Numerical investigation of the bridging and current flow of a positive DC streamer using a 1.5D model

Single streamers, at nanosecond-timescales, can be simulated using detailed computational models with a high-dimensional representation. These models are computationally impractical for parametric explorations and simulation of longer times, that can follow many-streamer pulsations and the influence of one streamer burst on the next. This work develops a 1.5D model of a positive DC streamer for simulations beyond the electrode-gap bridging phase, and uses it to parametrically explore the impact of different terms and operational parameters. The geometry of interest is that of a tip-to-plane electrode configuration under DC voltage, and the simulation is followed for the duration of one current pulse (order 500 ns). The numerical model uses an axisymmetric boundary element method to solve for the electric field, as well as a 'stack' of 3 different transient solvers to improve efficiency and allow solving over longer timescales. The model is able to resolve the development of the cathode sheath during the streamer bridging phase using a kinetic flux boundary condition. It also gives qualitative agreement to current waveforms using an equivalent experimental setup. The different phases of the current pulse (streamer propagation, bridging, and current-flow phase) are discussed in detail.