Theory of cyclotron resonance in a cylindrical non-neutral plasma

Resonances near the cyclotron frequency of a cylindrical non-neutral plasma column with radial density and angular velocity profiles are studied. Cold plasma and warm plasma models are used to consider the various multipole modes (eimtheta) for kz=0. For m=1 only a single resonance, a center of mass mode, is found. Its frequency is downshifted from the cyclotron frequency by an amount equal to the frequency of the low-frequency diocotron mode. For each m greater than 1 the cold plasma model gives a continuous absorption band with spatially localized absorption at each frequency, corresponding to a continuum of singular modes. In the warm plasma model, the continuuo go over to sets of discrete radially trapped azimuthally propagating Bernstein modes. For both cases, the plasma rotation Doppler-shifts the azimuthally propagating modes up in frequency. The angular velocity profile, together with plasma temperature, determine the spacing of the Bernstein modes within a band.