Stability of liquid metal in alternating electric field

The stability of liquid metal layer in an electric field is considered, when the field has a temporal periodic component. This case is an extension of the known Tonks-Frenkel theory of conductive liquid instability in a DC electric field. A periodic field of moderate intensity makes the initiation of instability of surface perturbations easier than the application of a DC field alone. A linear theory of surface perturbation growth in a periodic electric field is developed and applied for the analysis of situations typical for droplet formation in high voltage devices. Two examples of the instability are assessed: behavior of a liquid metal ion source in an oscillating electric field and the motion of the electrode melt in a vacuum arc under fluctuating arc voltage