Influence of finite ion Larmor radius effects on the ion resonance instability in a nonneutral plasma column

Abstract

The influence of finite ion Larmor radius effects on the ion resonance instability in a nonneutral plasma column aligned parallel to a uniform axial magnetic field B0êz is investigated. The analysis is carried out within the framework of a hybrid Vlasov-fluid model in which the ions are described by the Vlasov equation and the electrons are described as a macroscopic, cold fluid. Electrostatic stability properties are calculated for the case in which the equilibrium electron and ion density profiles are rectangular and the ion distribution function is specified by f0i=const×δ (H⊥−ωiPϑ−T̂i) G (vz). The resulting eigenvalue equation for the perturbed electrostatic potential φ̂l(r) is solved exactly to give a closed algebraic dispersion relation for the complex eigenfrequency ω. This dispersion relation is solved numerically, and it is shown that the growth rate of the ion resonance instability exhibits a sensitive dependence on plasma parameters. For example, finite ion Larmor radius effects can have a strong stabilizing influence for azimuthal mode numbers l⩾2, particularly when the equilibrium self-electric field is sufficiently weak. For the fundamental mode (l=1), however, stability properties are identical to those calculated from a macroscopic two-fluid model, and the growth rate is unaffected by the value of the ion Larmor radius.