# Analytical solution of space charge limited current for spherical and cylindrical objects

## Abstract

Analytical solutions for space charge limited currents in collisionless, electron-free sheaths are given for Cartesian, spherical, and cylindrical geometries. Constant current and current density are assumed. Until now, the problem of space charge limited current has not been solved either directly, in terms of series expansions, or numerically, for spherical and cylindrical objects. Analytical results show that the geometry of the system is important for determining the space charge limited current, sheath thickness, and sheath potential profile. This solution method can be used to solve similar nonlinear differential equations.

- Authors:

- Physics Department, Suleyman Demirel University, Isparta (Turkey)

- Publication Date:

- OSTI Identifier:
- 20779222

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Applied Physics Letters; Journal Volume: 88; Journal Issue: 18; Other Information: DOI: 10.1063/1.2201469; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANALYTICAL SOLUTION; BOUNDARY LAYERS; CURRENT DENSITY; CYLINDERS; DIFFERENTIAL EQUATIONS; ELECTRIC CURRENTS; ELECTRONS; GEOMETRY; NONLINEAR PROBLEMS; NUMERICAL ANALYSIS; PLASMA; PLASMA SHEATH; SERIES EXPANSION; SPACE CHARGE; SPHERES; THICKNESS

### Citation Formats

```
Oksuz, L.
```*Analytical solution of space charge limited current for spherical and cylindrical objects*. United States: N. p., 2006.
Web. doi:10.1063/1.2201469.

```
Oksuz, L.
```*Analytical solution of space charge limited current for spherical and cylindrical objects*. United States. doi:10.1063/1.2201469.

```
Oksuz, L. Mon .
"Analytical solution of space charge limited current for spherical and cylindrical objects". United States.
doi:10.1063/1.2201469.
```

```
@article{osti_20779222,
```

title = {Analytical solution of space charge limited current for spherical and cylindrical objects},

author = {Oksuz, L.},

abstractNote = {Analytical solutions for space charge limited currents in collisionless, electron-free sheaths are given for Cartesian, spherical, and cylindrical geometries. Constant current and current density are assumed. Until now, the problem of space charge limited current has not been solved either directly, in terms of series expansions, or numerically, for spherical and cylindrical objects. Analytical results show that the geometry of the system is important for determining the space charge limited current, sheath thickness, and sheath potential profile. This solution method can be used to solve similar nonlinear differential equations.},

doi = {10.1063/1.2201469},

journal = {Applied Physics Letters},

number = 18,

volume = 88,

place = {United States},

year = {Mon May 01 00:00:00 EDT 2006},

month = {Mon May 01 00:00:00 EDT 2006}

}

DOI: 10.1063/1.2201469

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