Explain how a reactor's isotopic depletion affects core performance over its life cycle.

Isotopic depletion, also known as fuel burnup, refers to the changes in the isotopic composition of the nuclear fuel as the reactor operates. This has several significant effects on core performance over its life cycle. Initially, the fuel is primarily composed of Uranium-235 (the fissile isotope) and Uranium-238 (the fertile isotope). As the reactor operates, Uranium-235 is consumed through fission, decreasing its concentration. Simultaneously, Uranium-238 is converted into Plutonium-239, which is also a fissile isotope. Other isotopes, such as fission products, also accumulate in the fuel. The most immediate effect of isotopic depletion is a decrease in the core's reactivity. As the concentration of Uranium-235 decreases, the ability of the core to sustain a chain reaction declines. To compensate for this loss of reactivity, control rods are gradually withdrawn or the boron concentration in the coolant is reduced. The buildup of fission products also contributes to the decrease in reactivity, as many fission products are neutron absorbers. The power distribution within the core also changes as isotopic depletion progresses. The regions of the core with higher initial enrichment or lower burnup tend to produce more power than the regions with lower enrichment or higher burnup. This can lead to a non-uniform power distribution and reduced fuel utilization. Fuel management strategies, such as fuel shuffling, are used to mitigate this effect and maintain a more uniform power distribution. The isotopic composition of the spent fuel also changes over time. As the fuel burns up, the concentration of Plutonium-239 increases, and the concentration of higher actinides, such as Americium and Curium, also increases. These changes in the isotopic composition affect the radiotoxicity and heat generation of the spent fuel. The Moderator Temperature Coefficient (MTC) is also affected by isotopic depletion. Typically, the MTC becomes more negative as fuel burnup increases.