1. “ Georeactor ” Detection with Gigaton Antineutrino Detectors Neutrinos and Arms Control Workshop February 5, 2004 Eugene Guillian University of Hawaii

2. Finding Hidden Nuclear Reactors  The focus of this conference is on detecting hidden man-made nuclear reactors  But there may be a natural nuclear reactor hidden in the Earth ‘ s core!

3. The “ Georeactor ” Model  An unorthodox model  Chief proponent: J.M.Herndon  The model  A fuel breeder fission reactor in the Earth ‘ s sub-core  Size: ~4 miles radius  Power: 3-10 TW

4. Man-made vs. Geo  Man-made:  (~500 reactors) x (~2 GW) = 1 TW  Georeactor:  3-10 TW If a georeactor exists, it will be the dominant source of antineutrinos!

5. Outline of Presentation 1. Georeactor detection strategy 2. Describe the georeactor model 3. Can a georeactor be detected with KamLAND? 4. What minimum conditions are necessary to detect a georeactor?

6. Strategy for Georeactor Detection  If a georeactor does not exist …

8. From commercial power plants Depends on the net power output Rate corrected to 100% livetime & efficiency Assume no neutrino oscillation

9. Corrected to 100% livetime & efficiency Neutrino oscillation effect included

10. Slope = average neutrino oscillation survival probability

11. = Average 2f = Spread

12. = Average f = Spread R min = (1-f) R max = (1+f)

13. Y-inercept = Georeactor Rate 0

14. Strategy for Georeactor Detection  If a georeactor does exist …

15. 10 TW georeactor

16. Nonzero Y-intercept (0.0742 events/day @ 10 TW)

17. Georeactor Detection Strategy  Plot observed rate against expected background rate  Fit line through data  Y-intercept = georeactor rate

18. The Georeactor Model  What we can all agree on: 1.The Earth is made of the same stuff as meteorites 2.In its earliest stages, the Earth was molten 3.The Earth gradually cooled, leaving all but the outer core in solid form

19. Melting a Rock  Very high temperature:  All of rock in liquid form  Lower temperature:  Slag solidifies  Alloys and opaque minerals still in liquid form  Slag floats

20. Apply This Observation to the Earth Very Hot! All Liquid

21. Apply This Observation to the Earth Cooler Slag solidifies, Floats to surface

22. Fission Fuel Trapped by Slag?  Actinides (U, Th, etc.) are lithophile (or oxiphile)  If given a chance, they combine with slag  Slag rises to surface as the Earth cools  Fission fuel found in the Earth ‘ s crust and mantle, not in the core  Therefore, a georeactor cannot form!

23. Fission Fuel Trapped by Slag?  Actinides (U, Th, etc.) are lithophile (or oxiphile)  If given a chance, they combine with slag  Slag rises to surface as the Earth cools  Fission fuel found in the Earth ‘ s crust and mantle, not in the core  Therefore, a georeactor cannot form! If there is enough oxygen

24. If There Were Insufficient Oxygen  Some of the U, Th will be in alloy and sulfide form  These sink as the Earth cools  Elements with largest atomic number should sink most  Therefore, fission fuel should sink to the center of the Earth  Georeactor can form!

25. How Can One Tell if the Earth Is Oxygen Poor or Not?  Slag has high oxygen content  Alloys and opaque minerals have low oxygen content  Alloy/Slag mass ratio  Strong correlation with oxygen content in a meteorite

26. Oxygen Level of the Earth Oxygen ContentHigh Low Alloy Slag Less Slag More Slag Meteorite Data Ordinary Chrondite Enstatite Chrondite

27. Oxygen Level of the Earth Oxygen ContentHigh Low Alloy Slag Less Slag More Slag Actinides trapped in slag Free actinides

28. Oxygen Level of the Earth Oxygen ContentHigh Low Alloy Slag Less Slag More Slag Alloy Slag Core Mantle =

29. Oxygen Level of the Earth Oxygen ContentHigh Low Alloy Slag Less Slag More Slag Core/Mantle ratio from seismic data

30. Measuring the Earth ‘ s Oxidation Level  Equate the following:  Core  alloy & opaque minerals  Mantle + Crust  silicates  Obtain Earth ‘ s mass ratio from density profile measured with seismic data  Compare with corresponding ratio in meteorites.  Oxygen Content of the Earth:  Same as meteorite with same mass ratio as the Earth ‘ s

31. Evidence for Oxygen-poor Earth Herndon, J.M. (1996) Proc. Natl. Acad. Sci. USA 93, 646-648. The Earth Seems to be Oxygen-poor!

