Unstable Cyclotron Oscillations in a Cylindrical Plasma Shell

Abstract

Longitudinal oscillations of a finite, cylindrical shell of plasma in a uniform axial magnetic field have been investigated. The ions are assumed to move initially in concentric Larmor orbits while the electrons are stationary. By neglecting random velocities, it is possible to obtain a dispersion relation for longitudinal (electrostatic) waves which is solved in the limit of short wavelength perturbations. The real parts of the frequencies of the disturbances are found to be integral multiples of the ion cyclotron frequency. Conditions for instability similar to those of the infinite plasma are also found which depend upon the thickness of the shell.