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In a previously published model of the atmospheric pressure radio frequency hollow cathode space-charge sheath, we showed that the inclusion of secondary and fast electrons, in addition to slow, thermalised electrons, give a wider space-charge sheath than with just slow electrons. In this work we extend this model by including collisions between ions and neutrals. This is done by considering the motion of the ions to be mobility limited. To account for the slow and the fast electrons observed in hollow cathodes, we specify an energy distribution function and from this determine the electron density in the sheath. In addition, we include secondary electrons created at the electrode surface. We look at the time evolution of the potential and the ion and electron densities in the sheath. This shows that while the ion density reaches a steady state, the electron density exhibits time dependent characteristics which are different from low frequency sheaths. We also compare the time dependent sheath structure for atmospheric and low gas pressures. |