Noise Techniques in Nuclear Systems

  • Imre Pázsit
  • Christophe Demazière


This chapter deals with neutron fluctuations in nuclear systems. Such neutron fluctuations, or neutron noise, fall into two categories: neutron noise in zero power systems and neutron noise in power reactors. The concepts, the theory, and the methodology of these fluctuations as well as their various applications for extracting information in a nonintrusive way about the system in question are described. A number of specific applications are described, where detection and analysis of zero power and power reactor noise make it possible to extract diagnostic information about the system by determining some parameters of the system during normal operation, or by detecting, identifying, and quantifying developing anomalies at an early stage and determining their severity. This chapter ends with an outline of future developments and actual issues in the field.


Noise Source Fuel Assembly Neutron Detector Spontaneous Fission Factorial Moment 
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  1. Adorján F, Czibók T, Kiss S, Krinizs K, Vgh J (2000) Core asymmetry evolution using static measurements and neutron noise analysis. Ann Nucl Energy 27(7):649–658CrossRefGoogle Scholar
  2. Baeten P (2004) Heuristic derivation of the Rossi-alpha formula for a pulsed neutron source. Ann Nucl Energy 31:43–53CrossRefGoogle Scholar
  3. Baeten P, Lafuente A, Janssens J, Kochetkov A, Pázsit I, Van Grieken G and Van den Eynde G (2010) Subcriticality determination using the 252Cf source-detector method. Ann Nucl Energy 37(5):672-680CrossRefGoogle Scholar
  4. Ballester D, Munoz-Cobo JL (2005) Feynman-Y function for a subcritical assembly with intrinsic spontaneous fissions driven by external pulsed sources. Ann Nucl Energy 32(5):493–519CrossRefGoogle Scholar
  5. Behringer K, Kosály G, Pázsit I (1979) Linear response of the neutron field to a propagating perturbation of moderator density (two-group theory of BWR noise). Nucl Sci Eng 72:304Google Scholar
  6. Bell GI (1965) On the stochastic theory of neutron transport. Nucl Sci Eng 21:390–401Google Scholar
  7. Bell GI, Glasstone S (1970) Nuclear reactor theory. Van Nostrand Reinhold Company, New YorkGoogle Scholar
  8. Bennett EF (1981) An experimental method for reactor-noise measurements of effective beta. ANL-81-72Google Scholar
  9. Blakeman ED (2009) Summary description of the 252Cf-source-driven noise analysis method for measurement of subcriticality. Oak Ridge National Laboratory internal report ORNL/TM-2008/187Google Scholar
  10. Böhnel K (1985) The effect of multiplication on the quantitative determination of spontaneous fissioning isotopes by neutron correlation analysis. Nucl Sci Eng 90:75Google Scholar
  11. Cacuci DG (1993) On chaotic dynamics in nuclear engineering systems. Nucl Technol 103: 303–309Google Scholar
  12. Cacuci DG, March-Leuba J, Perez RB (1986) Limit cycles and bifurcations in nuclear systems. Trans Am Nucl Soc 53:239Google Scholar
  13. Cifarelli D, Hage W (1986) Models for a three-parameter analysis of neutron signal correlation measurements for fissile material assay. Nucl Instrum Methods 251 (3):550–563CrossRefGoogle Scholar
