Stability of parallel flow of a multi-component cylindrical plasma to electrostatic perturbations

Sufficient conditions for the stability of parallel flow of a warm N-component cylindrical plasma to electrostatic perturbations are obtained. In the unperturbed state the jth plasma component is assumed to have axial velocity V_j0(r), r being the radial co-ordinate, and the equilibrium quantities are permitted to be arbitrary functions of r consistent with the zeroth-order equations. The L₂-norms of certain system variables are shown to be bounded uniformly in time. Circle theorems are obtained for the complex eigenfrequencies of any normal mode.