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

Abstract

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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l,m</inf> ) modes are derived and analyzed. Coherent radiation occurs near frequencies ω corresponding to the crossing points of the electromagntic modes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega^{2} = c^{2}k\min{\parallel}\max{2} + \omega\min{c}\max{2}(l,m)</tex> and the beam modes <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\omega = \upsilon_{\parallel}k_{\parallel} + (l + N) \Omega_{\parallel}</tex> where ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</inf> and Ω <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∥</inf> are the waveguide cutoff frequency and the electron cyclotron frequency, respectively, υ <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">parallel</inf> is the axial drift velocity of electrons, k <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∥</inf> is the wavenumber of the electromagnetic wave along the axis, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> is the number of wiggler periods along the azimuth.