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We construct an analytical model for the description of emission of undulator radiation (UR) harmonics with account for several sources of line broadening, including the efiect of a constant magnetic constituent. We compare it with that of the beam energy spread, emittance and focusing components. The analytical expressions obtained for the UR intensity and spectrum allow for profound analysis of homogeneous and inhomogeneous losses in their explicit form. We analyse the contributions to the fundamental frequency as well as to higher harmonics in long undulators. We study a possibility to compensate for the ofi-axis efiects in undulators by a properly imposed constant magnetic fleld and obtain an expression for the intensity of such compensating efiect. The results obtained are discussed in the context of their possible applications to free electron lasers (FEL). Recommendations for improvement of an UR harmonic line quality, profltable for FEL, are also proposed.

INHOMOGENEOUS AND HOMOGENEOUS LOSSES AND MAGNETIC FIELD EFFECT IN PLANAR UNDULATOR RADIATION