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The use of sparse particle-in-cell (PIC) algorithms to accelerate the standard explicit PIC scheme has recently been successfully applied in the context of single-frequency capacitively coupled plasma discharges [Garrigues et al., J. Appl. Phys. 129, 153303 (2021)]. We have extended the sparse PIC scheme to model dual-frequency capacitive discharges. Comparisons between standard and sparse PIC algorithms show that the plasma properties as well as the electron and ion distribution functions can be retrieved with a maximum error of 2%. This work opens the interest of using the sparse PIC algorithm to perform 2D and 3D simulations under real operating conditions of capacitively coupled plasma discharges. [ABSTRACT FROM AUTHOR]

In Paper I [Garrigues et al., Phys. Plasmas 31, 073907 (2024)], we have extended the sparse PIC approach already used in the literature with the offset scheme to reduce the grid-based error. In this study, we demonstrate the ability of the offset sparse PIC algorithm to model partially magnetized low-temperature plasmas by reducing the grid-based error. In the context of multi-cusp magnetic field configurations, the offset scheme reduces the error of the current collected at the walls to less than 5 % for more of the plasma conditions encountered in ion source applications. The formation of a double layer in the sheath region is also captured. In the context of the electron drift instability that occurs in the Hall thruster, the plasma properties as well as the ion velocity distribution function can be retrieved with a high enough precision without considering an initial regular grid with a smaller mesh resolution. The results also highlight the advantage of combining the electric potential at the nodes of the regular grid instead of directly combining the electric field from the component grids. Compared to the regular PIC algorithm, the typical speed-up factor is about three for a number of mesh nodes of 256 2 and five for 512 2 . [ABSTRACT FROM AUTHOR]

The use of a particle-in-cell (PIC) algorithm with an explicit scheme to model low temperature plasmas is challenging due to computational time constrains related to resolving both the electron Debye length in space and the inverse of a fraction of the plasma frequency in time. One recent publication [Ricketson and Cerfon, Plasma Phys. Control. Fusion 59, 024002 (2017)] has demonstrated the interest of using a sparse grid combination technique to accelerate the explicit PIC model. Simplest plasma conditions were considered. This paper is the demonstration of the capability and the effectiveness of the sparse grid combination technique embedded in the PIC algorithm (hereafter called "sparse PIC") to self-consistently model capacitively coupled radio frequency discharges. For two-dimensional calculations, the sparse PIC approach is shown to accurately reproduce the plasma profiles and the energy distribution functions compared to the standard PIC model. The plasma parameters obtained by these two numerical methods differ by less than 5%, while a speed up in the executable time between 2 and 5 is obtained depending on the setup. [ABSTRACT FROM AUTHOR]