Abstract
Orbital motions of magnetized and relativistic electron beams in free-electron lasers (FEL) with electromagnetic and magnetostatic wiggler are considered. The orbit and dispersion curves of an electromagnetic wiggler demonstrate the magnetoresonance when the transverse motion of electrons in the wiggler field is treated nonrelativistically. Magnetoresonance is also shown in the nonrelativistic case of the magnetostatic wiggler. It is shown that relativistic effects, due to the transverse motion of electron in the wiggler field, destroy the magnetoresonance in an electromagnetic wiggler and displace it in an electrostatic wiggler. Magnetoresonance in the growth rate of FEL in the nonrelativistic case and its destruction in the relativistic case are shown.
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