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The theory describing the effect of ion oscillations on the spectrum of outgoing microwave radiation in plasma-assisted slow-wave oscillators (pasotrons) is developed. It is shown that the most important are the variations of ion density in the potential well formed by electron beam in the space between the plasma gun and an aperture installed at the entrance to the interaction space. These fluctuations cause temporal variations in the Budker parameter that is responsible for the ion focusing of the beam. After the focal plane, the beam electrons radially diverge and are intercepted by the wall of a slow-wave structure. In the presence of oscillations in ion density, the beam interception also becomes time dependent, which affects the spectrum of microwave radiation. The results obtained allow one to interpret experimental data and can also be used for minimizing the ion sidebands in the spectrum of pasotron radiation.