Abstract Title: Enhanced Computational Modeling of Photoionization Rate and Streamer Formation

Enhanced Computational Modeling of Photoionization Rate and Streamer Formation

Accurate and computationally efficient modeling of the photoionization rate in a forming plasma is essential for predicting plasma behavior in large, physical systems. In this work, a fast, Fast Fourier Transform (FFT) based solution is proposed for photoionization in a cylindrical coordinate system. This approach allows for the transformation of the system into an algebraic one rather than a system of linear equations, greatly simplifying the solution. Verification of the spectral solution for photoionization with classical finite-difference solutions shows excellent agreement over a range of problem sizes. Furthermore, in practical implementations solved on massively parallel computers using linear algebraic solvers, the proposed FFT solution is 100 times faster for grid sizes of 10⁵ to 10⁷. Finally, the spectral method is incorporated into a finite-volume drift diffusion code for simulation of streamer phenomena that relies on photoionization for propagation. The calculated photoionization in the 1.25 cm 0.2 cm gap shows similar streamer speeds to those in other works. Thus, the FFT solution has proved to be a reliable solution for the calculation of the photoionization source term and can be included into existing numerical codes for the simulation of plasmas.

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