# Approximate expression for the electric potential around an absorbing particle in isotropic collisionless plasma

## Abstract

A new approximate expression for the potential distribution around an absorbing particle in isotropic collisionless plasma is proposed. The approximate expression is given by the sum of the Debye-Hückel potential with an effective screening length and the far-field asymptote obtained from the solution of the linearized Poisson equation. In contrast to analogous models, the effective screening length is not fixed but depends on the distance from the particle. This allows us to obtain a more accurate approximation for the potential distribution in the entire range of distances. The dependence of the screening length on the distance is predicted from the analysis of the charge density distribution function. This dependence contains two adjustable parameters, which are calculated by applying the procedure based on charge balance considerations. Using the obtained results, simple expressions for the parameters of the model are proposed. In addition, a simple expression for the characteristic screening length, which can be used to approximate the potential distribution near the particle, is obtained. The developed model potential is shown to be in excellent agreement with the solution of the nonlinear Poisson equation for typical conditions used in experiments with complex plasmas.

- Authors:

- Forschungsgruppe Komplexe Plasmen, Deutsches Zentrum für Luft- und Raumfahrt, Oberpfaffenhofen (Germany)
- (France)

- Publication Date:

- OSTI Identifier:
- 22410362

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 22; Journal Issue: 5; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; CHARGE DENSITY; COLLISIONLESS PLASMA; DISTRIBUTION FUNCTIONS; ELECTRIC POTENTIAL; LENGTH; MATHEMATICAL SOLUTIONS; PARTICLES; POISSON EQUATION; POTENTIALS; SCREENING

### Citation Formats

```
Semenov, I. L., E-mail: Igor.Semenov@dlr.de, Thomas, H. M., Khrapak, S. A., and Aix-Marseille-Université, CNRS, Laboratoire PIIM, UMR 7345, 13397 Marseille cedex 20.
```*Approximate expression for the electric potential around an absorbing particle in isotropic collisionless plasma*. United States: N. p., 2015.
Web. doi:10.1063/1.4921249.

```
Semenov, I. L., E-mail: Igor.Semenov@dlr.de, Thomas, H. M., Khrapak, S. A., & Aix-Marseille-Université, CNRS, Laboratoire PIIM, UMR 7345, 13397 Marseille cedex 20.
```*Approximate expression for the electric potential around an absorbing particle in isotropic collisionless plasma*. United States. doi:10.1063/1.4921249.

```
Semenov, I. L., E-mail: Igor.Semenov@dlr.de, Thomas, H. M., Khrapak, S. A., and Aix-Marseille-Université, CNRS, Laboratoire PIIM, UMR 7345, 13397 Marseille cedex 20. Fri .
"Approximate expression for the electric potential around an absorbing particle in isotropic collisionless plasma". United States. doi:10.1063/1.4921249.
```

```
@article{osti_22410362,
```

title = {Approximate expression for the electric potential around an absorbing particle in isotropic collisionless plasma},

author = {Semenov, I. L., E-mail: Igor.Semenov@dlr.de and Thomas, H. M. and Khrapak, S. A. and Aix-Marseille-Université, CNRS, Laboratoire PIIM, UMR 7345, 13397 Marseille cedex 20},

abstractNote = {A new approximate expression for the potential distribution around an absorbing particle in isotropic collisionless plasma is proposed. The approximate expression is given by the sum of the Debye-Hückel potential with an effective screening length and the far-field asymptote obtained from the solution of the linearized Poisson equation. In contrast to analogous models, the effective screening length is not fixed but depends on the distance from the particle. This allows us to obtain a more accurate approximation for the potential distribution in the entire range of distances. The dependence of the screening length on the distance is predicted from the analysis of the charge density distribution function. This dependence contains two adjustable parameters, which are calculated by applying the procedure based on charge balance considerations. Using the obtained results, simple expressions for the parameters of the model are proposed. In addition, a simple expression for the characteristic screening length, which can be used to approximate the potential distribution near the particle, is obtained. The developed model potential is shown to be in excellent agreement with the solution of the nonlinear Poisson equation for typical conditions used in experiments with complex plasmas.},

doi = {10.1063/1.4921249},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 5,

volume = 22,

place = {United States},

year = {2015},

month = {5}

}