A theory of ion-channel guiding in a planar wiggler is presented. For the sake of generality, a uniform static axial magnetic field is included in addition to the ion electrostatic field and wiggler magnetic field. The pendulum equation that describes the interaction between an electron and the radiation field is derived. A formula for the gain is then derived in the low-gain-per-pass limit. The results of a numerical study of gain enhancement due to the ion channel are presented and discussed.

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