Prediction models of the ionization coefficient and ionization cross-section based on multi-layer molecular parameters

Abstract

The prediction models were proposed to estimate the reduced Townsend ionization coefficient and ionization cross-section. A shape function of the reduced Townsend ionization coefficient curves was derived from the ionization collision probability model. The function had three parameters: the first ionization potential energy, Aα, and Bα. Aα and Bα were related to the molecule symmetry and size. The polarization of molecules could characterize the molecule’s symmetry. The multi-layer molecular cross-section (MMCS) was proposed to describe the contribution of electrons and molecule radius on different molecule surfaces to collisions. A prediction model of the ionization cross-section was also proposed based on Aα. The molecule parameters were calculated by the Beck3-Lee-Yang-Parr (B3LYP) method and the 6-311G** basis set. We used available data of 30 and 23 gases, respectively, to build the prediction models of reduced Townsend ionization coefficients and ionization cross-sections. The relationships among molecular parameters, Aα, Bα, and ionization cross-section were built up via nonlinear fittings. The determination coefficients R2 of the Aα, Bα, and ionization cross-section are 0.877, 0.887, and 0.838, respectively. The results showed that the accuracy of models positively correlated with the molecule’s symmetry and reduced electric field. That was mainly related to the accuracy of the MMCS model in predicting Aα. The MMCS model needed to be improved to describe the collision direction selectivity caused by the molecule asymmetry. Under a high reduced electric field, that error of Aα had less influence on the prediction results. However, the prediction results for single atoms with high symmetry were poor. That may be due to the absolute error of the model close to single atoms’ reduced Townsend ionization coefficients. The models could provide the basis for gas insulation prediction and discharge calculations, especially for symmetric molecules under high electric field.