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 10 10 cm −3 in a multi-dipole device.

An electron cyclotron resonance plasma source with a belt-type magnet assembly and slit antennas was developed for generating high density plasmas at low operating pressures. To enhance plasma confinement and avoid the disadvantages of quartz windows, a continuous arrangement of magnets and direct microwave injection from the slit antennas without quartz windows was used. This plasma source operated at an argon gas pressure of 0.4-1 mTorr and microwave power of 300-800 W. Electron temperature and ion density are dependent on the radial and axial position.