Reduced order modelling of streamers and their characterization by macroscopic parameters

Abstract

Electric discharges in gases occur at various scales, and are of both academic and practical interest for several reasons including understanding natural phenomena such as lightning, and for use in industrial applications. Streamers, self-propagating ionization fronts, are a particularly challenging regime to study. They are difficult to study computationally due to the necessity of resolving disparate length and time scales, and existing methods for understanding single streamers are impractical for scaling up to model the hundreds to thousands of streamers present in a streamer corona. Conversely, methods for simulating the full streamer corona rely on simplified models of single streamers which abstract away much of the relevant physics. This disconnect highlights the need for a simplified model of individual streamers which captures the core dynamics but is scalable to ensembles of many mutually interacting streamers. In this work, several such models are developed.

First, a 1.5D model of a single streamer was created wherein particles are treated one dimensionally and electric fields two dimensionally (axisymmetric). This model incorporates developments in modelling streamer processes such as photoionization that were not available in the days when 1.5D models were first invesitgated. Next, a 1.5D model was created with the governing equations solved in the reference frame of the streamer. The existence of such a quasi-steady frame has previously been hypothesized; this work gives a thorough evaluation of the validity of a steady-state streamer model and finds it to be a reasonable approximation on the time scale of electron motion. Based on the success of the quasi-steady model, a further simplification is made wherein streamers are characterized by a small set of macroscopic parameters: tip electric field, velocity, radius and background electric field.

A simple model is developed relating these various properties and an efficient graphical representation of their interdependencies is presented.