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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 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
The Form of the Slowing-Down Spectrum • The previous presentation showed that the slowing-down spectrum (E) is of the form
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.
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
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]
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.
Neutron Flux in Resonance Range • In summary, the neutron flux in the resonance energy range can be written in the form
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
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.
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?
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.