On the energy conservation electrostatic particle-in-cell/Monte Carlo simulation：Benchmark and application to the radio frequency discharges

We benchmark and analyze the error of energy conservation (EC) scheme in particle-in-cell/Monte Carlo (PIC/MC) algorithms by simulating the radio frequency discharge. The plasma heating behaviors and electron distributing functions obtained by one-dimensional (1D) simulation are analyzed. Both explicit and implicit algorithms are checked. The results showed that the EC scheme can eliminated the self-heating with wide grid spacing in both cases with a small reduction of the accuracies. In typical parameters, the EC implicit scheme has higher precision than EC explicit scheme. Some “numerical cooling” behaviors are observed and analyzed. Some other errors are also analyzed. The analysis showed that the EC implicit scheme can be used to qualitative estimation of some discharge problems with much less computational resource cost without much loss of accuracies.