Skip to main content

B N Theory: Advances and New Models for Neutron Leakage Calculation

  • Chapter
Advances in Nuclear Science and Technology

Part of the book series: Advances in Nuclear Science & Technology ((ANST,volume 24))

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. H. Hurwitz and P. F. Zweifel, Slowing down of neutrons by hydrogenous moderators, J. Appl. Phys., 26, 923–931 (1955)

    Article  MATH  ADS  Google Scholar 

  2. S. Glasstone and M. C. Edlund “Elements of Nuclear Reactor Theory”, §7.23, D. Van Nostrand Co., Inc. (1952)

    Google Scholar 

  3. A. M. Weinberg and E. P. Wigner “The Physical Theory of Neutron Chain Reactors”, p. 383, University of Chicago Press (1958)

    Google Scholar 

  4. D. J. Behrens, The effect of holes in a reacting material on the passage of neutrons, Proc. Phys. Soc., 62, 607–616 (1949)

    Article  MATH  ADS  Google Scholar 

  5. G. W. Schaefer and D. M. Parkyn, A Monte Carlo study of thermal utilisation factor and diffusion area: gas-cooled graphite-moderated lattices, Proc. Second Int. Conf. Peaceful Uses At. Ener., Geneva, Switzerland, September 1–13, 1958, Vol. 16, 496–502, A/CONF/15/P.310., United Nations (1958)

    Google Scholar 

  6. N. I. Laletin, Passage of neutrons in a heterogeneous medium, Proc. Second Int. Conf. Peaceful Uses At. Ener., Geneva, Switzerland, September 1–13, 1958, Vol. 16, 601–610, A/CONF/15/P.2189., United Nations (1958)

    Google Scholar 

  7. P. Benoist “Formulation générale et calcul pratique du coefficient de diffusion dans un réseau comportant des cavités”, Rapport CEA-R-1354, Commissariat à ľEnergie Atomique, Saclay (1959)

    Google Scholar 

  8. P. Benoist, Formulation générale et calcul pratique du coefficient de diffusion dans un réseau comportant des cavités, React. Sci., 13, 97–112 (1961)

    Google Scholar 

  9. P. Benoist “Théorie du coefficient de diffusion des neutrons dans un réseau comportant des cavités”, Rapport CEA-R-2278, Commissariat à ľEnergie Atomique, Saclay (1964)

    Google Scholar 

  10. P. Benoist, Streaming effects and collision probabilities in lattices, Nucl. Sci. Eng., 34, 285–307 (1968)

    Google Scholar 

  11. D. C. Leslie “The calculation of leakage and of flux distributions in systems with superimposed buckling”, Report AEEW-M-292, Atomic Energy Establishment, Winfrith, Dorset (1964)

    Google Scholar 

  12. D. C. Leslie, Weighting of diffusion coefficients in cell calculations, React. Sci. Tech., 16, 1–11 (1962)

    Google Scholar 

  13. V. C. Deniz “Constante de décroissance de la densité neutronique dans un réseau non-multiplicateur de dimensions finies”, Rapport CEA-R-2702, Commissariat à ľEnergie Atomique, Saclay (1965)

    Google Scholar 

  14. N. Corngold, P. Michael and W. Wollman, The time decay constants in neutron thermalization, Nucl. Sci. Eng., 15, 13–19 (1963)

    Google Scholar 

  15. K. H. Beckurts and K. Wirtz “Neutron Physics”, §10.3.3, p. 2.2.2., Springer-Verlag, New York (1964)

    MATH  Google Scholar 

  16. V. C. Deniz, Study of the kinetics of thermalized neutron populations in multiplying or nonmultiplying heterogeneous media, Nucl. Sci. Eng., 28, 397–403 (1967)

    Google Scholar 

  17. V. C. Deniz, J. G. Le Ho and M. Sagot, Study of lattices of graphite with empty channels by means of the pulsed source technique, Nucl. Sci. Eng., 32, 201–224 (1968)

