It is shown that an elementary semi-quantitative approach explains essential\r\nfeatures of the X-ray free-electron laser mechanism, in particular those of the\r\ngain and saturation lengths. Using mathematical methods and derivations\r\nsimpler than complete theories, this treatment reveals the basic physics that\r\ndominates the mechanism and makes it difficult to realise free-electron lasers for\r\nshort wavelengths. This approach can be specifically useful for teachers at\r\ndifferent levels and for colleagues interested in presenting X-ray free-electron\r\nlasers to non-specialized audiences
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