  The major disadvantages of nuclear fusion are the vast amounts of time and money which will have to be expended before any electricity is generated, even assuming that the technical/materials problems can eventually be solved  Development of other electricity supply technologies such as photovoltaic cells, which convert sunlight directly into electricity, could potentially eliminate the need for fusion before it is operational Disadvantages of Fusion

63. 4/2003 Rev 2 I.4.6 – slide 63 of 63 Where to Get More Information  Cember, H., Johnson, T. E., Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2008)  Martin, A., Harbison, S. A., Beach, K., Cole, P., An Introduction to Radiation Protection, 6 th Edition, Hodder Arnold, London (2012)  Glasstone, S., Sesonske, A., Nuclear Reactor Engineering, 4 th Edition, Dordrecht:Kluwer Academic Publishers (1995)  Friedberg, J., Plasma Physics and Fusion Energy, Cambridge University Press, Cambridge (2007)