As the fuel temperature increases, the motion of the fertile atomic nuclei increases and the width of the absorption resonances increases (although the height decreases to keep the area constant). This occurs mainly below 20 keV. The thermal reactor resonance escape factor p is reduced and, in combination with the flux distribution, this results in a change in reaction rates giving a decrease in reactivity [Eq. (1.1)]. Thus, for a fuel temperature increase, the reactivity decreases — so that afuei is negative.

However the opposite happens for 239Pu because, on absorption, fission may occur in the plutonium and the reactivity increases. Here afuel may be positive. Thus the actual Doppler coefficient is determined by a competi­tion between the two effects and it depends on the isotopic concentrations of 239Pu and 238U and their relative proximities. The plutonium effect is generally small.

The usual calculated values are approximately 10-5 8k j к and are designed to be negative. The coefficient is the main safety parameter of a design as we shall see in later sections.

The Doppler coefficient (afuei or dkffidT) in current liquid-metal fast breeder reactor designs varies as Г-1, so the Doppler coefficient is very often quoted in terms of the value of T dkeS/dT, the Doppler constant.

1.4.1.1 Moderator Coefficient in a Thermal Reactor

In a thermal reactor, 238U is a l/v absorber in which the absorption cross section decreases as the inverse of the square root of the energy of the neutrons. However the absorption in 235U falls off faster than this and the absorption for 239Pu falls off more slowly than this as the energy increases (Fig. 1.12).

Thus, in a plutonium dominated system, the coefficient is usually positive but is very small in magnitude, whereas in a 235U dominated system the coefficient is negative, but any value can result from this competition process.

However, the temperature of the system also has other effects which cannot be neglected: as the temperature and the energy E increases, the diffusion length increases, giving more leakage in small cores; the relative absorption in the fuel (/ = Е{ие1/1!л) increases for fine structure changes and the control rod effectiveness increases. These changes give, respectively, negative, positive, and negative contributions to a system temperature coefficient.

Thus the final moderator coefficient is very much a matter of balance and can either be positive or negative. It depends critically on the config­uration and makeup of the design.