    Google Scholar 

  18. M. M. R. Williams, Effective diffusion coefficients in heterogeneous media, Atomkernener., 18, 31–50 (1971)

    Google Scholar 

  19. E. M. Gelbard, Anisotropic neutron diffusion in lattices of the zero-power plutonium reactor experiments, Nucl. Sci. Eng., 54, 327–340 (1974)

    Google Scholar 

  20. D. S. Selengut, Diffusion coefficients for heterogeneous systems, Trans. Am. Nuc. Soc., 3, 398–399 (1960)

    Google Scholar 

  21. V. C. Deniz, A new consistent definition of the homogenized diffusion coefficient of a lattice, limitations of the homogenization concept, and discussion of previously defined coefficients, IAEA Proc. Spec. Mtg. Homog. Meth. React. Phys., Lugano, Switzerland, November 13–15, 1978, 521–530, TECDOC-231, International Atomic Energy Agency (1980)

    Google Scholar 

  22. V. C. Deniz, The homogenization procedure for lattices, homogenized diffusion coefficients, and the eigen-coefficient approach, ANS/ENS Proc. Int Topic, Mtg. Advanc. Math. Meth. Solut. Nucl. Engin. Prob., Munich, Germany, April 27–29, 1981, Vol. 1, 161–180, Kernforschungszentrum Karlsruhe (1981)

    Google Scholar 

  23. C. Carter, Streaming due to holes in a reactor, React. Sci. Tech.., 15, 76 (1961)

    Google Scholar 

  24. R. A. Bonalumi, A unified theory of cell diffusion coefficients, Energ. Nucl., 18, 395–409 (1971)

    ADS  Google Scholar 

  25. E. W. Larsen, Asymptotic solution of neutron transport problems for small mean free paths, J. Math. Phys., 15, 75–81 (1974)

    Article  ADS  Google Scholar 

  26. E. W. Larsen, Neutron transport and diffusion in inhomogeneous media. II, Nucl. Sci. Eng., 60, 357–368 (1976)

    Google Scholar 

  27. R. T. Chiang and J. Dorning, A spatially asymptotic solution to the energy-dependent ω-mode transport equation, Trans. Am. Nuc. Soc., 34, 280 (1980)

    Google Scholar 

  28. G. I. Marchuk “Numerical Methods for Nuclear Reactor Calculations”, §13, Consultants Bureau, Inc., New York (1959)

    Google Scholar 

  29. P. Köhler, A new definition of the cell diffusion coefficient, Nucl. Sci. Eng., 57, 333–335 (1975)

    Google Scholar 

  30. R. P. Hughes, A unified derivation of the various definitions of lattice cell diffusion coefficient, Nucl. Sci. Eng., 67, 85–90 (1978)

    Google Scholar 

  31. T. Duracz, On the homogenization of uniform lattices, Nucl. Sci. Eng., 74, 61–64 (1980)

    Google Scholar 

  32. E. W. Larsen and R. P. Hughes, Homogenized diffusion approximations to the neutron transport equation, Nucl. Sci. Eng., 73, 274–285 (1980)

    Google Scholar 

  33. P. Benoist, I. Petrovic and Z. Stankovski, Improvements in leakage calculations of nuclear reactor assemblies and consistent definition of cell leakage coefficients by an equivalence procedure, Proc. ANS/ENS Int. Top. Mtg. Advanc. Math. Comput. React. Phys., Pittsburgh, Pennsylvania, U.S.A., April 28–May 2, 1991, Vol. 3, 5.2-1–15.2-14, American Nuclear Society (1991)

    Google Scholar 

  34. P. Köhler and J. Ligou, Axial neutron streaming in gas-cooled reactors, Nucl. Sci. Eng., 54, 357–360 (1974)

    Google Scholar 

  35. P. Benoist, A simple model for the calculation of the sodium-voiding effect on neutron leakages in a fast reactor lattice, I Formalism, Nucl. Sci. Eng., 86, 22–40 (1984)