32. 3 He Evidence for Georeactor  Fission reactors produce 3 H  3 H decays to 3 He (half life ~ 12 years)

33. 3 He Measurements  In air:  R A = 3 He/ 4 He = 1.4 x 10 -6  From deep Earth:  R ≈ 8 x R A  Elevated deep Earth levels difficult to explain  Primordial 3 He and “ Just-so ” dilution scenarios  A georeactor naturally produces 3 He …

34. … and Just the Right Amount! SCALE Reactor Simulator (Oak Ridge) Deep Earth Measurement (mean and spread) Fig. 1, J.M.Herndon, Proc. Nat. Acad. Sci. USA, Mar. 18, 2003 (3047)

35. Other Phenomena  Georeactor as a fluctuating energy source for geomagnetism  3 of the 4 gas giants radiate twice as much heat as they receive  Oklo natural fission reactor (remnant)

36. Can a Georeactor Be Detected with KamLAND?  KamLAND  A 0.4 kton antineutrino detector  Currently, the largest such detector in the world  2-parameter fit  Slope (constrained)  Y-intercept (unconstrained)

37. Can a Georeactor Be Detected with KamLAND?  KamLAND  A 0.4 kton antineutrino detector  Currently, the largest such detector in the world  2-parameter fit  Slope (constrained)  Y-intercept (unconstrained) Solar neutrino experiments

38. Can a Georeactor Be Detected with KamLAND?  KamLAND  A 0.4 kton antineutrino detector  Currently, the largest such detector in the world  2-parameter fit  Slope (constrained)  Y-intercept (unconstrained) Georeactor Rate

39. Measuring the Georeactor Rate with KamLAND Slope constrained by solar neutrino measurements Slope ≈ 0.75 ± 0.15 Georeactor rate

40. Large Background Background Signal S/B ≈ 1/3 ~ 1/8

41. Slope Uncertainty 1  uncertainty in solar neutrino oscillation parameters (  m 2, sin 2 2  ) (rough estimate) Best fit

42. Can a Georeactor be Detected?  Use Error Ellipse to answer this question

43. Ellipse Equation

44. Measured georeactor e rate (y-intercept) True georeactor e rate Distance of measured rate from true value

45. Ellipse Equation Mueasured slope Best estimate of slope (from solar experiments) Distance of measured slope from best estimate

46. Ellipse Equation Correlation between slope and rate measurements

47. Ellipse Equation Confidence level of fit result

48. Ellipse Equation Ellipse Parameters They determine the size of the ellipse

49. Ellipse Equation Ellipse Parameters RgRgRgRg Georeactor rate T Exposure time <R> Average background rate f Spread in background rate mmmm Slope uncertainty Parameters depend on

50. Ellipse Parameters = average background rate f = fractional spread of background rate T = Exposure time R g = georeactor rate  m = oscillation probability uncertainty  m 0 = 0.75

51. Error Ellipse for KamLAND, 3 Years  ≈ 0.62 events/day  f ≈ 16% (i.e. RMS(R)/ = 0.16)  T = 3 years (12% down time fraction not included)  R g = 0.0742 events/day (10 TW georeactor)   m = 0.15 (slope uncertainty from solar meas.)  m 0 = 0.75 (slope = avg. surv. prob.)

