Streamers in air splitting into three branches

We investigate the branching of positive streamers in air and present the first systematic investigation of splitting into more than two branches. We study discharges in 100mbar artificial air that is exposed to voltage pulses of 10 kV applied to a needle electrode 160mm above a grounded plate. By imaging the discharge with two cameras from three angles, we establish that about every 200th branching event is a branching into three. Branching into three occurs more frequently for the relatively thicker streamers. In fact, we find that the surface of the total streamer cross-sections before and after a branching event is roughly the same. Copyright c © EPLA, 2013 Introduction. – When a high electric voltage is suddenly applied to ionisable matter like air, streamers occur as rapidly growing fingers of ionised matter that due to their shape and conductivity enhance the electric field at their heads. This allows them to penetrate into regions where the background field was below the breakdown value before they approached it. On their path, streamers are frequently seen to branch. The streamers form the primary path of a discharge that can later heat up and transform into a lightning leader [1,2] or a spark [3,4]. Streamers are also the main ingredient of huge sprite discharges in the thin air high above thunderstorms [5,6]. Streamers also have important applications in initiating gas chemistry in so-called corona reactors where the later heating phase is avoided by limiting the duration of the voltage pulse [7,8]. The streamer head consists of an ionisation wave that moves with velocities ranging from comparable to the local electron drift velocity to orders of magnitude faster. On these time scales, the energy is in the electrons and then in the excited and ionised atoms and molecules in the gas, while the background gas initially stays cold. This is the reason why this process is used for very energy efficient gas chemistry, with applications like, for example, gas and water cleaning [7,9–11], ozone generation [7], particle charging [7,12] or flow control [13,14]. An important factor for the gas treatment is which volume fraction of the gas is treated by the discharge, and this fraction clearly is determined by the branching behaviour. Another question concerns the similarity between streamers at normal pressure and sprite discharges at air pressures in the range from mbar to μbar at 40 to 90 km altitude in the atmosphere [6]. Recently Kanmae et al. [15] stated, citing a private communication with Ebert in 2010, that in contrast to sprite discharges, laboratory streamers typically split into two branches only. Indeed, many streamers form out of the primary inception cloud around a needle electrode [16], but a propagating streamer in the lab typically splits into only two branches. There are only occasional reports of splitting into three branches [17], but these events could be a misinterpretation of images that show only a two-dimensional projection of the actual three-dimensional branching event. Theory cannot follow the full branching dynamics either. The present stage of understanding is that the streamer can run into an unstable state that occurs when the streamer radius becomes much larger than the thickness of the space charge layer around the streamer head. This state is susceptible to a Laplacian instability ([18] and references therein). While this instability can develop into streamer branching in a fully deterministic manner, electron density fluctuations in the leading edge of the ionisation front accelerate the branching process. However, present simulations only can determine the time and conditions of branching, but not the evolution of the branching structure after the instability. Studies on the full electrical discharge trees are based on dielectric breakdown models [19–21]. In these studies,