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The hollow cathode is known as a source of high-density plasmas. This property is due to the hollow-cathode effect (HCE), which can be explained by the oscillations of fast electrons between repelling potentials of opposing space-charge sheaths. At atmospheric pressure, one should be able to create an HCE by adjusting the dimension of the hollow cathode. Experiments show that the dimensions could be as large as 500, so that the sheath thickness may be on the order of 100. Theoretical models of the atmospheric-pressure sheaths based on the conventional Child-Langmuir approach give the sheath thicknesses on the order of 10, which contradicts the experiments. We introduce here a new model which takes into account three groups of electrons: slow, fast, and secondary. By adding a group of fast and secondary electrons, we show that the sheath thickness increases as compared with only slow electrons present.