Spectrum of Electrostatic Modes in a Cylindrical Non-neutral Plasma of Arbitrary Density

The eigenvalue problem governing small amplitude electrostatic modes in a cylindrical column of non-neutral plasma is solved using a finite difference method. The eigenvalue problem is considered as a system of differential equations. A finite difference approximation using a staggered grid converts this system to a generalized matrix eigenvalue problem which is solved using readily available library subroutines. Important features of the spectrum, such as degenerate eigenvalues, sequences of eigenvalues, continua, and unstable modes, are well represented by the method.