A theory is developed for a free-electron laser with electromagnetic wiggler and ion-channel guiding. The electron trajectories due to a large amplitude backward propagating electromagnetic wiggler and an ion-channel electrostatic field are obtained and the stability of orbits is discussed. Then the gain equation describing the interaction between an electron and the radiation field is derived in the low-gain-per-pass limit. The results of a numerical study of electron orbits and gain are presented and discussed. It is shown that the maximum gain obtained in an electromagnetic wiggler is about twice the maximum gain obtained in a magnetostatic wiggler.
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