Simulation benchmarks of the PIC-MCC codes XPDP1 and VSim for capacitively coupled plasma helium discharges

To comprehend the kinetic processes of low-pressure, low-temperature capacitive discharges in various gases, the particle-in-cell Monte Carlo collision (PIC-MCC) simulation has become an indispensable tool. Turner et al. conducted detailed benchmarks of five 1-D PIC-MCC codes for low-pressure capacitively coupled plasma (CCP) discharge. However, the benchmarks were based on the assumption that after an ionizing collision, the residual energy is divided exactly equally between the primary and secondary electrons and the corresponding algorithm was implemented. The condition is ideal but not general and therefore this not only makes the benchmarks of other codes more difficult but introduces much complexity. In this work, the XPDP1 code and VSim simulation package have been benchmarked against each other using the same four cases of CCP He discharge without the assumption, giving good agreement. The discrepancy due to the assumption has been studied using VSim as the algorithm has been implemented correctly and made available to its users. It is also found that the cross-sections play an important role in the CCP discharges and the plasma densities using newly implemented ones from LXCat database are very different from those using original functional cross sections in the XPDP1 code. This suggests one should use more realistic cross sections from either experiments or first-principles calculations. Simulation performance is also studied and compared. These simulation results are more general for comparison and the detailed benchmarks will be presented and discussed.