Incipient electric field determination for bush and streamer stage in dielectric liquid under energy balance condition

This paper introduces a new approach for streamer advance mechanism in dielectric liquid. The existing of bush-like streamer shape early and then a tree structure shape after that has been given an over view and definition by devising a breakdown index for dielectric liquid which reach a value of 25. The deviation of streamer velocity from low values of tens of meter per second, until several kilometer per second from bush-like shape, until complete breakdown has been discussed too. These different stages have been studied on an energy balance concepts. In this paper using energy balance analysis, different critical applied fields have been obtained. These values reach 2.18 MV/cm for one branch channel in bush-like streamer shape and 21.5 MV/cm, for tree streamer. After that, the initial streamer velocities concerning these stages have been introduced. From these analysis the dissociation of dielectric liquids starts when the streamer velocity reach the sound speed in air, 331 m/s. In addition, the dissociation field depends mainly on the physical values of the dielectric medium, such as density, and permittivity have been introduced. In this paper the dissociation starts at an electric field value of 21.5 MV/cm for nearly all dielectric liquids, This result is equal to tree streamer inception value, which can be considered as a new introduced finding. A new energy equation relating injected energy electric field, velocity and new deduced breakdown index in dielectric liquid has been devised. The streamer may stop or continue its advance until complete breakdown. According to many published data for streamer, there is no clear explanation for streamer stopping and continuing it advance. In this paper, the streamer must advance ahead of the bush zone in the gap toward the opposite electrode when the prospective electric field at 66% of the gap achieves a breakdown index of 25. This result can be considered as a new criterion for streamer growth until crossing the gap. These new equations and findings have been applied to several experimental works and achieve good results.