Modelling Streamers as Quasi-Steady Structures Characterized by Macroscopic Parameters

Abstract:

Many atmospheric discharges occur as, or are initiated by, streamer corona structures. In recent years, the state-of-the-art in modelling individual streamers has progressed significantly, with many groups independently producing high-fidelity models that show good agreement amongst themselves and with experimental data. Despite this advanced understanding of individual streamers, the larger scale streamer corona remains difficult to model due to the many orders of magnitude variation in length and time scales that must be resolved and the effects of large numbers of streamers mutually interacting. Consequently, the limited attempts at modelling the full corona must rely on simplified representations of individual streamers.

In this work, the authors develop such simplified models of individual streamers, with a focus on a reduced order physics model of streamers that accurately captures the important macroscopic behavior needed for a streamer corona model. This model starts by considering a 1.5D description of streamers, where the particle fluid equations are solved in one dimension along the streamer axis and the electric field is treated 2D axisymmetrically. This base model is then translated into the reference frame of the streamer, resulting in a model of a streamer that propagates as a self-similar ionization front that is quasi-steady, meaning that its macroscopic parameters (velocity, tip electric field, radius and internal field) evolve on time scales much longer than the time scale of electron dynamics. The macroscopic parameters of these quasi-steady streamers are then used as a basis for a system to uniquely characterize streamers. For example, should the radius and internal field of a streamer be known, it is possible to use the characterization to immediately determine the velocity and electric field at the tip and, using the 1.5D quasi-steady model, determine a reasonable estimate for parameters such as channel current and charge density that would be needed for a streamer corona model. This system of characterizing quasi-steady streamers is presented graphically and is shown to do a good job of capturing the parameter space typically spanned by streamers at sea-level atmospheric pressure conditions through comparison with a wide range of detailed models and experiments.