# Theoretical and experimental study of elliptical Debye clusters

## Abstract

An elliptical Debye cluster is a system of n identical charged particles interacting through a screened Coulomb potential and confined in a two-dimensional anisotropic parabolic well. A model for this system has been developed with three parameters: n, the well anisotropy {alpha}{sup 2}, and the Debye shielding parameter {kappa}. From numerical solutions of the model, it is shown that the breathing mode persists as the anisotropy increases, and that the normalized, squared breathing frequency increases linearly with {alpha}{sup 2}. Elliptical clusters with n=49 and 15 particles were studied experimentally. The anisotropic potential well was created using a rectangular aperture (17.5x30.2 mm) placed on a flat electrode. The well anisotropy was determined by measuring the center-of-mass (c.m.) oscillation frequencies along the major and minor axes of the resulting elliptical clusters using both driven and thermal oscillations. The two methods give results that are in good agreement. For n=49 particles, the square of the ratios of the c.m. frequencies was {alpha}{sup 2}=2.9{+-}0.1. From a measurement of the breathing frequency, the shielding parameter was found to be {kappa}=2.1{+-}0.2. For n=15 particles, {alpha}{sup 2}=2.8{+-}0.1 and {kappa}=1.9{+-}0.2, demonstrating that an analysis using the model gives consistent results.

- Authors:

- Department of Physics and Astronomy, Ohio Northern University, Ada, Ohio 45810 (United States)

- Publication Date:

- OSTI Identifier:
- 20979408

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Applied Physics; Journal Volume: 101; Journal Issue: 11; Other Information: DOI: 10.1063/1.2743822; (c) 2007 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; ANISOTROPY; APERTURES; CENTER-OF-MASS SYSTEM; CHARGED PARTICLES; COULOMB FIELD; ELECTRODES; NUMERICAL SOLUTION; OSCILLATIONS; PLASMA; PLASMA CONFINEMENT; PLASMA WAVES; POTENTIALS; SHIELDING; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Sheridan, T. E., Wells, K. D., Garee, M. J., and Herrick, A. C.
```*Theoretical and experimental study of elliptical Debye clusters*. United States: N. p., 2007.
Web. doi:10.1063/1.2743822.

```
Sheridan, T. E., Wells, K. D., Garee, M. J., & Herrick, A. C.
```*Theoretical and experimental study of elliptical Debye clusters*. United States. doi:10.1063/1.2743822.

```
Sheridan, T. E., Wells, K. D., Garee, M. J., and Herrick, A. C. Fri .
"Theoretical and experimental study of elliptical Debye clusters". United States.
doi:10.1063/1.2743822.
```

```
@article{osti_20979408,
```

title = {Theoretical and experimental study of elliptical Debye clusters},

author = {Sheridan, T. E. and Wells, K. D. and Garee, M. J. and Herrick, A. C.},

abstractNote = {An elliptical Debye cluster is a system of n identical charged particles interacting through a screened Coulomb potential and confined in a two-dimensional anisotropic parabolic well. A model for this system has been developed with three parameters: n, the well anisotropy {alpha}{sup 2}, and the Debye shielding parameter {kappa}. From numerical solutions of the model, it is shown that the breathing mode persists as the anisotropy increases, and that the normalized, squared breathing frequency increases linearly with {alpha}{sup 2}. Elliptical clusters with n=49 and 15 particles were studied experimentally. The anisotropic potential well was created using a rectangular aperture (17.5x30.2 mm) placed on a flat electrode. The well anisotropy was determined by measuring the center-of-mass (c.m.) oscillation frequencies along the major and minor axes of the resulting elliptical clusters using both driven and thermal oscillations. The two methods give results that are in good agreement. For n=49 particles, the square of the ratios of the c.m. frequencies was {alpha}{sup 2}=2.9{+-}0.1. From a measurement of the breathing frequency, the shielding parameter was found to be {kappa}=2.1{+-}0.2. For n=15 particles, {alpha}{sup 2}=2.8{+-}0.1 and {kappa}=1.9{+-}0.2, demonstrating that an analysis using the model gives consistent results.},

doi = {10.1063/1.2743822},

journal = {Journal of Applied Physics},

number = 11,

volume = 101,

place = {United States},

year = {Fri Jun 01 00:00:00 EDT 2007},

month = {Fri Jun 01 00:00:00 EDT 2007}

}