The Generation IV gas-cooled fast reactor (GCFR) is intended to have a closed fuel cycle: During irradiation enough fissile material is produced to allow refueling of the same reactor, adding only fertile material. This is the well-known "zero breeding gain" objective. In this paper a theoretical framework is derived to track compositional changes of the fuel during irradiation, cooldown, and reprocessing, in order to calculate the reactivity of the new fuel compared to the original fuel material. Using first-order perturbation theory, the effect of variations of the initial fuel composition on the reprocessed material and breeding gain can be calculated. The theory is applied to the fuel cycle of a 600 MW(thermal) GCFR. The result is that the change of material composition during cooldown has a nonnegligible effect on the breeding gain. A truly closed fuel cycle can be obtained if the reprocessing efficiency is high enough (<1% loss). If this high efficiency cannot be obtained, adding a small amount of minor actinides (Np, Am, Cm) to the new fuel results in a zero breeding gain. Perturbation theory provides a powerful tool to estimate the effects of changing fuel cycle parameters.
