Sheath expansion of two-dimensional grid electrodes subjected to short pulses of negative high-voltage

Sheath expansion was investigated for two-dimensional (2D) grid electrodes which consist of a periodic array of cylindrical electrodes when short pulses of negative high-voltage were applied to the electrodes immersed in plasmas. In the sheath expansion model, a geometric function which describes the electrode system is crucial to numerically calculate the temporal evolution of a sheath boundary. In this paper, the 2D geometric function of grid electrodes was obtained by using XOOPIC (particle-in-cell) simulation. When the ratio between the diameter of cylindrical electrodes and grid spacing is fixed, we found that the geometric functions and the temporal evolutions of the sheath boundary for grid electrodes are identical in normalized coordinates. The numerical calculation results of the temporal evolutions of the sheath boundary showed reasonable agreements with the experimental measurements carried out in argon plasmas produced by hot filament discharges with neutral gas pressure of ∼0.4 mTorr and plasma density in the order of 1010 cm−3 in a multi-dipole device.