Energy barrier for ion field emission from a dielectric liquid sphere

Ion field emission from the surface of a dielectric liquid is commonly modeled as a kinetic process with an energy barrier lowered by the strength of the electric field. Expressions for the energy barrier exist for simplified cases such as a planar surface and a conducting sphere. This article derives an analytical expression for the more general case of a dielectric sphere, which is the continuum model and geometry for most cases of interest. The energy barrier is computed using the method of image charges, and compared to existing expressions for simpler models. The energy barrier increases at decreasing dielectric constant and decreasing radius of curvature. Ion emission from typical systems (the ideal Taylor cone and charged nanodroplets) differs substantially when calculated with either our model or with existing simpler models.