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

Coherent electromagnetic radiation from a thin rotating annular ring of relativistic electrons with axial drift, and confined between concentric cylinders comprising a coaxial waveguide, is studied theoretically. The electrons are assumed to move in quasihelical orbits under the combined action of a uniform axial magnetic field and an azimuthally periodic wiggler magnetic field. The instability analysis is based on the linearized Vlasov-Maxwell equations for the perturbations about a self-consistent beam equilibrium. The dispersion equations for the transverse magnetic (TMl,m) modes are derived and analyzed. Coherent radiation occurs near frequencies ω corresponding to the crossing points of the electromagntic modes and the beam modes where ωcand Ω∥are the waveguide cutoff frequency and the electron cyclotron frequency, respectively, υparallelis the axial drift velocity of electrons, k∥is the wavenumber of the electromagnetic wave along the axis, and is the number of wiggler periods along the azimuth.