Fluid sheath models supposing cold ions, i.e. neglecting ion thermal energy, usually do not take into account energetic spectrum caused by collisions of ions with neutrals. These collisions are involved only in the Newton equation of motion as an effective friction force describing the rate of the mean momentum lost due to collisions. We suggest an alternative description taking into account the whole ion energy spectrum, which is based on the statistical description of the last ion collision before reaching given position in the sheath. We show that for short ion mean free paths the ion beam is far from the monoenergetic state. Nevertheless, the Newtonian equation of motion adequately describes the average ion energy if the ion mean free path in the expression for the friction force is chosen as a double of the real ion mean free path of the ion charge exchange collisions.
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