J. Plasma Physic* (1983), vol. 30, part 1, pp. 133-151 133 Printed in Great Britain Plasma boundary motion and the ion-acoustic wave By N. St. J. BRAITHWAITE AND L. M. WICKENSf Department of Engineering Science, Parks Road, Oxford Ion-acoustic waves can be launched into plasmas by applying an oscillating voltage wave form to an electrode. The precise mechanism by which these waves are launched from such an electrode is not fully understood. The work described here examines the modelling of sheath edge motion in connexion with acoustic wave launching in both planar and spherical geometries. A novel demonstration of the applicability of the kinetic Bohm criterion is given by using the method of characteristics. A characteristics analysis is also used to show that an expanding, but decelerating, non-planar sheath can give rise to quasi-neutral compression- like features in a plasma. It is also shown that in planar geometry neither this kind of expansion, nor an oscillatory sheath motion, generates compression-like features. 1. Introduction By applying a voltage wave form to an electrode immersed in a plasma, the space-charge sheath adjacent to the electrode can be caused to expand or contract. Information regarding the changes in the sheath is propagated through- out the plasma and it is mainly the disturbance in the plasma which is studied here. The space-charge sheath is bounded on one side by the electrode surface and on the other by a notional sheath-plasma boundary (hereafter termed the sheath edge) beyond which electronic and ionic particle number densities are so nearly equal that a quasi-neutral plasma model can be employed. It is well established that motion of the sheath edge in response to voltage wave forms can give rise to rarefactive disturbances travelling at the ion-acoustic speed in the quasi-neutral plasma (Allen & Andrews 1970; Prewett & Allen 1973; Wickens 1980; Coates 1982). In addition, ion-acoustic waves (quasi-neutral rarefactions and com- pressions of ion number density) have been launched from electrostatic probes, presumably by causing sheath edge oscillations (e.g. Misra & Schott 1973; Chen & Schott 1977; Coates 1982), although there has been no clear description of the mechanism by which the acoustic waves are launched. For example, if a voltage wave form is applied to an electrode biased into ion saturation, positive ions move towards the electrode and not away from it. This motion of ions towards the electrode has been shown, under planar geometry and zero ionization condi- tions, to give rise to only rarefactive disturbances for both collapsing and expanding sheaths (Allen & Andrews 1970; Wickens 1980). The mechanism by which the compressive component of ion-acoustic waves can be generated is less clear. t Present address: Theoretical Physics Division, UKAEA Harwell, Didcot, Oxon.