HIGH-FREQUENCY ELECTROSTATIC MODES IN NONNEUTRAL PLASMAS

A fluid description is employed to derive the dispersion relation for cyclotron modes in a cylindrical non-neutral plasma of radius R confined by a uniform magnetic field B = B0e2 inside a chamber with conducting walls of radius R0. In contrast to the theory of Gould and LaPointe [Phys. Rev. Lett. 67, 3685 (1991); Phys. Fluids B 4, 2038 (1992)] the model includes the diamagnetic drift but omits finite Larmor radius effects. The density and the temperature of the unperturbed state are taken to be n(r) = n0(l-r2/R2) and T(r) = T0(l-r 2/R2)γ-1, where γ is the adiabatic index, so that the r-dependent slow rotation frequency is ω r≈-[δ(l-r2l2R2) + ∈(l-r 2/R2)γ-2]Ω/2, where Ω = qB0/Mc is the ion gyrofrequency, δ = 4πn 0q2/MΩ2, and ∈ = 4γT 0/MΩ2R2. For the linearized fluid equations together with the Poisson equation the eigenvalue problem is solved in the limit δ≪1, ∈≪1. The eigenfrequencies for high-frequency electrostatic modes with wave vectors satisfying k·B = 0 (Bernstein modes) are found in the form ω = -Ω + Δω, where Δω/Ω contains terms proportional to δ and ∈. Solutions are obtained and compared with experiment and the theory of Gould and LaPointe. The present theory predicts that at a given T0 modes with m>1 propagate only when the density is less than a critical value that increases with m, and that Δω normalized by the diocotron frequency depends only on the ratio of the Debye length to the plasma radius and hence is independent of B and M. The predictions of the two theories differ in several other respects; future observations may serve to decide between them. © 1995 American Institute of Physics.