# Criterion for bulk behavior of a Yukawa disk

## Abstract

A Yukawa disk is a two-dimensional system of n particles interacting through a Yukawa potential (i.e., a screened Coulomb or Debye potential) with Debye length {lambda} and confined in an isotropic parabolic well where the single-particle oscillation frequency is {omega}{sub 0}. One example of a Yukawa disk is a two-dimensional complex (dusty) plasma. The emergence of bulk (macroscopic) behavior in a strongly coupled Yukawa disk is studied by considering the dependence of the normalized, squared breathing frequency {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} (i.e., the bulk modulus) on n, {lambda}, the disk radius R{sub 0}, and the nearest-neighbor distance a. An analytical expression for {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} is derived for the bulk limit, R{sub 0}>>{lambda}, with a/{lambda} finite. In the plasma regime a < or approx. {lambda}, so that each particle interacts with many other particles, {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx_equal}4 independent of a/{lambda}. In the nearest-neighbor regime a > or approx. {lambda}, short-range interactions dominate and {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx}a/{lambda}. Computational solutions of the model for n=100-3200 particles approach the theoretical bulk limit as n increases. Solutions with n=3200 and a/{lambda} between 0.25 and 0.5 are found to give the best approximation to an unbounded plasma.

- Authors:

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

- Publication Date:

- OSTI Identifier:
- 20974867

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physics of Plasmas; Journal Volume: 14; Journal Issue: 3; Other Information: DOI: 10.1063/1.2713722; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; APPROXIMATIONS; DEBYE LENGTH; INTERACTION RANGE; OSCILLATIONS; PLASMA; PLASMA WAVES; TWO-DIMENSIONAL CALCULATIONS; YUKAWA POTENTIAL

### Citation Formats

```
Sheridan, T. E.
```*Criterion for bulk behavior of a Yukawa disk*. United States: N. p., 2007.
Web. doi:10.1063/1.2713722.

```
Sheridan, T. E.
```*Criterion for bulk behavior of a Yukawa disk*. United States. doi:10.1063/1.2713722.

```
Sheridan, T. E. Thu .
"Criterion for bulk behavior of a Yukawa disk". United States.
doi:10.1063/1.2713722.
```

```
@article{osti_20974867,
```

title = {Criterion for bulk behavior of a Yukawa disk},

author = {Sheridan, T. E.},

abstractNote = {A Yukawa disk is a two-dimensional system of n particles interacting through a Yukawa potential (i.e., a screened Coulomb or Debye potential) with Debye length {lambda} and confined in an isotropic parabolic well where the single-particle oscillation frequency is {omega}{sub 0}. One example of a Yukawa disk is a two-dimensional complex (dusty) plasma. The emergence of bulk (macroscopic) behavior in a strongly coupled Yukawa disk is studied by considering the dependence of the normalized, squared breathing frequency {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} (i.e., the bulk modulus) on n, {lambda}, the disk radius R{sub 0}, and the nearest-neighbor distance a. An analytical expression for {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2} is derived for the bulk limit, R{sub 0}>>{lambda}, with a/{lambda} finite. In the plasma regime a < or approx. {lambda}, so that each particle interacts with many other particles, {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx_equal}4 independent of a/{lambda}. In the nearest-neighbor regime a > or approx. {lambda}, short-range interactions dominate and {omega}{sub br}{sup 2}/{omega}{sub 0}{sup 2}{approx}a/{lambda}. Computational solutions of the model for n=100-3200 particles approach the theoretical bulk limit as n increases. Solutions with n=3200 and a/{lambda} between 0.25 and 0.5 are found to give the best approximation to an unbounded plasma.},

doi = {10.1063/1.2713722},

journal = {Physics of Plasmas},

number = 3,

volume = 14,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}