Impact of particle number and cell size on energy-conserving PIC applied to RF-driven bounded plasmas

Recent studies have shown that variations in particle-per-cell count and cell size can significantly affect the accuracy of 1D implicit energy- and charge-conserving electrostatic particle-in-cell simulations of capacitively coupled radio frequency discharges, even when the sheath is resolved and the quasi-neutral region is relaxed. This challenges the expected advantages of implicit schemes and may stem from the complexity of active stochastic sheath heating. To test whether passive sheaths can mitigate this issue, we study a similar 1D discharge with perpendicular electron heating, which produces passive sheath dynamics. We find that the same resolution sensitivity persists: coarser spatial resolution requires more particles per cell and still yields reduced accuracy compared to well resolved solutions. Furthermore, we observe that in our implementations, it is difficult to identify simulation parameters (time step, cell size, and particle-per-cell count) where implicit schemes are both more accurate and faster than momentum-conserving explicit codes. On non-uniform grids, we show that energy-conserving explicit and implicit methods yield similar results when the time step is small. Finally, we explore how trends in the resultant discharge characteristics vary with reduced resolution in energy-conserving simulations beyond what is feasible with momentum-conserving explicit schemes and find that while overall trends are generally preserved, the specific values and the magnitude of their changes can differ significantly.