Generation of electromagnetic radiation from a rotating electron ring in a rippled magnetic field

Calculations show that modes resembling the free‐electron laser (FEL) instability are excited when electrons move in quasicircular orbits under the combined action of a uniform axial magnetic field and an azimuthally periodic wiggler magnetic field. In the model, a thin annular ring of rotating electrons is confined in a hollow cylindrical waveguide, or between concentric cylinders comprising a coaxial waveguide, and the dispersion equations for the transverse magnetic (TM l m ) modes are derived and analyzed. Coherent radiation occurs near frequencies ω corresponding to the crossing points of the electromagnetic modes ω=ω c (l,m) and the beam modes ω=(l+N)Ω∥, where ω c and Ω∥ are the waveguide cutoff frequency and the electron cyclotron frequency, respectively, and N is the number of wiggler periods.