WAVES AND INSTABILITIES IN A FINITE PLASMA

A dispersion relation is derived for electrostatic waves in a plasma confined between planes which perfectly reflect the particles but have no effect on the fields. A uniform magnetic field perpendicular to the planes is assumed. Both classical and quantum-mechanical derivations are given. In the quantum-mechanical derivation some terms appear which do not appear in the classical derivation. These terms are due to finite de Broglie wavelength of the particles. The classical dispersion relation is applied to the investigation of volume and surface plasma oscillations and volume and surface ion sound waves in an unmagnetized plasma and to volume waves in magnetized plasmas. Volume waves are characterized by a discrete set of parallel wavenumbers. The damping or growth of volume waves is nearly the same as that of a corresponding infinite plasma wave. The damping of surface waves is quite different.