The effect of an electric field on flute oscillations of a tenuous plasma

Oscillations are discussed for three typical distributions of plasma space-charge, corresponding to the following radial distributions of the plasma rotation velocity: monotonic without point of inflexion, monotonic with point of inflexion, and non-monotonic. It is shown that for distributions without point of inflexion, as in the theory of perfect-fluid flow, Rayleigh's theorem holds: such flows are stable. The instability which results when points of inflexion are present is considered, and is shown to be correlated with the diocotron instability familiar in plasma theory. It is found that the effects of the finite Larmor radius in plasma oscillations play the same role as viscosity does in the flow of an actual fluid. By considering these effects it has been possible to determine the limits of applicability of Rayleigh's theorem.