Longitudinal Oscillations in a Nonuniform Plasma

Abstract

Longitudinal electron oscillations in a bounded plasma slab immersed in a magnetic field are analyzed using hydrodynamic equations. Resonance conditions are given for an arbitrary density distribution. In the zero magnetic field limit, the present results may account for some main features of Tonks' and Dattner's experiments. The behavior of these resonances and the possibility of damping due to thermal effects is discussed. It is found that the magnetic field tends to "push" the perturbations further into regions near the walls and keep the bulk of the plasma free from oscillations.