Anode streamer branching

An analytical investigation of the problem on stability of a locally flat ionization front corresponding to some region of the streamer surface is performed using complete electrodynamic relations on the streamer surface. Electrodynamic boundary conditions, which allow for the continuity of the total electric current (displacement current and conduction current) on the boundary, are derived. The solution of the problem on stability of the initial stationary state for the chosen region, which may be both the streamer head and its side surface, is constructed in a local coordinate system. A characteristic equation is obtained which, in addition to generalization of previously known results, includes new effects and makes it possible to find the limits of the region of streamer surface instability. The hypothesis is formulated that the observed instability of the streamer surface results in streamer branching, and the criterion of the emergence of branching is derived. This criterion makes it possible to explain some experimentally observed features of the branching process. It is shown that a short streamer is stable; however, when the critical size is reached, secondary formations may branch out from the streamer which correspond to the branching process.