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Rubidium vapor-cell atomic clocks are the “workhorse” of precise timekeeping for many GNSS missions. As is well known, the alkali rf-discharge lamp in these clocks is not only responsible for producing the atomic clock signal; it also has a significant influence on the clock's output frequency via the light-shift effect. Here, we discuss our discovery of self-pulsing in alkali rf-discharge lamps, which has the potential to periodically vary a Rb clock's signal-to-noise ratio and (via the light-shift effect) the clock's frequency. This self-pulsing is low frequency, on the order of one hertz in our experiments, and is not related to the self-pulsing reported a number of years ago by Robert Shaw, which was near 10 kHz and due to ion-acoustic wave generation in the discharge.