Ion Waves in Bounded Plasma

Abstract

The role of the charge sheath at the wall of a discharge in determining the appropriate boundary conditions for a low frequency wave in a low pressure discharge is discussed by means of a hydrodynamical model. It is found that Bohm's condition for the mean ion velocity holds even when oscillations are present. The electron dynamics is neglected and the dispersion relation shows the existence of a principal mode which propagates along the tube just as in an infinite medium; all other modes are damped. Analysis of the dynamics of the oscillating sheath shows that it behaves like a battery, transferring the electrostatic oscillation to the wall with no distortion and no impedance.