    Google Scholar 

  36. P. Benoist and T. Duracz, A simple model for the calculation of the sodium-voiding effect on neutron leakages in a fast reactor lattice, II Numerical results for hexagonal lattice, Nucl. Sci, Eng., 86, 41–46 (1984)

    Google Scholar 

  37. P. Benoist, Integral transport theory formalism for diffusion coefficients calculations in Wigner-Seitz cells, Nucl. Sci.Eng., 77, 1–12 (1981); see also: Corrigendum, Nucl. Sci. Eng., 78, 198 (1981)

    Google Scholar 

  38. C. Yang and P. Benoist, Scattering anisotropy and neutron leakage in reactor lattices, Nucl. Sci. Eng., 86, 47–62 (1984)

    Google Scholar 

  39. E. Eisemann “Anisotropic diffusion in gas-cooled fast breeder reactors”, EURFNR-1019 (English translation of Report KFK-1577), Kernforschungzentrum, Karlsruhe (1972)

    Google Scholar 

  40. E. M. Gelbard and R. Lell, Monte Carlo treatment of fundamental-mode neutron leakage in presence of voids, Nucl. Sci. Eng., 63, 9–32 (1977)

    Google Scholar 

  41. E. M. Gelbard, D. C. Wade, R. W. Schaefer and R. E. Phillips, Calculations of void streaming in the Argone gas-cooled fast reactor critical experiment, Nucl. Sci. Eng., 64, 624–637 (1977)

    Google Scholar 

  42. P. Köhler, Calculations of the radial and axial diffusion coefficient for a hexagonal lattice of a high-temperature reactor with block elements, Nucl. Sci. Eng., 78, 113–120 (1981)

    Google Scholar 

  43. T. Duracz, Parallel neutron diffusion in plane lattices with voids, Nucl. Sci. Eng., 81, 471: (1982)

    Google Scholar 

  44. E. M. Gelbard and R. P. Hughes, Lattice eigenvalue as a function of buckling: Correction to first-order perturbation theory, Nucl. Sci. Eng., 70, 262–273 (1979)

    Google Scholar 

  45. E. M. Gelbard and R. Pego, Monte Carlo computation of directional diffusion coefficients, Proc. ANS Topic. Mtg. Comput. Meth. Nucl. Engin., Williamsburg, Virginia, U.S.A., April 23–25, 1979, Vol. 2, 9–19, American Nuclear Society (1979)

    Google Scholar 

  46. E. W. Larsen and M. Williams, Neutron drift in heterogeneous media, Nucl. Sci. Eng., 65, 290–302 (1978)

    Google Scholar 

  47. R. P. Hughes, Complex buckling modes in asymmetric cell lattice, Nucl. Sci. Eng., 69, 430–441 (1979)

    Google Scholar 

  48. T. Duracz, Plane asymmetric cell lattices with superimposed small buckling, Nucl. Sci. Eng., 76, 175–180 (1980)

    Google Scholar 

  49. E. M. Gelbard, Streaming in lattices, in: “Advances in Nuclear Sciences and Technology”, Vol. 15, 223–400, J. Lewins, M. Becker Eds., Plenum Press, New York (1983)

    Google Scholar 

  50. V. C. Deniz, The theory of neutron leakage in reactor lattices, in: “CRC Handbook of Nuclear Reactor Calculations”, Vol. 2, 409–508, CRC Press, Boca Raton, Florida (1986)

    Google Scholar 

  51. P. Benoist “Homogenization theory in reactor lattices”, Note CEA-N-2471, Commissariat à ľEnergie Atomique, Saclay (1986)

    Google Scholar 

  52. M. Lam-Hime “Homogénéisation: résolution de ľéquation de transport en mode fondamental”, Note CEA-N-2223, Commissariat à ľEnergie Atomique, Saclay (1981)

