Discharge inception near dielectric bodies: The Meek criterion revisited

Summary form only given. We study the inception of positive streamer discharges from a sharp dielectric body in a sub-breakdown electric field on the basis of the Meek criterion. The criterion is widely used in the high voltage technology where discharges are to be avoided. We take into account the high non-uniformity of the electric field around the tip of a dielectric particle, which makes it important where an electron avalanche starts and which electric field lines it follows. We also study the influence of the spatial distribution of the initial electrons that start the avalanches. This initial spread of electrons is possible when, for example, the electrons are instantaneously injected around the tip of the dielectric. This finds its application when lightning inception is studied from ice particles in thunderclouds and the initial electrons are produced by highly energetic cosmic particles bombarding our atmosphere. We consider a wide class of dielectric particles of various shapes, sizes, as well as dielectric permittivities and select those that are favorable for discharge inception. We found that the frequency dependence of the dielectric permittivity can significantly slow down discharge development. We complement our phenomenological findings with full timedependent simulations of discharge development in cylindrical geometry.