Numerical Methods to Approximately Calculate Photoionization Rate in Two-dimensional Space*

Numerical Methods to Approximately Calculate Photoionization Rate in Two-dimensional Space

Anahita Alibalazadeh, Andrew Fierro, Jane Lehr, Mark Gilmore, Justin Smith

University of New Mexico, Albuquerque, NM, USA

Numerical methods are mathematical techniques used to approximate the solutions to problems that are difficult to solve analytically. The main goal in this work is to solve the most widely used model for photoionization calculation introduced by Zheleznyak in a two-dimensional axisymmetric space directly using experimental data, rather than approximation-based data that has been used previously. The results are then compared with the Helmholtz model which is a conversion of integral form to a set of differential equations. A fast numerical method, Variation of Parameters, to approximate photoionization rate solution is introduced. The method involved solves second-order differential equation (DE) with boundary conditions. These Helmholtz equations were traditionally solved using numerical methods such as finite difference or finite volume coupled to a linear solver library resulting in large matrix calculations. The Variation of Parameters method is applied to the photoionization problems in air and is used to calculate the approximate solution in two-dimensional space and compared with the solution to the Helmholtz equation. The photoionization solution obtained using the current method is also incorporated into a 2D axisymmetric fluid model to investigate plasma formation with photoionization source term. The method has several advantages; the most important one is that it is fast and does not require large-scale matrices compared to other numerical methods.

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.