We have calculated the on-axis spectrum of spontaneous radiation emitted by an electron moving along a planar undulator that has a magnetic profile along the axis that approximates a square wave. (This could be obtained in practice by driving a ferromagnetic undulator into saturation by "excessive" current in the windings). We find considerable enhancement of the harmonic radiation spectrum. We compare the harmonic power emitted by an electron moving through an undulator having a sine-wave field profile with the radiation emitted from an undulator having a "square-wave" profile; the latter is approximated by the first three Fourier components of the undulator magnetic field profile along the axial direction. Examples are computed for 40MeV electrons taking K < 1, for spontaneous radiation emitted along the axis of the system. The emission at harmonics f > 1 is greatly enhanced for the approximate square-wave magnetic profile: the ratio of the power emitted at f=5 by the "square-wave" undulator to that of the sine-wave undulator is about 15 (whereas the corresponding ratio at f=1 is only 1.5). While this enhancement might be expected because of the appreciable n=1 and n=5 Fourier components of the undulator field, higher odd harmonics are enhanced even more (e.g., x1000 at f= 11). FEL gain at the harmonics should be enhanced by similar factors.
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