The Liquid Metal Ion Source as an Electrically Driven Vena Contracta, and some Comments on LMIS Stability

Abstract
This paper discusses recent items of progress in understanding liquid-metal ion source (LMIS) behaviour, in the more general context of electrohydrodynamics. (1) Like the Taylor-Gilbert cone, the phenomenon of the vena contracta has been known for several hundred years. It is argued that the cusp-on-a-cone shape of an operating LMIS is a similar phenomenon, except that the forces acting are electrical rather than gravitational, and the pressure in the jet is negative rather than positive. (2) In discussing LMIS stability in engineering terms, mechanisms affecting the jet shape can be classified as giving negative feedback (stabilising), or positive feedback (destabilising). Effects associated with field evaporation andlor space charges give negative feedback, effects associated with pressure changes positive feedback. Attention is drawn to the arguments of Ganan-Calvo about the role of 'supercritical' flow as a stabilising factor against hydrodynamic disturbances. (3) Electrohydrodynamic spraying is superficially very similar to LMIS operation, and both sprayers and ion sources adopt a cusp-on-a-cone (or 'cone-jet') shape. But the accepted theoretical explanations of the driving mechanisms are different. Confirmation is offered that the LMIS story is the correct one for very highly conducting liquids, and that a difference in driving mechanism is plausible.