Two-dimensional cylindrical plasma at low gas pressure

Abstract

A two-dimensional fluid model for collisionless cylindrical plasma of arbitrary aspect ratio is developed, assuming direct ionization and uniform electron temperature. It is shown that contrary to the diffusion case, typical for collision dominated plasma, the plasma density distribution in the two-dimensional collisionless plasma cannot be represented as the product of corresponding one-dimensional solutions and depends on the aspect ratio. The solutions for very short and very long collisionless plasma cylinders with finite aspect ratios showed that the plasma density distribution in the direction of the nearest wall practically coincides with the plasma density distribution of the corresponding one-dimensional model, while the plasma density distribution in the direction of the remote wall coincides with that typical for the diffusion model: cosine distribution in the axial direction for long plasma cylinders and the Bessel function distribution in the radial direction for short plasma cylinders. The ionization frequency and spatial distributions of the plasma density, the ion flux to the wall and the ion ejecting angle with respect to the plasma boundary are found for a wide range of aspect ratios, and analytical representations for these quantities are given for some limiting cases.