UC San Diego

This Dissertation consists of solutions to two major problems. Chapter 2 presents theory and numerical calculations of electrostatic Bernstein modes in an inhomogeneous cylindrical plasma column. These modes rely on finite Larmor radius (FLR) 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 analytic WKB theory. A previous version of the theory[6] 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 of the WKB theory avoids this approximation using the exact cold fluid plasma response and does a better job of reproducing the numerical frequency spectrum. The effect of multiple ion species on the mode spectrum is also considered, to make contact with experiments that observe cyclotron modes in a multi-species pure ion plasma.[1]

Chapter 3 presents theory and numerical calculation for the finite-length diocotron mode frequency with arbitrary azimuthal mode number. The numerical calculation solves a bounce-averaged version of the Vlasov equation to determine the perturbed potential in the presence of the mode, along with its frequency. The analytic theory is also obtained from the bounce averaged Vlasov equation, but we derive a theorem that allows us to obtain an effective fluid theory consistent with the full Vlasov theory, which integrates out the surface phase space associated with the bouncing motion, considerably simplifying the analysis. We use this effective fluid theory to derive frequency shifts for finite-length cylindrical plasmas, and find good agreement with experiment and with our numerical bounce-averaged Vlasov theory.