What condition must be met for a reactor to continue operating after extra reactivity is added to overcome Xe poisoning?

For a reactor to continue operating effectively after introducing extra reactivity to counteract xenon poisoning, it is essential that the xenon population does not increase. Xenon-135 is a significant neutron absorber, and its presence can lead to a situation where it inhibits the reactor's ability to sustain fission reactions, particularly in the short term after a power change or manipulation of reactivity.

If the xenon population is increasing, it indicates that the xenon is accumulating in the reactor, which would further suppress neutron availability and thus hinder criticality. Therefore, maintaining a stable or decreasing xenon population is crucial for the reactor's continued operation. This ensures that despite the additional reactivity introduced, the fission process remains viable and efficient.

In summary, preventing an increase in the xenon population allows the reactor to manage its reactivity more effectively and ensures that the added reactivity is sufficient to maintain a stable operating condition.