Time Dependence of the Slowing-Down and Diffusion Processes

  • K. H. Beckurts
  • K. Wirtz

Abstract

In this chapter, we shall study the behavior of neutron fields with nonstationary sources. In doing so we shall round out our discussion of the diffusion and slowing-down processes and in particular prepare ourselves to understand those important methods of measurement that employ non-stationary sources (these methods will be discussed in Chapter 18). First we shall consider the time-dependent slowing-down process in the absence of diffusion, then the timedependent diffusion process in the absence of slowing down, and finally the spacetime distribution during moderation, though only in the age approximation. We shall almost always assume a very short pulse of neutrons as the source (S (t)~δ (t)). In practice, this is the most important case. Also, with suitable normalization the resulting (E, t) can be considered as the probability that a neutron produced at time zero has the energy E at time t. Thus the life history of an “ average “ neutron can be read directly from the solution Φ (E, t). If we integrate the time-dependent solution over all t, we must again find the result we obtained earlier for a stationary source. In Sec. 9.4, we shall consider, in addition, the case in which the neutron sources are periodic in time.

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References

General

  1. Amaldi, E.: Loc. cit. especially § 70 and § 124.Google Scholar
  2. Von Dardel, G. F.: The Interaction of Neutrons with Matter Studied with a Pulsed-Neutron Source, Trans. Roy. Inst. Technol. Stockholm 75, 1954.MATHGoogle Scholar
  3. Marshak, R. E.: The Slowing Down of Neutrons, Rev. Mod. Phys. 19, 185 (1947).MathSciNetADSCrossRefGoogle Scholar
  4. Weinberg, A. M., and L. C. Noderer: Theory of Neutron Chain Reactions, AECD-3471 (1951), especially p. 1–82: The Time-Dependent Diffusion Equation.Google Scholar

Special Time Dependence of the Slowing-Down Process in Hydrogen

  1. Dyad’kin, G., and E. P. Batalina: Atomnaya Energiya 10, 5 (1961).Google Scholar
  2. Ornstein, L. S., and G. E. Uhlenbeck: Physica 4, 478 (1937).ADSCrossRefGoogle Scholar

Time Dependence of the Slowing-Down Process in Media with A ǂ 1

  1. Kazarnovsky, M. V.: Thesis, Moscow 1955.Google Scholar
  2. Koppel, J. U.: Nucl. Sci. Eng. 8, 157 (1960).Google Scholar
  3. Eriksson, K.-E.: Arkiv Fysik 16, 1 (1959).MathSciNetMATHGoogle Scholar
  4. Svartholm, N.: Trans. Chalmers Univ. Technol., Gothenburg 164, 1955.Google Scholar
  5. Waller, I.: Geneva 1958 P/153 Vol. 16 p. 450.Google Scholar

Solutions of ∇2Φ+B2Φ=0

  1. Sjöstrand, N. G.: Nukleonik 1, 89 (1958);Google Scholar
  2. Sjöstrand, N. G.: Arkiv Fysik 13, 229 (1958).MATHGoogle Scholar

Neutron Waves

  1. Raievski, V., and J. Horowitz: Compt. Rend. 238, 1993 (1954)Google Scholar

Transport Theory and Pulsed Moderators

  1. Bowden, R. L.: TID-18884 (1963).Google Scholar
  2. Daitch, P. B., and D. B. Ebeoglu: Nucl. Sci. Eng. 17, 212 (1962).Google Scholar
  3. Kladnik, R.: Nukleonik 6, 147 (1964).Google Scholar
  4. Sjöstrand, N. G-.: Arkiv Fysik 15, 147 (1959).Google Scholar
  5. Wing, G. M.: An Introduction to Transport Theory; New York: John Wiley and Sons Inc., 1963.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1964

Authors and Affiliations

  • K. H. Beckurts
    • 1
  • K. Wirtz
    • 1
  1. 1.Kernforschungszentrum KarlsruheGermany

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