# Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory

## Abstract

The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindrical probe characteristics obtained from the correct potential profile (M solution) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.

- Authors:

- Theoretical Physics Division, PINSTECH, P. O. Nilore, 44000 Islamabad (Pakistan)

- Publication Date:

- OSTI Identifier:
- 22599950

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 23; Journal Issue: 8; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ARGON; BOHM CRITERION; CATIONS; COMPARATIVE EVALUATIONS; CYLINDRICAL CONFIGURATION; PLASMA PRESSURE; PROBES; SPHERICAL CONFIGURATION

### Citation Formats

```
Din, Alif.
```*Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory*. United States: N. p., 2016.
Web. doi:10.1063/1.4960319.

```
Din, Alif.
```*Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory*. United States. doi:10.1063/1.4960319.

```
Din, Alif. Mon .
"Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory". United States.
doi:10.1063/1.4960319.
```

```
@article{osti_22599950,
```

title = {Bohm-criterion approximation versus optimal matched solution for a cylindrical probe in radial-motion theory},

author = {Din, Alif},

abstractNote = {The theory of positive-ion collection by a probe immersed in a low-pressure plasma was reviewed and extended by Allen et al. [Proc. Phys. Soc. 70, 297 (1957)]. The numerical computations for cylindrical and spherical probes in a sheath region were presented by F. F. Chen [J. Nucl. Energy C 7, 41 (1965)]. Here, in this paper, the sheath and presheath solutions for a cylindrical probe are matched through a numerical matching procedure to yield “matched” potential profile or “M solution.” The solution based on the Bohm criterion approach “B solution” is discussed for this particular problem. The comparison of cylindrical probe characteristics obtained from the correct potential profile (M solution) and the approximated Bohm-criterion approach are different. This raises questions about the correctness of cylindrical probe theories relying only on the Bohm-criterion approach. Also the comparison between theoretical and experimental ion current characteristics shows that in an argon plasma the ions motion towards the probe is almost radial.},

doi = {10.1063/1.4960319},

journal = {Physics of Plasmas},

number = 8,

volume = 23,

place = {United States},

year = {Mon Aug 15 00:00:00 EDT 2016},

month = {Mon Aug 15 00:00:00 EDT 2016}

}