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 (TM
l,m
) modes are derived and analyzed. Coherent radiation occurs near frequencies ω corresponding to the crossing points of the electromagntic modes
\omega^{2} = c^{2}k\min{\parallel}\max{2} + \omega\min{c}\max{2}(l,m)
and the beam modes
\omega = \upsilon_{\parallel}k_{\parallel} + (l + N) \Omega_{\parallel}
where ω
c
and Ω
∥
are the waveguide cutoff frequency and the electron cyclotron frequency, respectively, υ
parallel
is the axial drift velocity of electrons, k
∥
is the wavenumber of the electromagnetic wave along the axis, and
N
is the number of wiggler periods along the azimuth.