Smooth joining of plasma and sheath. Case I: transverse to the discharge axis

Abstract

This paper treats the problem of joining plasma and sheath when the direction of treatment is transverse to the discharge axis. The plasma balance equations of number and momentum are solved from the centre of the plasma to the wall in the cases of parallel-plate and cylindrical geometries about the rare gases. Different approximations are used for plasma and sheath, and the boundary values of both sides are joined continuously, not only in their own values but also in their first derivatives. This is called the 'smooth joining' of plasma and sheath. The point joining plasma and sheath is determined uniquely by means of the sheath equation or the requirement that the Poisson equation be solved for non-negative net charges. Some physical quantities are calculated, and their profiles are drawn from the centre of the plasma to the wall.