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Building on recent experimental and numerical evidence of different glow modes in atmospheric plasmas, this paper reports a systematic study of these modes in radio-frequency (RF) glow discharges in atmospheric helium. Using a one-dimensional (1-D) hybrid computer model, we present detailed characterization of three glow modes, namely the α mode, the α-γ transitional mode, and the γ-mode in a 13.56-MHz atmospheric glow discharge over a wide range of root mean square (RMS) current density from 5 mA/cm2 to 110 mA/cm2. Our focus is on sheath dynamics through spatial and temporal profiles of charged densities, electric field, electron mean energy, sheath thickness, and sheath voltage, and when appropriate our results are compared against experimental data of atmospheric glow discharges and that of glow discharges at reduced gas pressure below 1 torr. Fundamental characteristics of the three glow modes are shown to be distinctively different, and these can be used as a hitherto unavailable route to tailor the operation of radio-frequency atmospheric glow discharges to their intended applications.