    Google Scholar 

  53. R. Roy, A. Hébert and G. Marleau, Consistent B n theory for slab lattices, Nucl. Sci. Eng., 115, 112–128 (1993)

    Google Scholar 

  54. J. M. Halsall “CACTUS, A characteristics solution to the neutron transport equation in complicated geometries”, Report AEEW-R 1291, Atomic Energy Establishment, Winfrith (1980)

    Google Scholar 

  55. P. Benoist and I. Petrovic “TIBERE: Une méthode de calcul de ľeffet de ľhétérogénéité ďun réseau sur les fuites de neutrons” (including the English translation), Note CEA-N-2707, Commissariat à ľEnergie Atomique, Saclay (1992)

    Google Scholar 

  56. I. Petrovic “Amélioration du modèle de fuites de neutrons dans le schéma de calcul des conditions critiques et des paramètres homogénéisés ďun réacteur nucléaire”, Note CEA-N-2730, Commissariat à ľEnergie Atomique, Saclay (1993)

    Google Scholar 

  57. P. Benoist, J. Mondot and I. Petrovic, Calculation and Experimental Investigation of Void Effect — A Simplified Theoretical Model for Space-Dependent Leakage Treatment of Heterogeneous Assemblies, Nucl. Sci. Eng., 118, 197:216 (1994)

    Google Scholar 

  58. I. Petrovic, P. Benoist and G. Marleau, A simplified heterogeneous B1 model with isotropically-reflected neutrons on assembly boundary, Proc. ANS/ENS Int. Conf. Math. Comput. React. Phys. Environm. Analy., Portland, Oregon, U.S.A., April 30–May 4, 1995, Vol. 1, 792:801, American Nuclear Society (1995)

    Google Scholar 

  59. I. Petrovic, P. Benoist and G. Marleau, A quasi-isotropic reflecting boundary condition for the TIBERE heterogeneous leakage model, Nucl. Sci. Eng., 122, 151:166(1996)

    Google Scholar 

  60. H. Honeck, THERMOS: A thermalization transport theory code for reactor lattice calculations, BNL-5826, Brookhaven National Laboratory (1961)

    Google Scholar 

  61. R. Bonalumi, Neutron first collision probabilities in reactor physics, Energ. Nucl., 8, 326:336 (1961)

    Google Scholar 

  62. I. Carlvik, A method for calculating collision probabilities in general cylindrical geometry and applications to the flux distributions and Dancoff factors, Proc. Third Int. Conf. Peaceful Uses At. Ener., Geneva, Switzerland, August 31–September 9, 1964, Vol. 2, 225:231, A/CONF/28/P.681., United Nations (1965)

    Google Scholar 

  63. A. Kavenoky, “Calcul et utilisation des probabilités de première collision pour des milieux hétérogènes à une dimension”, Note CEA-N-1077, Commissariat à ľEnergie Atomique, Saclay (1969)

    Google Scholar 

  64. J. R. Askew, Some boundary condition problems arising in the application of collision probability methods, Proc. Sem. Numeric. React. Calcul., Vienna, Austria, January 17–21, 1972, 343:356, International Atomic Energy Agency (1972)

    Google Scholar 

  65. A. Kavenoky, Status of integral transport theory, ANS/ENS Proc. Int Topic. Mtg. Advanc. Math. Meth. Solut. Nucl. Engin. Prob., Munich, Germany, April 27–29, 1981, Vol. 1, 133:143, Kernforschungszentrum Karlsruhe (1981)

    Google Scholar 

  66. R. Sanchez and N. J. McCormick, A review of neutron transport approximations, Nucl. Sci. Eng., 80, 481:535 (1982)

    Google Scholar 

  67. M. M. Anderson and H. C. Honeck, An interface current technique for two-dimensional cell calculations, Proc. Conf. Math. Mod. Comput. Techn. Analy. Nucl. Syst., Ann Arbor, Michigan, U.S.A., April 9–11, 1973, CONF-730414, Vol. I, p. I-53, U.S. Atomic Energy Commission (1973)

