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The effects of the frequency on the electrical characteristics in a dielectric barrier discharge in pure helium excited by repetitive voltage pulses with the frequency f from 5 to 500 kHz are systematically investigated by means of a 1-D fluid model under different operating conditions, including gap width dg, secondary electron emission coefficient γ, dielectric thickness ds, and dielectric constant εr. The important characteristic quantities of describing the pulse discharge, i.e., discharge current density Jg, averaged electron density Nave, averaged dissipated power density Pave, and the axial distributions of both electron density Ne and electron temperature Te, are calculated and analyzed in detail. This paper gives the following significant results. Nave increases with increasing f and Pave is almost proportional to f. Especially, there is a characteristic frequency of ~ 50 kHz, namely, when f is lower than ~ 50 kHz, Jm1 (peak value of Jg in the first discharge) decreases evidently with increasing f, and then changes very slightly for fs larger than ~ 50 kHz. In addition, with the increase of f , Jm2 (peak value of Jg in the second discharge) increases very slightly for small ds and the reverse is true for large ds . The frequency dependence of Jm2 for different εrsis similar to that by changing ds. For a fixed frequency, the change of Jm1 with γ is very small, which differs from that at low frequencies. In addition, Jm1 and Jm2 decrease with increasing ds and increase with increasing εr, but there are almost constant ΔJm1 and ΔJm2 for high frequencies. When the frequency is larger than ~ 50 kHz, there will be the second pe- k of Ne outside the cathode sheath in the first discharge, and both large ds and small εr can result in the formation of the evident peak of Ne nearby the momentary anode. It should be noted that the analysis in this paper pertains only to the incompressible motion of the plasma.