Stability of cylindrical rotating plasmas to axisymmetric electrostatic perturbations

Necessary and sufficient conditions for the exponential stability of an N-component, warm or cold, rotating cylindrical plasma to axisymmetric electrostatic perturbations are obtained. The plasma is immersed in an axial magnetic field B₀(r), where r is the radial co-ordinate, and the equilibrium quantities are permitted to be arbitrary functions of r consistent with the 0-order equations. The maximal growth rate of an unstable system is shown to be determined by a maximum principle.