# Unified model of the rf plasma sheath: Part 2, Asymptotic connection formulae

## Abstract

A previously-developed approximation to the first integral of the Poisson equation enables one to obtain solutions for the voltage- current characteristics of a radio-frequency (rf) plasma sheath that are valid over the whole range of inertial response of the ions to an imposed rf voltage or current-specified conditions. The theory reproduced the time-dependent voltage-current characteristics of the two extreme cases corresponding to the Lieberman rf sheath theory and the Metze-Ernie-Oskam theory. In this paper the sheath model is connected to the plasma bulk description, and a prescription is given for the ion relaxation time constant, which determines the time-dependent ion impact energy on the electrode surface. It appears that this connected model should be applicable to those high density, low pressure plasmas in which the Debye length is a small fraction of the ion mean free path, which itself is a small fraction of the plasma dimension.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 274143

- Report Number(s):
- SAND-96-1948

ON: DE96014005

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: Aug 1996

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION; PLASMA SHEATH; MATHEMATICAL MODELS; PLASMA; PLASMA DENSITY; LANGMUIR FREQUENCY; ION DENSITY; RADIOWAVE RADIATION; KHZ RANGE 100-1000

### Citation Formats

```
Riley, M.E.
```*Unified model of the rf plasma sheath: Part 2, Asymptotic connection formulae*. United States: N. p., 1996.
Web. doi:10.2172/274143.

```
Riley, M.E.
```*Unified model of the rf plasma sheath: Part 2, Asymptotic connection formulae*. United States. doi:10.2172/274143.

```
Riley, M.E. Thu .
"Unified model of the rf plasma sheath: Part 2, Asymptotic connection formulae". United States.
doi:10.2172/274143. https://www.osti.gov/servlets/purl/274143.
```

```
@article{osti_274143,
```

title = {Unified model of the rf plasma sheath: Part 2, Asymptotic connection formulae},

author = {Riley, M.E.},

abstractNote = {A previously-developed approximation to the first integral of the Poisson equation enables one to obtain solutions for the voltage- current characteristics of a radio-frequency (rf) plasma sheath that are valid over the whole range of inertial response of the ions to an imposed rf voltage or current-specified conditions. The theory reproduced the time-dependent voltage-current characteristics of the two extreme cases corresponding to the Lieberman rf sheath theory and the Metze-Ernie-Oskam theory. In this paper the sheath model is connected to the plasma bulk description, and a prescription is given for the ion relaxation time constant, which determines the time-dependent ion impact energy on the electrode surface. It appears that this connected model should be applicable to those high density, low pressure plasmas in which the Debye length is a small fraction of the ion mean free path, which itself is a small fraction of the plasma dimension.},

doi = {10.2172/274143},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Thu Aug 01 00:00:00 EDT 1996},

month = {Thu Aug 01 00:00:00 EDT 1996}

}