Bernstein modes in a non-neutral plasma column

This paper presents theory and numerical calculations of electrostatic Bernstein modes in an inhomogeneous cylindrical plasma column. These modes rely on finite Larmor radius effects to propagate radially across the column until they are reflected when their frequency matches the upper hybrid frequency. This reflection sets up an internal normal mode on the column and also mode-couples to the electrostatic surface cyclotron wave (which allows the normal mode to be excited and observed using external electrodes). Numerical results predicting the mode spectra, using a novel linear Vlasov code on a cylindrical grid, are presented and compared to an analytical Wentzel Kramers Brillouin (WKB) theory. A previous version of the theory [D. H. E. Dubin, Phys. Plasmas 20(4), 042120 (2013)] expanded the plasma response in powers of 1/B, approximating the local upper hybrid frequency, and consequently, its frequency predictions are spuriously shifted with respect to the numerical results presented here. A new version...