"Models to Calculate Photoionization Rate in Air"*

The most widely used model to calculate photoionization produced by nonthermal gas discharge in fluid simulations belongs to Zheleznyak et al. However, several assumptions have been applied to the development of this classical integral model. The main goal in this work is to solve the classical integral model directly using experimental data, rather than approximation-based data that has been used previously. To do so, the modified model derived from the original one is introduced. Detailed analysis of these two models has been implemented. A quantitative analysis of results obtained using experimental data from Sandia Plasma Research Facility (SPRF) and those gained from the analytically approximated model, derived from the original integral model, is performed. The validity of the modified model using experimental data is demonstrated by direct comparisons of the results. The photon propagation function was investigated while the conditions such as plasma volume, pressure, and power are varied. The introduced modified model is used in a two-dimensional axisymmetric model to numerically investigate plasma streamer formation. The Helmholtz model, which is a conversion of integral form to a set of differential equations, is solved using numerical methods and compared to the modified model. This work enables the extension of the classical integral model to arbitrary gases to obtain photoionization rates if the underlying physical data is known.

Reference: Zhelezniak, M. B., Mnatsakanian, A. K., & Sizykh, S. V. E. (1982). Photoionization of nitrogen and oxygen mixtures by radiation from a gas discharge. High Temperature Science, 20(3), 357-362.

This work was supported by the U.S.DOE under award no. DE-SC0020217.