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This work explores a possible mechanism for the onset of a poorly-understood, low-frequency plasma wave that arises in the plume region of thermionic hollow cathodes used for electric propulsion systems. This phenomenon is often referred to as the plume mode instability. Previous experimental measurements and descriptions of the wave are first reviewed. These results are often interpreted as an ionization wave, although there no direct evidence. Simulations that resolve the oscillation suggest that nonclassical electron heating via ion acoustic waves is critically linked to this behavior. Initial experiments, presented herein, show that the plume mode instability is a spatially localized phenomenon where large oscillations in ion acoustic wave amplitude are able to drive fluctuations in plasma resistivity and electron temperature. The phase relationship between temperature and density is shown to be consistent with a changing ionization rate, ultimately making the experimental connection to an ionization driven mode. Synthesizing this evidence, a physically plausible mechanism for the onset and growth of the instability is devised. It is proposed that predator-prey behavior between the electrons and neutral atoms, a process that is mediated by ionization, could be destabilized by the temperature fluctuations caused by the ion acoustic waves. A 0-dimensional, analytical model for a predator-prey instability is derived. This system of equations is analyzed under three different scenarios for the dominant form of electron collisionality: Coulomb collisions, large and constant collisions, and saturated wave-driven collisions. The result of the Coulomb collision analysis shows that the wave is ultimately damped by plasma diffusion and the neutral influx from the cathode. The other two conditions provide a stability criterion. If enhanced ionization due to temperature fluctuations exceeds the losses to diffusion and the influx of neutral atoms, then the wave begins to grow. The onset criterion is manipulated to show that it can be interpreted as a critical electron temperature that varies weakly on the neutral density. This is shown to be equivalent to a critical discharge voltage. The theory is then evaluated using experimental data over a broad range of discharge currents and mass flow rates. The theoretical growth rate and oscillation frequency are found to be positively correlated to the measured wave amplitude and frequency, respectively. This result corroborates our theory that the plume mode wave is likely a predator-prey ionization instability that is driven unstable by temperature fluctuations made possible by the presence of enhanced Ohmic heating of electrons due to the ion acoustic turbulence. Lastly, the presence of waves is examined experimentally under an applied magnetic field -- an environment that is more representative of a cathode used in a Hall effect thruster. It is shown that the plume mode instability is ultimately damped with increasing magnetic field and that rotating anti-drift waves can form in the same frequency band. The keeper oscillations typically associated with the plume mode wave are likely the result of anti-drift waves when operating in a Hall effect thruster.