Two-Dimensional Collisionless Weakly-Ionized Plama in Fluid Approximation

Abstract

Summary form only given. In laboratories and various applications, plasmas are always multidimensional. In basic research experiments and in the majority of plasma processing reactors, the finite plasma cylinder is the most common plasma shape. In the diffusion limit described by the Schottky model, the two-dimensional plasma density profile for a finite cylinder of length 2L and diameter 2R is the product of the corresponding one-dimensional solutions, namely, n(x,r)/n0 = cos(pix/2L) . J0(2.4r/R). Because of this, even when the Schottky model is not applicable (such as in the cases of collisionless ions, or variable ion mobility), the representation of the plasma spatial distribution by the product of the corresponding one-dimensional solutions has remained a common approach at low gas pressures. In this presentation, numerical solutions for the two-dimensional fluid model of a collisionless weakly-ionized plasma cylinder for arbitrary aspect ratios L/R will be demonstrated. The behavior of the ionization frequency, plasma densities at the radial and axial boundaries, the spatial plasma profile, the plasma flux, as well as the entering angle of ions at the plasma boundary for a wide range of the aspect ratio will be analyzed. The obtained results w ill show that for cylindrical collisionless plasma, the spatial plasma profile cannot be represented by the product of the corresponding one-dimensional solutions. Moreover, in the limiting cases of small and large aspect ratios, the plasma distribution along the longer length (L or R) approaches the diffusion distribution, which corresponds to the highly collisional ion motion, although the ion motion in this direction is collisionless.