New Treatment of Eigenmode Analysis for an Inhomogeneous Vlasov Plasma

A new eigenmode analysis is presented for an inhomogeneous Vlasov plasma based on an integral equation in the wavenumber space. The effects of finite Larmor radius can be taken into account even for the case of \(k ρ ᵢ 1\) where k is a measure of the wavenumber in the direction of spatial inhomogeneity and ρ i is the ion Larmor radius. The eigenfrequency is determined from a compact “quantization condition” which is an extension of the Bohr-Sommerfeld “quantization condition” for second order differential equations.