| Sparks and lightning are ubiquitous phenomena. So-called high altitude lightning is presently a very active field of research. Spark-like processes are also used in numerous technical processes. All these discharges initially grow as narrow channels that can branch many times. For a long time this process was too complex for quantitative understanding and too rapid for detailed experimental characterization. But recently, appropriate experimental and theoretical methods have become available. The applicant participates in planning and evaluating experiments with nanosecond resolution as well as in computations of a PDE model with adaptive grid refinement. However, since the problem consists of coherent structures on a range of length scales, direct computation of the large-scale structures from the PDEs is not possible. The present project therefore addresses a model reduction: the minimal model for the growth of discharge channels consists of two reaction drift diffusion equations for the densities of electrons and ions. The equations are coupled in a threefold nonlinear way to the electric field. This model actually generates a spatial structure with propagating ionization fronts and space charge layers surrounding a rather inert channel body. The separation of frontwidth and channel radius leads to a dynamic self-focusing of the electric field at the tip of the channel. The model describes not only the propagation, but also the spontaneous branching of discharge channels due to a Laplacian instability. The purpose of the project is to eliminate the width of the ionization front and space charge. |