    Google Scholar 

  68. R. Sanchez, Approximate solutions of the two-dimensional integral transport equation by collision probability methods, Nucl. Sci. Eng., 64, 384:404 (1977)

    Google Scholar 

  69. P. Benoist, “Amélioration du modèle TIBERE”, Unpublished document, Commissariat à ľEnergie Atomique, Saclay (1992)

    Google Scholar 

  70. R. Sanchez, J. Mondot, Z. Stankovski, A. Cossic and I. Zmijarevic, APOLLO-2: A user-oriented, portable, modular code for multigroup transport assembly calculations”, Nuc. Sci. Eng., 100, 352:362 (1988)

    Google Scholar 

  71. W. C. Bickley and J. Naylor, A short table of the functions Ki n (x) from n=1 to 16, Phil, Mag., 20, 343:347 (1935)

    Google Scholar 

  72. G. Marleau, A. Hébert and R. Roy, New computational methods used in the lattice code DRAGON, Proc. ANS Int. Topic. Mtg. Advanc. React. Phys., Charleston, South Carolina, U.S.A., March 8–11, 1992, American Nuclear Society (1992)

    Google Scholar 

  73. J. L. Vujic, and S. M. Slater, MAGGENTA: Multiassembly general geometry neutron transport theory code, Proc. ANS/ENS Int. Conf. Math. Comput. React. Phys. Environm. Analy., Portland, Oregon, U.S.A., April 30–May 4, 1995, Vol. 2, 1168:1170, American Nuclear Society (1995)

    Google Scholar 

  74. J. L. Vujic, GTRAN2: An advanced transport theory code for advanced assembly calculations, Proc. ANS/ENS Joint Int. Conf. Math. Meth. Supercomp. Nucl. Applic., Karlsruhe, Germany., April 19–23, 1993, 695:704, Kernforschungszentrum Karlsruhe (1993)

    Google Scholar 

  75. X. Wohleber, to be presented as a Ph.D. thesis at the University of Paris XI, Orsay, France (1997)

    Google Scholar 

  76. J. Bussac and P. Reuss, “Traité de Neutronique”, Hermann, Paris (1978)

    Google Scholar 

  77. R. Bonalumi, Diffusion equation and cell homogenization made rigorous, Energ. Nucl., 21, 231:244 (1974)

    Google Scholar 

  78. A. Kavenoky, The SPH homogenization method, IAEA Proc. Spec. Mtg. Homog. Meth. React. Phys., Lugano, Switzerland, November 13–15, 1978, 181:187, TECDOC-231, International Atomic Energy Agency (1980)

    Google Scholar 

  79. J. Mondot, Dé termination de constantes équivalentes pour les calculs de diffusion aux différences finies, IAEA Proc. Spec. Mtg. Homog. Meth. React. Phys., Lugano, Switzerland, November 13–15, 1978, 389:404, TECDOC-231, International Atomic Energy Agency (1980)

    Google Scholar 

  80. K. Koebke, A new approach to homogenization and group condensation, IAEA Proc. Spec. Mtg. Homog. Meth. React. Phys., Lugano, Switzerland, November 13–15, 1978, 303:322, TECDOC-231, International Atomic Energy Agency (1980)

    Google Scholar 

  81. A. F. Henry, B. A. Worley and A. A. Morshed, Spatial homogenization of diffusion theory parameters, IAEA Proc. Spec. Mtg. Homog. Meth. React. Phys., Lugano, Switzerland, November 13–15, 1978, 275:302, TECDOC-231, International Atomic Energy Agency (1980)

    Google Scholar 

  82. D. V. Altiparmakov, On the boundary conditions in cylindrical cell approximation, IAEA Proc. Spec. Mtg. Homog. Meth. React. Phys., Lugano, Switzerland, November 13–15, 1978, 27:42, TECDOC-231, International Atomic Energy Agency (1980)

