The free electron laser instability is investigated for a tenuous circulating electron beam propagating perpendicular to a uniform magnetic field B 0 , and transverse wiggler field modeled by B. sin ky, in planar geometry. Unlike the rippled-field magnetron which operates at Brillouin flow, the present analysis assumes a low-density electron beam with w. 4D '. Making use of a macroscopic cold-fluid model for the electrons coupled with Maxwell's equations for the fields, it is found that wave perturbations with ordinary-mode polarization (6 EIIBo and 6 BiBO) amplify with characteristic maximum growth rate Im(6w) = wp(D./2v2cko) and emission
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