New understandings in the theory of liquid-metal ion sources

This paper summarises some recent improvements in our theoretical understanding of liquid-metal ion sources. (a) Some years ago it was shown how the standard formula for pressure difference across a charged conducting liquid surface could be derived directly from the laws of thermodynamics. This is now proved equivalent to the minimisation of an unfamiliar form of generalised free energy. (b) A simpler derivation of Mairʹs formula for LMIS current / voltage characteristics can be obtained by applying Newtonʹs Second Law to the motion of the liquid cone as a whole. (c) Results of modelling the effect of viscous drag on LMIS current / voltage characteristics, by incorporating a negative base-pressure into the Forbes-Ljepojevic LMIS modelling program, are reported: trends obtained are in qualitative agreement with experiment. (d) Initial results are reported from research that aims to develop a full time-dependent treatment of LMIS electrohydrodynamics. It seems that, under the combined influence of gravitational and electrostatic forces, the surface of a conducting liquid can develop into a highly disorganised state.