52. KamLAND, 3 Years

53. KamLAND, How Many Years? 40 years for 90% confidence level!

54. Effect of Background Spread

55. Reducing the Background Level

56. Slope Uncertainty Improvements

57. Detector Size

58. 1 Gigaton = 2,500,000 Gigaton Detector

59. Go ~ 2.5 km along axis! Gigaton Detector

60. Summary of Results  Georeactor will NOT be observed with KamLAND  Large spread in background rate helps  Low background level   Georeactor detectable with small detector

61. Summary of Results  Slope uncertainty  Improved knowledge helps somewhat  A ~10 2 increase in detector size allows georeactor detection  1 Gigaton = 2.5 million x KamLAND Most antineutrinos detected by a gigaton detector will be from the georeactor!

62. Event Rate @ Gigaton Detector  0.0742 events/day  0.4 kton  10 TW x 2,500,000 ≈ 200,000 events/day Expected rate from man-made reactors: 20,000 ev/day

63. Caveat  In this analysis, information from the antineutrino energy spectrum was not used.  Therefore the statement that KamLAND cannot say anything meaningful about a georeactor is premature  Setting 90% limit may be possible  Positive identification, however, is impossible

64. Conclusion  An array of gigaton detectors whose primary aim is arms control will definitely allow the detection of a georeactor (if it exists)  The detection of a georeactor will have giant repercussions on our understanding of planet formation and geophysics

65. Evidence for Oxygen-poor Earth (2)  If we accept that the Earth was made from molten meteorites, the following mass ratios must hold Mass(core) Mass(alloys, opaque minerals) = Mass(mantle) Mass(slag) Using density profile from seismic data Meteorite data

66. Evidence for Oxygen-poor Earth (3) Herndon, J.M. (1996) Proc. Natl. Acad. Sci. USA 93, 646-648. The Earth Seems to be Oxygen-poor!

67. Earth ‘ s Interior from Two Models

68. 3 He/ 4 He from the Georeactor Model SCALE Reactor Simulator (Oak Ridge) Deep Earth Measurement (mean and spread) Fig. 1, J.M.Herndon, Proc. Nat. Acad. Sci. USA, Mar. 18, 2003 (3047)

69. Detection Strategy Background (commercial nuclear reactors) Signal (georeactor) Slope = average oscillation survival probability

70. Detection Strategy Slope constrained by solar neutrino measurements Slope ≈ 0.75 ± 0.15 Georeactor rate

71. Slope Uncertainty 1  uncertainty in solar neutrino oscillation parameters (  m 2, sin 2 2  ) (rough estimate) Best fit

72. Slope Uncertainty

73. Measuring the Georeactor Power  Fit a line through data:  observed vs. expected rate x i = expected e rate y i = observed e rate  i = stat. err. y i i = bin index b = georeactor rate m = commercial reactor e avg. survival probability m 0 = best estimate from solar experiments  m = estimated uncertainty

74. Measuring the Georeactor Power  Fit a line through data:  observed vs. expected rate x i = expected e rate y i = observed e rate  i = stat. err. y i i = bin index b = georeactor rate m = commercial reactor ne avg. survival probability m 0 = best estimate from solar n experiments  m = estimated uncertainty Measure this

75. Line Fit to Data

76. What Conditions are Necessary to Detect a 10 TW Georeactor?  Detector size  Signal and background scale by the same factor  Exposure time  Overall increase in statistics  Slope (average survival probability)  Uncertainty that is independent of exposure time  Improvement over time with more/better solar measurements  Commercial reactor background  Spread in background level

77. Error Contour Formula

78. = average background rate f = fractional spread of background rate T = Exposure time R g = georeactor rate  m = oscillation probability uncertainty  m 0 = 0.75

79. KamLAND, 3 Years

80. KamLAND, How Many Years?

81. Summary of Results  Improved knowledge of neutrino oscillation parameters help, but not enough to allow KamLAND to detect a georeactor  A x100 increase in detector size will allow 99% detection of a 10TW georeactor, even under high background conditions as in KamLAND  Don ‘ t need to go all the way to a gigaton (x2000), although it will allow a comfortable margin