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REACTIVITY COEFFICIENTS
DOE-HDBK-1019/2-93 Reactor Theory (Nuclear Parameters)
Moderator Temperature Coefficient
The change in reactivity per degree change in temperature is called the temperature coefficient
of reactivity. Because different materials in the reactor have different reactivity changes with
temperature and the various materials are at different temperatures during reactor operation,
several different temperature coefficients are used. Usually, the two dominant temperature
coefficients are the moderator temperature coefficient and the fuel temperature coefficient.
The change in reactivity per degree change in moderator temperature is called the moderator
temperature coefficient of reactivity. The magnitude and sign (+ or -) of the moderator
temperature coefficient is primarily a function of the moderator-to-fuel ratio. If a reactor is
under moderated, it will have a negative moderator temperature coefficient. If a reactor is over
moderated, it will have a positive moderator temperature coefficient. A negative moderator
temperature coefficient is desirable because of its self-regulating effect. For example, an
increase in reactivity causes the reactor to produce more power. This raises the temperature of
the core and adds negative reactivity, which slows down, or turns, the power rise.
Fuel Temperature Coefficient
Another temperature coefficient of reactivity, the fuel temperature coefficient, has a greater effect
than the moderator temperature coefficient for some reactors. The fuel temperature coefficient
is the change in reactivity per degree change in fuel temperature. This coefficient is also called
the "prompt" temperature coefficient because an increase in reactor power causes an immediate
change in fuel temperature. A negative fuel temperature coefficient is generally considered to
be even more important than a negative moderator temperature coefficient because fuel
temperature immediately increases following an increase in reactor power. The time for heat to
be transferred to the moderator is measured in seconds. In the event of a large positive reactivity
insertion, the moderator temperature cannot turn the power rise for several seconds, whereas the
fuel temperature coefficient starts adding negative reactivity immediately.
Another name applied to the fuel temperature coefficient of reactivity is the fuel doppler
reactivity coefficient. This name is applied because in typical low enrichment, light water-
moderated, thermal reactors the fuel temperature coefficient of reactivity is negative and is the
result of the doppler effect, also called doppler broadening. The phenomenon of the doppler
effect is caused by an apparent broadening of the resonances due to thermal motion of nuclei as
illustrated in Figure 3. Stationary nuclei absorb only neutrons of energy Eo. If the nucleus is
moving away from the neutron, the velocity (and energy) of the neutron must be greater than Eo
to undergo resonance absorption. Likewise, if the nucleus is moving toward the neutron, the
neutron needs less energy than Eo to be absorbed. Raising the temperature causes the nuclei to
vibrate more rapidly within their lattice structures, effectively broadening the energy range of
neutrons that may be resonantly absorbed in the fuel. Two nuclides present in large amounts in
the fuel of some reactors with large resonant peaks that dominate the doppler effect are
uranium-238 and plutonium-240.
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