  14. Croft S, Bourva LC-A (2000) The measurement of passive neutron multiplicity counter gate utilisation factors and comparisons with theory. Nucl Instrum Methods 453 (3):553–568CrossRefGoogle Scholar
  15. Czibók T, Kiss G, Kiss S, Krinizs K, Végh J (2003) Regular neutron noise diagnostics measurements at the Hungarian Paks NPP. Prog Nucl Energy 43:67–74CrossRefGoogle Scholar
  16. D’Auria F et al (1997) State of the art report on boiling water reactor stability – appendix B: methods for evaluating decay ratio. NEA report NEA/CSNI/R(96) 21, pp 333–341Google Scholar
  17. Degweker SB (1998) Simple formulae for interpretation of the dead time alpha (first moment) method of reactor noise. Ann Nucl Energy 26(15):1267–1273CrossRefGoogle Scholar
  18. Degweker SB (1999) An exact solution for a non-extending dead time problem in passive neutron assay. Ann Nucl Energy 25(15):387–401CrossRefGoogle Scholar
  19. Degweker SB (2000) Some variants of the Feynman alpha method in critical and accelerator driven sub critical systems. Ann Nucl Energy 27(14):1245–1257CrossRefGoogle Scholar
  20. Degweker SB (2003) Reactor noise in accelerator driven systems. Ann Nucl Energy 30:223CrossRefGoogle Scholar
  21. Degweker SB, Rana YS (2007) Reactor noise in accelerator driven system – II. Ann Nucl Energy 34:463–482CrossRefGoogle Scholar
  22. Demazière C (2004) Development of a 2-D 2-group neutron noise simulator. Ann Nucl Energy 19:647–680CrossRefGoogle Scholar
  23. Demazière C (2006) Analysis methods for the determination of possible unseated fuel assemblies in BWRs. Int J Nucl Energy Sci Technol 2(3):167–188CrossRefGoogle Scholar
  24. Demazière C, Pázsit I (2002) Online determination of the MTC (moderator temperature coefficient) by neutron noise and gamma-thermometer signals. In: Ruan D, Fantoni PF (eds) Power plant surveillance and diagnostics – modern approaches and advanced applications, Physica Verlag/Springer, Heidelberg, pp 135–157, ISBN 3–540–43247–7Google Scholar
  25. Demazière C, Pázsit I (2004) Development of a method for measuring the MTC by noise analysis and its experimental verification in Ringhals-2. Nucl Sci Eng 148 (1):1–29Google Scholar
  26. Demazière C, Pázsit I (2005) On the possibility of the space-dependence of the stability indicator (decay ratio) of a BWR. Ann Nucl Energy 32(12):1305–1322CrossRefGoogle Scholar
  27. Demazière C, Pázsit I (2008) Numerical tools applied to power reactor noise analysis. Prog Nucl Energy 51:67–81CrossRefGoogle Scholar
  28. Demazière C, Sunde C, Arzhanov V, Pázsit I (2003) Final report on the research project Ringhals diagnostics and monitoring, Stage 8. Chalmers report CTH-RF-177/RR-10, Chalmers University of Technology, GöteborgGoogle Scholar
  29. Enqvist A, Pázsit I, Pozzi SA (2006) The number distribution of neutrons and gamma photons generated in a multiplying sample. Nucl Instrum Methods 566:598–608CrossRefGoogle Scholar
  30. Enqvist A, Pázsit I, Avdic S (2010) Sample characterization using both neutron and gamma multiplicities. Nucl Instrum Methods A 615:62–69CrossRefGoogle Scholar
  31. Ensslin N, Harker WC, Krick MS, Langner DG, Pickrell MM, Stewart JE (1998) Application guide to neutron multiplicity counting. Los Alamos report LA-13422-MGoogle Scholar
  32. Fry DN (1971) Experience in reactor malfunction diagnosis using on-line noise analysis. Nucl Technol 10(3):273–282Google Scholar
