Cathode Protrusion Growth in High Electric Fields

We present a model for simulating the deformation of a protrusion under high electric fields. The model couples gas phase transport with thermal transport, electrostatic fields, and current density in the electrode. The electric fields are high enough to induce electron field emission via the Fowler-Nordheim model. The resulting current density in the electrode material causes Ohmic heating, and eventually melting. While in the liquid phase the protrusion tip deforms, thus modifying the local surface field enhancement factor. The local surface electric field enhancement factor, beta, evolves from an initial value (~13) to a lower one due to surface tension causing increased rounding to the tip shape. The shape evolves to one in which the field emission is low enough to cause a reduction in the Ohmic heating, which in turn allows the tip to resolidify.