How to balance computational cost and accuracy of the model for negative hydrogen ion sources? A level-lumping strategy

Abstract

In this work, a level-lumping strategy is proposed, which could accurately reproduce the plasma characteristics in negative hydrogen ion sources with much higher efficiency. Based on the vibrational distribution function (VDF), the vibrationally excited levels H2 (ν = 1–14) are lumped into one group (1G), two groups (2G), three groups (3G) and four groups (4G). By comparing the results obtained by different models, the accuracy of this level-lumping method is evaluated by using the global model approach. The results indicated that the 1G model fails to reproduce the VDF, and thus the H− generation is significantly underestimated, with the relative difference in the H− density from the individual-levels model higher than 60% in the pressure range between 1 Pa and 5 Pa. Although the 2G model performs better than the 1G model, the discrepancy from the individual-levels model is still obvious. When the vibrational levels are lumped into 3G, a much better performance is observed, i.e. the relative difference in the H− density is only 9.4% at 5 Pa. The best agreement with the individual-levels model is achieved by the 4G model, and the relative difference in the H− density is below 5% at pressures above 3 Pa. Considering the balance between computational cost and accuracy, although more groups are helpful to reproduce the VDF perfectly, the 4G model is the best option. The level-lumping approach proposed in this work could help us to significantly decrease the number of equations to be solved in the model, and thus dramatically reduce the computational time and make the accurate chemical kinetics become compatible with multi-dimensional models.