  33. Fry DN, Kryter RC, Robinson JC (1974) Analysis of neutron-density oscillations resulting from core barrel motion in the Palisades nuclear power plant. Oak Ridge National Laboratory internal report ORNL-TM-4570Google Scholar
  34. Ginestar D, Miró R, Verdú G, Hennig D (2002) A transient modal analysis of a BWR instability event. J Nucl Sci Technol 39(5):554–563CrossRefGoogle Scholar
  35. Ginestar D, Verdú G, Miro R (2006) Singular system analysis of the local power range monitor (LPRM) readings of a boiling water reactor (BWR) in an unstable event. Int J Nucl Energ Sci Technol 2(3):253–265.CrossRefGoogle Scholar
  36. Graves HW Jr (1979) Nuclear fuel management. Wiley, New YorkGoogle Scholar
  37. Hage W, Cifarelli D (1985) On the factorial moments of the neutron multiplicity distribution of fission cascades. Nucl Instrum Methods 236(1):165–177CrossRefGoogle Scholar
  38. Harris DR (1964) Naval reactor physics handbook, vol I. United States Atomic Energy Commission, Washington, pp 1010–1142Google Scholar
  39. Hennig D (1999) A study on boiling water reactor stability behaviour. Nucl Technol 126(1):10–31MathSciNetGoogle Scholar
  40. Henry AF (1958) The application of reactor kinetics to the analysis of experiments. Nucl Sci Eng 3:52–70Google Scholar
  41. Henry AF (1975) Nuclear-reactor analysis. The MIT Press, CambridgeGoogle Scholar
  42. Hotta A, Suzawa Y, Takeuchi H (1997) Development of BWR regional instability model and verification based on Ringhals 1 test. Ann Nucl Energy 24(17):1403–1427CrossRefGoogle Scholar
  43. Karlsson JK-H, Pázsit I, Gill RD (1997) Spectral and correlation analysis of soft X-ray signals from the Joint European Torus tokamak. Fusion Eng Des 34–35:175–178CrossRefGoogle Scholar
  44. Karlsson JK-H, Pzsit I (1998) Analysis of core barrel vibration in Ringhals2, 3 and 4 for several fuel cycles. Chalmers internal report CTH-RF-135/RR-5Google Scholar
  45. Karlsson JK-H, Pzsit I (1999) Localisation of a channel instability in the Forskmark-1 boiling water reactor. Ann Nucl Energi 26(13):1183–1204CrossRefGoogle Scholar
  46. Kitamura Y, Pázsit I, Wright J, Yamamoto A, Yamane Y (2005) Derivation of pulsed Feynman- and Rossi-alpha formulae including delayed neutrons. Ann Nucl Energy 32:671–692CrossRefGoogle Scholar
  47. Kitamura Y, Taguchi K, Misawa T, Pázsit I, Yamamoto A, Yamane Y, Ichihara C, Nakamura H, Oigawa H (2006) Calculation of the stochastic pulsed Rossi-alpha formula and its experimental verification. Prog Nucl Energy 48:37–50CrossRefGoogle Scholar
  48. Kleiss E, van Dam H (1978) Analysis of neutron detector response to bubbles in a water moderated reactor. Ann Nucl Energy 6(7–8):385–398Google Scholar
  49. Konno H, Kanemoto S, Takeuchi Y (1999) Parametric stochastic stability and decay ratio for a stochastic non-linear BWR model below the Hopf bifurcation. Ann Nucl Energy 26:1465Google Scholar
  50. Kosály G (1975) Investigation of the local component of power-reactor noise via diffusion theory. KFKI report, KFKI-75–27Google Scholar
  51. Kosály G (1980) Noise investigations in boiling-water and pressurized-water reactors. Prog Nucl Energy 5:145–199CrossRefGoogle Scholar
  52. Kosály G, Meskó L (1972a) Remarks on the transfer function relating inlet temperature fluctuations to neutron noise. Atomkernenergie 20:33–36Google Scholar
