NUMERICAL-CALCULATION OF AXISYMMETRICAL ELECTROSTATIC MODES FOR COLD FINITE-LENGTH NONNEUTRAL PLASMAS

A numerical calculation of mode frequencies for cold, non-neutral plasmas is reported. The numerical method can be applied to any axisymmetric plasma shape in a trap. Here, it is used to study axisymmetric electrostatic modes in a long conducting cylinder. These modes were previously studied by Prasad and O'Neil [Phys. Fluids 26, 665 (1983)] and by Dubin [Phys. Rev. Lett. 66, 2076 (1991)]. In contrast to Dubin's calculation, the effects of a nearby cylindrical wall, including its influence on the shape of the plasma equilibrium, are considered. It is found that for plasmas with aspect ratios (length divided by diameter) near unity the numerical results can be approximately obtained by judiciously combining Dubin's calculation, and the Trivelpiece-Gould dispersion relation for infinitely-long geometry. For aspect ratios larger than about three, the Trivelpiece-Gould dispersion relation can be used in a simple way to obtain the numerically-computed mode frequencies with an accuracy of 1%, or better. The potential use of this calculation as a plasma diagnostic is also discussed, and it is argued that at the present level of accuracy (1-2%) its usefulness is marginal, but that an improvement by an order of magnitude might make it more interesting. © 1995 American Institute of Physics.