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Resonance Absorption

Resonance Absorption. B. Rouben McMaster University Course EP 6D03 – Nuclear Reactor Analysis (Reactor Physics) 2009 Jan.-Apr. Contents. A look at the effect of resonance absorption during neutron slowing down . Reference: Duderstadt & Hamilton, Sections I.C.

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Resonance Absorption

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  1. Resonance Absorption B. Rouben McMaster University Course EP 6D03 – Nuclear Reactor Analysis (Reactor Physics) 2009 Jan.-Apr.

  2. Contents • A look at the effect of resonance absorption during neutron slowing down. • Reference: Duderstadt & Hamilton, Sections I.C

  3. The Form of the Slowing-Down Spectrum • The previous presentation showed that the slowing-down spectrum (E) is of the form

  4. E(E) From the general form of the slowing-down spectrum, we can deduce the following simplified statements on the product E(E): 1) If absorption is neglected, and with the assumption that the scattering cross section does not depend on energy,E(E) is constant (flat) with E. 2) Including absorption, and if the absorption cross section is smooth with E, then E(E) will decrease smoothly for decreasing E. These statements are shown in graphical form on the following slide.

  5. E(E) with Smooth Absorption

  6. Resonances • However, neutron absorption is not smooth in the fuel, on account of the myriad of resonances in the energy range between ~1 eV and ~100 keV. • In resonances, the absorption cross section increases by orders of magnitude over a very narrow energy range (or width). Resonances can be “resolved” (i.e., well separated) or “non-resolved” (i.e., they are so close that they seem superimposed). cont’d

  7. Resonances (cont.) • Within a resolved resonance, the cross section varies dramatically with energy, as per the single-level Breit-Wigner formula [Eq. (2.35) in Duderstadt & Hamilton]

  8. Resonances (cont.) • At the resonance energy, the neutron flux goes through a significant dip on account of the very high absorption cross section. • As a result of the dip in flux, the total absorption in the resonance is reduced relative to the “background” flux value, i.e., the product a is smaller than if the flux were unaffected. This is called “resonance self shielding”. • On account of resonances then, the slowing-down flux will be deformed relative to the smooth curve in the previous slide, as shown in the next figure.

  9. E(E) with Resonances

  10. Neutron Flux in Resonance Range • In summary, the neutron flux in the resonance energy range can be written in the form

  11. Temperature Dependence of Resonances • Resonances are Doppler broadened as temperature increases. • This comes about as the result of the greater random motion of nuclei at higher temperatures. Because of this greater random motion, there is a greater possibility for the neutron speed (relative to the nucleus) to correspond exactly to the energy of the resonance. • As a result, the resonance broadens (in terms of the neutron energy E), while its peak is reduced: in other words, absorptions in the resonance are “smeared” (redistributed) over a wider range of neutron energies. cont’d

  12. Temperature Dependence of Resonances (cont.) • The actual area under the resonance is not changed by the Doppler broadening. • However, since the resonance peak is reduced by the Doppler broadening, the flux dip within the resonance is reduced, and as a result, the self-shielding within the resonance is reduced, i.e., the number of interactions () within the resonance is increased. • If the resonance is a capture resonance, the number of captures is increased at higher temperatures. If it’s a fission resonance, fissions are increased. • In most reactors, capture resonances are more important than fission resonances, and consequently system reactivity is reduced at higher temperatures.

  13. Lumping of Fuel • It was discovered early in the history of reactor technology that criticality was easier to attain if the fuel were “lumped” (e.g., into channels) rather than homogeneously mixed with the moderator. • Can you think of reasons why reactivity is increased when lumping the fuel? Which factors are affected by the lumping, and in what direction?

  14. Summary • Resonance absorption is an important “player” in the reactivity balance within the neutron cycle. • While there are fission resonances, resonance capture dominates in most thermal reactors. • In the standard CANDU reactor, resonance capture amounts to about 90 milli-k of negative reactivity. • Doppler effects broaden resonances. • In most thermal reactors, Doppler broadening results in a negative reactivity component as the fuel temperature increases.

  15. END

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