Numerical Simulations and Conformal Analysis of Growing and Branching Negative Discharge Streamers

Abstract—The dynamics of an anode-directed streamer can be described by advection-diffusion equations for the charged parti-cles, including a local field-dependent impact ionization term, and coupled to the Poisson equation for the electric field. We present the results of new simulations that use a local uniform grid refinement strategy. Even on very fine grids, provided the electric field is high enough, the streamer appears to branch spontaneously. These re-sults are supported by new analytical solutions based on a moving boundary approximation. Index Terms—Local grid refinement, minimal streamer model, moving boundary approximation, negative streamers. D ISCHARGE streamers can emerge when a strong poten-tial is applied to a sufficiently large sample of noncon-ducting matter like a gas. They consist of channels of nonequi-librium plasma that is generated at the channel tip. The rapid propagation of the tip is characterized by local self-induced en-hancement of the electric field. For anode directed streamers, essential properties of the process can be analyzed within a minimal model which con-tains only two charged species (electrons and positive ions), an impact ionization reaction, and the Poisson equation of electrostatics. The model can be applied to nonattaching gases like nitrogen or argon. In dimensionless units, it is [1