    Google Scholar 

  83. K. S. Smith, Assembly homogenization techniques for light water reactor analysis, Prog. Nucl. Ener., 17, 303:335(1986)

    Google Scholar 

  84. A. Hébert, Développement de la methode SPH: Homogénéisation de cellules dans un réseau non uniform et calcul des paramètres de réflecteur, Note CEA-N-2209, Commissariat à ľEnergie Atomique, Saclay (1981)

    Google Scholar 

  85. A. Hébert and P. Benoist, A consistent technique for the global homogenization of a pressurized water reactor assembly, Nuc. Sci. Eng., 109, 360:372 (1991)

    Google Scholar 

  86. A. Hébert and G. Mathonnière, Development of a third-generation Superhomogénéisation method for the homogenization of a pressurized water reactor assembly, Nuc. Sci. Eng., 115, 129:141 (1993)

    Google Scholar 

  87. K. Koebke, Advances in homogenization and dehomogenization, ANS/ENS Proc. Int Topic. Mtg. Advanc. Math. Meth. Solut. Nucl. Engin. Prob., Munich, Germany, April 27–29, 1981, Vol. 2, 59:73, Kernforschungszentrum Karlsruhe (1981)

    Google Scholar 

  88. E. Tanker and A. F. Henry, Finite difference group-diffusion theory parameters that reproduce reference results, Trans. Am. Nuc. Soc., 50, 280 (1985)

    Google Scholar 

  89. J. J. Lautard, S. Loubiere and C. Fedon-Magnaud, Three dimensional pin by pin core diffusion calculation, Proc. ANS/ENS Int. Top. Mtg. Advanc. Math. Comput. React. Phys., Pittsburgh, Pennsylvania, U.S.A., April 28–May 2, 1991, Vol. 2, 6.11-1:6.11-10, American Nuclear Society (1991)

    Google Scholar 

  90. J. Mondot, J. C. Gauthier, P. Chaucheprat, J. P. Chauvin, C. Garzenne, J. C. Lefebvre and A. Vallée, EPICURE: An experimental program devoted to the validation of the calculational schemes for plutonium recycling in PWRs, Proc. ENS Int. Conf. Phys. React. Operation, Design and Computation (PHYSOR’90), Marseilles, France, April 23–26, 1990, Vol. 1, VI-53:VI-64, European Nuclear Society (1990)

    Google Scholar 

  91. M. S. Milgram, Estimation of axial diffusion processes by analog Monte Carlo: theory, tests and examples, Ann. Nucl. Ener., to be published in summer or autumn 1996

    Google Scholar 

  92. G. Marleau and M. S. Milgram, A DRAGON-MCNP comparison of axial diffusion subcoefficients, Trans. Am. Nuc. Soc., 72, 163:164 (1995)

    Google Scholar 

  93. J. Briesmeister, Ed., MCNP — A general Monte Carlo code for neutron and photon transport, Version 4, Report LA-7396-M, Rev. 2, Los Alamos National Laboratory (1991)

    Google Scholar 

  94. I. Petrovic, J. Vujic and P. Benoist, Validation of the heterogeneous leakage models TIBERE and TIBERE-2 on BWR and HTGR lattices, being submitted to Nuc. Sci. Eng.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Kluwer Academic Publishers

About this chapter

Cite this chapter

Petrovic, I., Benoist, P. (2002). B N Theory: Advances and New Models for Neutron Leakage Calculation. In: Lewins, J., Becker, M. (eds) Advances in Nuclear Science and Technology. Advances in Nuclear Science & Technology, vol 24. Springer, Boston, MA. https://doi.org/10.1007/0-306-47811-0_6

Download citation

  • DOI: https://doi.org/10.1007/0-306-47811-0_6

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-45515-5

  • Online ISBN: 978-0-306-47811-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics