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The pseudoglow and glow discharge behavior of a 0.5-mm metallic-dielectric electrode gap in helium under atmospheric pressure was examined as a function of ac voltage between 0.3 and 32 kHz. The number of discharge current pulses per half-cycle within the pseudoglow was found to diminish with rising frequency, as opposed to the increase observed with rising voltage. The reduction in the rise time and the quasi-monotonic decreases in amplitude of the successive discrete current pulses within the pseudoglow were attributed to the enhanced Penning ionization due to an increase in the number of energetic precursors (metastables and dimers) over the first quadrant in each half cycle. The interruption in the discharge pulse sequence, caused by a change in polarity of the ac field, greatly reduced the precursors' concentration and resulted in the first incipient pulse of the pseudoglow having the shortest rise time and width in the pulse sequence. The increase in frequency at constant voltage caused a gradual decrease in the number of discharge current pulses within the pseudoglow, until at ca. 10 kHz and beyond only a single pulse glow discharge took place. The influence of argon, nitrogen, hydrogen, and oxygen impurities was studied and interpreted in terms of Penning ionization and electron attachment.