  53. Kosály G, Meskó L (1972b) Investigation of the cross correlation of coolant temperature fluctuations via the axial dependent two point model of heat transfer. Atomkernenergie 20:91–94Google Scholar
  54. Kuang ZF, Pázsit I (1999) The general backward theory of neutron fluctuations in subcritical systems with multiple emission sources. Il Nuovo Cimento 112 A:1067–1092Google Scholar
  55. Kuang ZF, Pázsit I (2002) The generalised theory of neutron noise in a random medium. Proc R Soc A 458:232–252CrossRefGoogle Scholar
  56. Lamarsh JR (2002) Introduction to nuclear reactor theory. American Nuclear Society, LaGrange ParkGoogle Scholar
  57. Larsson V, Demazière C (2009) Comparative study of 2-group P1 and diffusion theories for the calculation of the neutron noise in 1D 2-region system. Ann Nucl Energy 36(10):1574–1587CrossRefGoogle Scholar
  58. Lathouwers D, Agung A, van der Hagen THJJ, van Dam H, Pain CC, De Oliveira CRE, Goddard AJH (2003) Dynamics modeling and stability analysis of a fluidized bed nuclear reactor. Prog Nucl Energy 43(1–4):437–443CrossRefGoogle Scholar
  59. Makai M, Kalya Z, Nemes I, Pos I, Pór G (2007) Evaluating new methods for direct measurement of the moderator temperature coefficient in nuclear power plants during normal operation. In: Proceedings of the 17th symposium of AER on VVER reactor physics and reactor safety, Yalta, September 24–29, 2007Google Scholar
  60. March-Leuba J, Cacuci DG, Perez RB (1983) Nonlinear dynamics of boiling water reactors. Trans Am Nucl Soc 45:725Google Scholar
  61. March-Leuba J, Cacuci DG, Perez RB (1984) Universality and aperiodic behavior of nuclear reactors. Nucl Sci Eng 86:401–404Google Scholar
  62. March-Leuba J, Cacuci DG, Perez RB (1986a) Nonlinear dynamics and stability of boiling water reactors, I: qualitative analysis. Nucl Sci Eng 93:111–123Google Scholar
  63. March-Leuba J, Cacuci DG, Perez RB (1986b) Nonlinear dynamics and stability of Boiling Water Reactors, II: quantitative Analysis. Nucl Sci Eng 93:124–136Google Scholar
  64. Mellier F (Co-ordinator) (2005) The MUSE experiments for sub critical neutronics validation. Final report of the EU-supported project MUSE, Contract No: FIKW-CT-2000-00063Google Scholar
  65. Mihalczo JT et al (1990) Dynamic subcriticality measurements using the 252Cf-source-driven neutron noise method. Nucl Sci Eng 104:314–338Google Scholar
  66. Miro R, Ginestar D, Hennig D, Verdu G (2000) On the regional oscillation phenomenon in BWRs. Prog Nucl Energy 36(2):189–229CrossRefGoogle Scholar
  67. Mogilner AI, Zolotukhin VG (1961) Atomnaya Energiya 10:377Google Scholar
  68. Munoz-Cobo JL, Perez RB, Verdú G (1987) Stochastic neutron transport theory: neutron counting statistics in nuclear assemblies. Nucl Sci Eng 95(2):83–105Google Scholar
  69. Munoz-Cobo JL, Chiva S, Sekhri A (2004) A reduced order model of BWR dynamics with subcooled boiling and modal kinetics: application to out of phase oscillations. Ann Nucl Energy 31(10):1135–1162CrossRefGoogle Scholar
  70. Munoz-Cobo JL, Pena J, Gonzalez E (2008) Rossi-alpha and Feynmann Y functions for non-Poissonian pulsed sources of neutrons in the stochastic pulsing method: application to subcriticality monitoring in ADS and comparison with the results of Poissonian pulsed neutron sources. Ann Nucl Energy 35(12): 2375–2386CrossRefGoogle Scholar
