Normalized ion distribution function in expanding sheaths of 2D grid electrodes

Abstract

Ion distributions in expanding collisionless sheaths of two-dimensional (2D) grid electrodes were studied by using XOOPIC (particle-in-cell) simulations when short pulses of negative high-voltage were applied to electrodes immersed in plasmas. 2D grid electrodes consist of a periodic array of cylindrical electrodes, and the opening ratio of the grid electrodes is defined by the ratio of the spacing between cylindrical electrodes to the periodic length of the grid electrodes. In this paper, we introduce a normalized ion distribution function in normalized coordinates, and it is shown by simulation that the normalized ion distribution function depends only on the opening ratio of the grid electrodes. When the opening ratio of the grid electrodes is fixed, the ion distribution in expanding sheaths can be easily found in various conditions using only a single run of a PIC simulation, and the computation time can be significantly reduced.