Computational Model for Photoionization in Pure SF6 Streamer at 1-15 atm

TL;DR

This work develops a non-local, Helmholtz-based computational model for SF$_6$ photoionization in pure SF$_6$ within 1–15 atm, anchored to Zheleznyak’s photoionization theory and Pancheshnyi’s spectral formulation. The photon production and absorption processes are calibrated using UV emission data, with a three-term Helmholtz representation of the absorption function that enables efficient PDE-based computation of the photoionization source ${S}_{\text{ph}}$ via ${S}_{\text{ph}} = \sum_j S_{\text{ph}}^j$ and ${\nabla^2 S_{\text{ph}}^j} - (\lambda_j p)^2 S_{\text{ph}}^j = -A_j p^2 I(r)$. Comparative studies show that the non-local model improves numerical convergence and yields more accurate streamer structures than simplified approaches; artificially increasing ${S}_{\text{ph}}$ by 50× significantly underestimates positive-streamer breakdown voltages (by >0.5 kV) and alters propagation (reducing head shrinking and lowering head field by >700 Td) while having limited impact on negative streamers. The work provides a concise set of Helmholtz parameters across 1–15 atm and discusses the limitations of 2D modeling for high-pressure breakdown, highlighting the need for 3D validation and potential extensions to gas mixtures. Overall, the framework advances quantitative predictions of SF$_6$ breakdown and streamer dynamics by capturing non-local photoionization effects essential for accurate insulation performance assessments.

Abstract

Photoionization plays a crucial role in achieving accurate quantitative predictions in SF6 streamer simulations, but accurate models for SF6 photoionization remains limited, motivating this paper. First, we develop a computational model for SF6 photoionization and provide the detailed theoretical modeling process, as well as comparison between experiment and simulation. A concise summary of model parameters within the comprehensive pressure range of 1 - 15 atm is provided for direct reference. Then, we perform comparative studies against simplified approaches. The results demonstrate that the proposed model effectively captures the non-local effects of SF6 photoionization, enhancing both the spatial numerical convergence and the accuracy of the streamer structure. Finally, we perform comparative studies by artificially increasing the photoionization intensity through multiplying the photoionization source term Sph by a factor of 50 (50*Sph) relative to the baseline intensity. Regarding breakdown voltage prediction, 50*Sph leads to a significant underestimation of the breakdown voltage for positive streamers, introducing errors greater than 0.5 kV, while exerting a small impact on negative streamers. Regarding streamer propagation dynamics, the radius of the positive streamer head exhibits pronounced shrinking, and 50*Sph reduces this shrinking and significantly lowers the head field by more than 700 Td. In contrast, 50*Sph has little impact on the morphology of the negative streamers and slightly enhances the head field by less than 30 Td.

Figures (13)

• Figure 1: Further calibrated SF$_6$ emission spectrum based on original spectral data of Forand et al.doi:10.1139/p86-048. The identification of different radiation transitions of F I is indicated.
• Figure 2: Excitation functions for direct dissociative excitation from SF$_6$ to F I 78.1 nm and F I 75.1 nm
• Figure 3: Ionizing radiation efficiency of F I 78.1 nm and F I 75.1 nm as a function of the reduced electric field. The recommended value of $\frac{v_{\text{u}}}{v_{\mathrm{i}}}$ employed in photoionization model is indicated
• Figure 4: Comparison of the calculated $\frac{{p}_{\mathrm{q}, k}}{{p}+{p}_{\mathrm{q}, k}} \xi_k \frac{{v}_{\mathrm{u}, k}}{{v}_{\mathrm{i}}} \frac{{g}_k({R})}{{p}}$ term. In the legend, [78.1] denotes the term corresponding to the 78.1 nm radiation ($k=78.1$), and [75.1] denotes the term corresponding to the 75.1 nm radiation ($k=75.1$). The combined contribution is obtained by adding [78.1] to the [75.1] term multiplying by factors of 1×, 5×, 10×
• Figure 5: Reproduced data for SF$_6$ spectrally resolved photoionization efficiency $\xi_{\lambda}$ and SF$_6$ photoionization cross section $\sigma_{\text{photoion }}$ reported by Holland et al.DMPHolland_1992, SF$_6$ photoabsorption cross section $\sigma_{\text{photoabs }}$ reported by Ying et al.10.1063/1.465149.