  71. OECD (2002) Reactor surveillance and diagnostics. In: Proceedings of the SMORN conferences.
  72. Oguma R (1997) Application of noise analysis for the study of core local instability at Forsmark 1. SKI report 97:42, Statens Kärnkraftinspektion (Swedish Nuclear Power Inspectorate), StockholmGoogle Scholar
  73. Ott KO, Neuhold RJ (1985) Introductory nuclear reactor dynamics. American Nuclear Society, La Grange ParkGoogle Scholar
  74. Pacilio N (1970) Reactor-noise analysis in the time domain. United States Atomic Energy Commission, WashingtonGoogle Scholar
  75. Pál L (1958) On the theory of stochastic processes in nuclear reactors. Nuovo Cimento, Supplemento 7:25–42MATHCrossRefGoogle Scholar
  76. Pál L, Pázsit I (2006) Neutron fluctuations in a multiplying medium randomly varying in time. Phys Scripta 74(1):62–70MATHCrossRefGoogle Scholar
  77. Pál L, Pázsit I (2007) Theory of neutron noise in a temporally fluctuating multiplying medium. Nucl Sci Eng 155(3):425–440Google Scholar
  78. Pázsit I (1992) Dynamic transfer function calculations for core diagnostics. Ann Nucl Energy 19:303–312CrossRefGoogle Scholar
  79. Pázsit I (1995) Determination of reactor stability in case of dual oscillations. Ann Nucl Energy 22:377–387CrossRefGoogle Scholar
  80. Pázsit I (2002) Neutron noise theory in the P1 approximation. Prog Nucl Energy 40:217–236CrossRefGoogle Scholar
  81. Pázsit I (2003) Hugo van Dam and the dynamic adjoint function. Ann Nucl Energy 30:1757–1775CrossRefGoogle Scholar
  82. Pázsit I, Glckler O (1988) On the neutron noise diagnostics of PWR control vibrations, III: application at a power plant. Nucl Sci Eng 99(4):313–328Google Scholar
  83. Pázsit I, Garis NS, Glöckler O (1994) BWR instrument tube vibrations: interpretation of measurements and simulations. Ann Nucl Energy 21(12): 759–786CrossRefGoogle Scholar
  84. Pázsit I, Glöckler O (1996) On the neutron noise diagnostics of PWR control vibrations, IV: application of neural networks. Nucl Sci Eng 124(1):167–177Google Scholar
  85. Pázsit I, Kitamura M (1996) The role of neural networks in reactor diagnostics and control. Adv Nucl Sci Technol 24:95–130CrossRefGoogle Scholar
  86. Pázsit I, Pál L (2008) Neutron fluctuations – a treatise on the physics of branching processes. Elsevier Ltd., London/New York/TokyoMATHGoogle Scholar
  87. Pázsit I, Pozzi SA (2005) Calculation of gamma multiplicities in a multiplying sample for the assay of nuclear materials. Nucl Instrum Methods A 555: 340–346CrossRefGoogle Scholar
  88. Pázsit I, Karlsson JK-H, Garis NS (1998) Some developments in core-barrel vibration diagnostics. Ann Nucl Energy 25(13):1079–1093CrossRefGoogle Scholar
  89. Pázsit I, Kuang ZF, Prinja AK (2002) A unified theory of zero power and power reactor noise via backward master equations. Ann Nucl Energy 29(2):169–192CrossRefGoogle Scholar
  90. Pázsit I, Demaziére C, Sunde C, Bernitt C, Hernándes-Solz A (2008) Final report on the research project ringhals diagnostics and monitoring stage 12. Chalmers internal report CTH-NT-220/RR-14Google Scholar
  91. Pokol G, Pór G, Zoletnik S, The W7-AS Team (2007) Application of a bandpower correlation method to the statistical analysis of MHD bursts in quiescent Wendelstein-7 AS stellarator plasmas. Plasma Phys Control Fusion 49: 1391–1408CrossRefGoogle Scholar
  92. Pór G (1981) Investigations on the phase at low frequencies of the CPSD between detectors in the Borssele PWR power plant. ECN -81–131 reportGoogle Scholar
  93. Pór G, Izsák E, Valkó J (1985) Some results of noise measurements in a PWR NPP. Prog Nucl Energy 15:387–393CrossRefGoogle Scholar
  94. Pór G, Berta M, Csuvar M (2003) Measurement of the coolant flow rate using correlation of temperature fluctuations. Prog Nucl Energy 43:281–288CrossRefGoogle Scholar
  95. Saito K (1979) Source papers in reactor noise. Prog Nucl Energy 3(3):157–218CrossRefGoogle Scholar
  96. Sanchez R (1989) Linear kinetic theory in stochastic media. J Math Phys 30:2498–2511MathSciNetMATHCrossRefGoogle Scholar
  97. Sanchez R, Pomraning GC (1991) A statistical analysis of the double heterogeneity problem. Ann Nucl Energy 18(7):371–395CrossRefGoogle Scholar
