Applying Conformal Mapping to simulate the generation of species in Nanosecond Pulsed Discharges in a tip-to-tip geometry

Nanosecond pulsed plasmas (NPPs) are used to generate reactive species in many applications such as combustion, flow control and medicine¹. Here, we report a new conformal transformation (CT) that maps the hyperboloids representing the electrodes in the one-dimensional tip-to-tip geometry (TTG) onto concentric circles in a plane. The map is based on the stereographic projection of the hyperboloids that forms an extended Poincaré disk. The species concentrations are obtained in the TTG by coupling the drift-diffusion model of planar geometry modified using this CT function to BOLSIG+². Applying CT to modify the governing equations significantly reduces the computational expense³ by only requiring the simulation of the planar geometry to characterize species concentration in any electrode configuration. We demonstrate the utility of CT by applying it to a TTG and comparing to experiments and other simulations.

[1] I. V. Adamovich, M. Nishihara, I. Choi, et al. Phys Plasmas 16, 113505 (2009).

[2] T. Piskin, V. Podolsky, S. Macheret, and J. Poggie, J. Phys. D. Appl. Phys., 52, 304002 (2019).

[3] I. Shojaei, H. Rahami and A. Kaveh, Appl. Math. Model., 40, 7768 (2016).