The temperature coefficient depends on burn-up, temperature, cell geometry (lumping) and reactor geometry (leakage). The burn-up dependence is due to the build-up of 233U, Pu and fission products.

This depends upon the type of fuel cycle (U-Th or low enriched U) and upon the fuel-management scheme.

The insertion of control rods gives a more negative temperature coefficient because the absorption of a black absorber tends to remain constant with temperature while the fuel absorption decreases. Calculations made without rods are then conservative. The temperature coefficient has to be calculated as function of time in the case of batch loading. In case of continuous reloading there will be no time-dependence after the equilibrium composition is achieved, but the running-in period again requires a time-dependent investigation.

The worst possible temperature coefficient (calculated considering burn-up condition and Xe concentration) must be assumed for accident analysis.

The temperature coefficient is temperature-dependent. The Doppler coefficient decreases with increasing temperature. The moderator coefficient is often negative at room temperature and tends to become positive (or less negative) at operating temperature, depending on the reactor composition. If Pu and Xe have a strong influence, the temperature coefficient tends to become negative again at very high temperature. An example of the breakdown of the various components of the temperature coefficient is given in Table 11.1<2) for an HTR with Th fuel cycle. See also Fig. 11.1.<2)

As already mentioned the temperature coefficient can be strongly influenced by the fuel and reactor geometry. The fuel geometry and its cooling system influences not only the temperature coefficient, but also the delay with which the moderator temperature coefficient is responding to a transient. The part of the moderator which is intimately mixed with the fuel responds promptly, while the remaining moderator responds with various delays. If the moderator is separately cooled, this delay can be very large (a re-entrant cooling of the AGR type would keep the moderator at a practically constant temperature and eliminate a great part of the moderator temperature coefficient). Unfortunately these factors are usually fixed by other considerations. The fuel cycle optimization, temperature limitations and total power output largely determine the fuel and reactor geometry.

Any strong modification of the temperature coefficient will tend again to shift the reactor away from the economically optimum case. Such modifications are not usually necessary because if the moderator temperature coefficient is positive, the overall coefficient remains usually negative in HTRs. Furthermore, even a positive overall temperature coefficient would not exclude the possibility of a safe reactor operation because of the great time delay associated with the positive moderator coefficient (the prompt coefficient is always strongly negative).

If a more stabilizing temperature coefficient is anyhow required, beside geometrical changes, composition changes are possible. The moderator temperature coefficient can be modified in given temperature intervals introducing absorbing isotopes whose absorption cross-section increases with energy.

The positive contribution of low-lying fission resonances can be counteracted by the addition of isotopes having absorption resonances in about the same energy range (e. g. 103Rh to compensate 233U resonances and Er to compensate 239Pu resonance).

Those absorbers are, of course, adversely affecting the neutron economy. In a more economical way modifications of the temperature coefficient can sometimes be obtained changing the neutron spectrum with a modification of the fuel to moderator ratio or changing the Doppler effect with a modification of the fertile loading. This would practically mean a reactor optimization with a constraint on the value of the temperature coefficient.

References

1. P. U. Fischer and N. F. Wikner, An interim report on the temperature coefficient of the 40 Mw(e) HTGR, GA-2307; 1961.

2. R. C. Dahlberg, Physics of gas cooled reactors, ANS CONF-720901.