  98. Shiralkar B (2005) BWR stability analysis – phenomena and requirements. Talk given at the workshop on status and perspectives of coupled code analysis for BWRs, Royal Institute of Technology, Stockholm, June 27–28, 2005Google Scholar
  99. Sjöstrand NG (1956) Measurements on a subcritical reactor using a pulsed neutron source. Arkiv för Fysik 11:233–246Google Scholar
  100. Stacey WM Jr (1969) Space-time nuclear reactor kinetics. Academic, New YorkGoogle Scholar
  101. Takeuchi Y, Takigawa Y, Uematsu H (1994) A study on boiling water reactor regional stability from the viewpoint of higher harmonics. Nucl Technol 106 (3):300–314Google Scholar
  102. Thie JA (1959) Dynamic behavior of boiling reactors. ANL-5849, Argonne National LaboratoryGoogle Scholar
  103. Thie JA (1963) Reactor noise. Rowman & Littlefield, New YorkGoogle Scholar
  104. Thie JA (1977) Neutron noise sources in PWRs. Prog Nucl Energy 1(2–4):283–292CrossRefGoogle Scholar
  105. Thie JA (1981) Power reactor noise. American Nuclear Society, La Grange ParkGoogle Scholar
  106. Uhrig RE (ed) (1966) Proceedings of the symposium on neutron noise, waves and pulse propagation, GainesvilleGoogle Scholar
  107. Uhrig RE (1970) Random noise in nuclear reactor systems. Ronald Press, New YorkGoogle Scholar
  108. van Dam H (1975) A perturbation method for analysis of detector response to parametric fluctuations in reactors. Atomkernenergie 25:70Google Scholar
  109. van Dam H (1976) Neutron noise in boiling water reactors. Atomkernenergie 27:8Google Scholar
  110. van Dam H (2000) Self-stabilizing criticality waves. Ann Nucl Energy 27(16):1505–1521CrossRefGoogle Scholar
  111. van der Hagen THJJ, Hoogenboom JE, van Dam H (1992) A multi dimensional multigroup diffusion model for the determination of the frequency-dependent field of view of a neutron detector. Nucl Sci Eng 110:237–253Google Scholar
  112. van der Hagen THJJ, Pázsit I, Thomson O, Melkerson B (1994) Methods for the determination of the in-phase and out-of-phase stability characteristics of a boiling water reactor. Nucl Technol 107(2):193–214Google Scholar
  113. Verdú G, Ginestar D, Vidal V, Miró R (1998) Modal decomposition method for BWR stability analysis. J Nucl Sci Technol 35(8):538–546Google Scholar
  114. Wach D, Kosály G (1974) Investigation of the joint effect of local and global driving sources in in-core neutron noise measurements, Atomkernenergie 23(4):244–250Google Scholar
  115. Watson HW, Galton F (1873) Educational Times 19:103Google Scholar
  116. Weinberg AM, Schweinler HC (1948) Theory of oscillating absorber in a chain reactor. Phys Rev 74:851–863MathSciNetMATHCrossRefGoogle Scholar
  117. Williams MMR (1974) Random processes in nuclear reactors. Pergamon Press, OxfordGoogle Scholar
  118. Yadigaroglu G, Bergles AE (1972) Fundamental and higher-mode density wave oscillations in two-phase flow. Trans ASME J Heat Transfer 94(2):189–195CrossRefGoogle Scholar
  119. Yamane Y, Pázsit I (1998) Heuristic derivation of Rossi-alpha formula with delayed neutrons and correlated source. Ann Nucl Energy 25:1373–1382CrossRefGoogle Scholar
  120. Yamane Y, Takemoto Y, Imai T (1999) Effective delayed neutron fraction measurements in FCA-XIX cores by using modified Bennett method. Prog Nucl Energy 35(2):183–194CrossRefGoogle Scholar
  121. Yamane Y, Kitamura Y, Kataoka H, Ishitani K, Shiroya S (2002) Application of variance-to-mean method to accelerator-driven subcritical system. In: PHYSOR-2002 international conference on the new frontiers of nuclear technology: reactor physics, safety and high-performance computing, Seoul, October 7–10, 2002Google Scholar
  122. Zinzani F, Demazière C, Sunde C (2008) Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities. Ann Nucl Energy 35(11):2109–2125CrossRefGoogle Scholar

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Imre Pázsit
    • 1
  • Christophe Demazière
    • 1
  1. 1.Department of Nuclear EngineeringChalmers University of TechnologyGöteborgSweden

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