Edge-to-center plasma density ratio in high density plasma sources

Abstract

The flux of positive ions leaving a classical low-temperature plasma discharge is proportional to the plasma density at the plasma–sheath edge, and the edge-to-center plasma density ratio, the so-called hl factor, normally depends only on the discharge size and the neutral gas pressure. The ion flux leaving the discharge is therefore linearly proportional to the central plasma density. The hl factor has been previously derived by solving the plasma transport equations over a large pressure range, with the assumption of constant neutral gas density within the discharge. Tonks and Langmuir derived the low pressure (collisionless) solution of this problem in 1929. More recent works have shown that the neutral gas density is no longer constant when the plasma pressure becomes comparable to the neutral gas pressure. In this paper, we solve the plasma transport equations in this new situation and we propose a new expression for the hl factor. It is shown that hl becomes a function of the central plasma density which implies that the ion flux leaving the discharge is no longer proportional to this density. This effect has to be included in particle and energy balance equations used in global models of high density plasma sources.