A HYDRODYNAMICAL STUDY OF THE INSTABILITY OF A PLANAR LIQUID METAL ION SOURCE (SUMMARY)

Abstract

Liquid metal ion sources (LMIS) are of interest in diverse areas of technology since they provide a high brightness, quasi-point source of ions for high resolution ion beam lithography, microfabrication, surface analysis and other potential applications[l]. The technical difficulties of building and operating stable sources have been largely overcome. The basic physics of source operation and ion formation is, however, still incompletely understood. Krohn and Ringo first described the fundamental processes of ion emission from liquid metal tips in a strong electric field[2]. Subsequently, Gomer[3] and others[4-81 analyzed the mechanism of LMIS and developed theoretical models to explain the shape and size of the ion emitting region. The electrohydrodynamical effect, that is, the onset of instability and breakdown, which appears for a critical voltage applied on the tips was first studied by Zeleny[9] and Taylor[lO]. Recently, Chung et. a1.[7] made an analytical and numerical study of the equilibrium shape and stability of an electrically stressed fluid with an axially symmetric arbitrary shaped surface in the quasi-electrohydrostatic limit. They did a stability analysis required for physically acceptable shapes using a general mechanical criterion applied earlier by Zeleny[9] in his analysis of the stability of charged droplets. Chung, et. a1.[7,8] used their results to argue that Taylor had not utilized any proper stability criterion. Furthermore, it was demonstrated by them that, in fact, Taylor used only an equilibrium condition for the establishment of a infinite cone in the hydrostatic limit. Explicity, Chung, et. al. have shown that it is not possible to physically form a liquid (i.e., deformable) structure with a Taylor or any other conical configuration by the application of an increasing electric field under quasi-hydrostatic conditions. When a proper stability analysis is made, it is found that the Taylor cone is not a stable equilibrium shape in either the hydrostatic or hydrodynamic limit[8]. This has been confirmed by Zheng and Linsu from a numerical solution of the Navier-Stokes equation[ll], and also discussed by Gabovich[4]. Miskovsky et. al.[12] subsequently developed an electrohydrodynamic capillary wave theory for ion and droplet emission in electrically stressed conducting viscous fluids based on a mathematical fromalism introduced by Melcher, et. a1.[13,14] and Grossmann et. a1.[15]. As the simplest analytical application of this theory we have chosen a model consisting of a planar fluid surface supported on a rigid electrode a distance 'a' below the unperturbed surface. A parallel planar counterelectrode is at a distance 'b' from the unperturbed surface. The same model was recently used by Pregenzer[l6], to study high power liquid metal ion diodes for inertial confinement fusion experiments at Sandia National Laboratories. She included graviational effects, but neglected the viscosity of the fluid. In our study, we apply the electrohydrodynamic capillary wave theory to a planar model of a LMIS, which also includes viscosity. Instead of the Bernoulli equation, as used by Pregenzer, we have solved the Navier-Stokes equation subject to a time-dependment Laplace-Young stress boundary condition, which now includes the frictional tensor. The effects of surface tension, viscosity and gravity on the critical electric field were analyzed. Although it was found that the surface tension dominates both gravity and viscosity in determining the critical electric field for breakdown, viscous effects are important, and significantly so for the higher mass liquid metals.