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The propagation of electron surface waves can be used to sustain long plasma columns. The relation between the axial distribution of the electron density observed along the plasma column and the corresponding power distribution of the surface wave that produces it is investigated. It is found that the electron density decreases almost linearly along the plasma column in the direction of the wave propagation. This is explained by assuming that the number of electrons produced over a given axial length is proportional to the wave power absorbed over that same length.