Benchmarking the calculation of electrically insulating properties of complex gas mixtures using a multi-term Boltzmann equation model

Abstract

The accurate calculation of DC breakdown voltage thresholds solely from elementary electron-neutral interactions in complex gas mixtures using a multi-term Boltzmann equation (BE) kinetic model is demonstrated. SF6:N2 mixtures in the 100 Td < E/N < 400 Td field regime are explored to benchmark the model’s effectiveness. A ten-term BE model is found to yield DC breakdown voltages which, on average, agree within 3% of experimental measurements. A two-term BE model is also applied in order to characterize the error introduced in all calculations by the two-term approximation. These discrepancies are largest in pure N2 where error is greater than 10% for diffusion coefficients, within 6% for particular vibrational rate coefficients, and within 5% for breakdown voltages. However, this error falls to within 1% for most parameters and breakdown voltages in mixtures with large SF6 content.

The comparison of two-term Boltzmann approximation and Monte-Carlo solutions for e+Ar0 plasma

“…Also, there are studies considering the higher-order terms of the expansion in Legendre polynomials [16][17][18][19][20]. These approaches can be partially applied when the VDF becomes rather anisotropic.…”

Determination and assessment of a complete and self-consistent electron-neutral collision cross-section set for the C4F7N molecule

“…For this reason, the Boltzmann equation solver Bolsig+ (version 12/2019), representing the two-term approximation method, is used here to ease the iterative modifications of the cross-sections due to its short computing time [43]. A multi-term approximation code MultiBolt is also used at the end of the iterations to obtain more accurate swarm parameters as a function of E/N [44,45].…”

“…For pure C 4 F 7 N, the ionization rate coefficient k i , attachment rate coefficient k a and longitudinal electron diffusion coefficient ND L are also included in the comparison. The electron swarm parameters are calculated by Bolsig+ [43] and MultiBolt [44,45]. In Bolsig+, the numerical solutions of the Boltzmann equation are determined by the two-term approximation.…”

Robust approximation rules for critical electric field of dielectric gas mixtures

“…This computational sieve approach to rapidly explore, trial, and assess potential scenarios then informs the design of targeted and efficient experiments and solution prototypes. For example, insight through large simulations of breakdown scenarios in often complex geometries [9] or detailed kinetic calculations of electron energy distribution functions (EEDFs) in gas mixtures over density or pressure windows [10] are now capable with advances in computing. This being said, these non-trivial computational tasks can also present their own challenges and barriers to entry, such as advanced computational domain knowledge or access to sufficient computing power or time.…”