Secondary emission effects on streamer branching in transient non-uniform short-gap discharges

A new approach is presented for calculation of photoionization rates, in fully three-dimensional grids, that improves the accuracy of the secondary processes calculation without significantly compromising the efficiency of the numerical algorithm. The method is based on generating a coarser secondary grid and interpolating the photoionization values between the two meshes, in order to overcome the enormous effort required for calculation of photoionization in gas discharge problems. A comprehensive study of the effects of photoionization, photoemission and background ionization in a short point-plane gap in air at atmospheric pressure is then presented, by using the above approach for the secondary processes in two dimensions, in conjunction with the two-dimensional axisymmetric finite-element flux-corrected transport algorithm. The secondary processes are modelled individually within a wide range of parametric values to reflect the uncertainty in the experimental data, and their effect on streamer development and propagation is investigated. The significant reduction in time required for the calculations makes numerical modelling an essential tool for better understanding of the very important yet not well understood physical processes central to the propagation and development of streamers. Finally, numerical branching is observed under certain conditions in the absence of an adequate supply of electrons in high field regions.