Limits on the single-pass higher harmonics FEL operation

The analysis of Dattoli et al. (1984) for the conditions under which good single-pass FEL higher harmonic performances are obtainable, through the exploitation of the Lawson-Penner limit and supermode theory, is generalized. It is noted that under suitable conditions, a low energy accelerating device may be used to obtain FEL operation in the visible and UV regions. A relationship is derived which implies that, with increasing energy and order of harmonic, the limits imposed by the requirements for matching the laser and e-beam cross sections become more and more severe.