Electrohydrodynamic instabilities and the energy spread of ions drawn from liquid metals

This paper aims at shedding some light on the beam energy spread versus current curves of liquid metal ion sources (LMISs). Although Knauer's collisionless space-charge broadening model originally gave almost perfect agreement with experiment, deviations were discovered later at low and high currents. To make matters worse, as more metals were investigated, complete disagreement was found in certain cases. Although the low-current deviation from Knauer's model is not well understood and only tentative explanations can be given, the high-current deviation has been explained in terms of a self-sustaining instability that sets in at a critical current, the value of which varies greatly from metal to metal. This instability violates a basic premise of Knauer's model, namely that the ions' paths do not cross after their emission. Calculations show that, for metals for which there is total disagreement with Knauer's model, the instability sets in almost from the onset. An important result of this work is the development of a stability criterion for LMISs. It is shown that a low evaporation field and a high surface tension are two principal factors that improve stability. The stability is also affected, to a lesser extent, by the liquid density and charge-to-mass ratio of the ions.