THE EFFECTS OF GRAVITATIONAL AND HYDROSTATIC PRESSURE ON THE EQUILIBRIUM SHAPE OF A CONDUCTING FLUID IN AN ELECTRIC FIELD : APPLICATION TO LIQUID METAL ION SOURCES

摘要

We have derived a partial differential equation that can be solved explicitly for the equilibrium shape of an electrostatically stressed fluid subject to gravitational and hydrostatic pressure effects. The model assumes only axial symmetry, the Laplace stress conditions for mechanical equilibrium and conservation of volume before onset of instability. To obtain the sequence of deformed surfaces as a function of applied voltage, we use the capillary wave model and an iterative procedure to solve Laplace's equation for arbitrary geometry. Initial numerical results demonstrate the importance of pressure in obtaining stable equilibrium configurations.