# Two-dimensional and three-dimensional Coulomb clusters in parabolic traps

## Abstract

We consider the shell structure of Coulomb clusters in an axially symmetric parabolic trap exhibiting a confining potential U{sub c}(ρ,z)=(mω{sup 2}/2)(ρ{sup 2}+αz{sup 2}). Assuming an anisotropic parameter α = 4 (corresponding to experiments employing a cusp magnetic trap under microgravity conditions), we have calculated cluster configurations for particle numbers N = 3 to 30. We have shown that clusters with N ≤ 12 initially remain flat, transitioning to three-dimensional configurations as N increases. For N = 8, we have calculated the configurations of minimal potential energy for all values of α and found the points of configuration transitions. For N = 13 and 23, we discuss the influence of both the shielding and anisotropic parameter on potential energy, cluster size, and shell structure.

- Authors:

- Joint Institute for High Temperatures, Russian Academy of Sciences, Moscow 125412 (Russian Federation)
- (State University), Dolgoprudny 141700, Moscow Region (Russian Federation)
- (CASPER), Baylor University, Waco, Texas 76798-7310 (United States)
- Center for Astrophysics, Space Physics, and Engineering Research (CASPER), Baylor University, Waco, Texas 76798-7310 (United States)

- Publication Date:

- OSTI Identifier:
- 22303669

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; AXIAL SYMMETRY; CONFIGURATION; CUSPED GEOMETRIES; NITROGEN 13; POTENTIAL ENERGY; POTENTIALS; SHIELDING; THREE-DIMENSIONAL CALCULATIONS; TRAPS; TWO-DIMENSIONAL CALCULATIONS

### Citation Formats

```
D'yachkov, L. G., E-mail: dyachk@mail.ru, Myasnikov, M. I., E-mail: miasnikovmi@mail.ru, Petrov, O. F., Moscow Institute of Physics and Technology, Center for Astrophysics, Space Physics, and Engineering Research, Hyde, T. W., Kong, J., and Matthews, L.
```*Two-dimensional and three-dimensional Coulomb clusters in parabolic traps*. United States: N. p., 2014.
Web. doi:10.1063/1.4885637.

```
D'yachkov, L. G., E-mail: dyachk@mail.ru, Myasnikov, M. I., E-mail: miasnikovmi@mail.ru, Petrov, O. F., Moscow Institute of Physics and Technology, Center for Astrophysics, Space Physics, and Engineering Research, Hyde, T. W., Kong, J., & Matthews, L.
```*Two-dimensional and three-dimensional Coulomb clusters in parabolic traps*. United States. doi:10.1063/1.4885637.

```
D'yachkov, L. G., E-mail: dyachk@mail.ru, Myasnikov, M. I., E-mail: miasnikovmi@mail.ru, Petrov, O. F., Moscow Institute of Physics and Technology, Center for Astrophysics, Space Physics, and Engineering Research, Hyde, T. W., Kong, J., and Matthews, L. Mon .
"Two-dimensional and three-dimensional Coulomb clusters in parabolic traps". United States. doi:10.1063/1.4885637.
```

```
@article{osti_22303669,
```

title = {Two-dimensional and three-dimensional Coulomb clusters in parabolic traps},

author = {D'yachkov, L. G., E-mail: dyachk@mail.ru and Myasnikov, M. I., E-mail: miasnikovmi@mail.ru and Petrov, O. F. and Moscow Institute of Physics and Technology and Center for Astrophysics, Space Physics, and Engineering Research and Hyde, T. W. and Kong, J. and Matthews, L.},

abstractNote = {We consider the shell structure of Coulomb clusters in an axially symmetric parabolic trap exhibiting a confining potential U{sub c}(ρ,z)=(mω{sup 2}/2)(ρ{sup 2}+αz{sup 2}). Assuming an anisotropic parameter α = 4 (corresponding to experiments employing a cusp magnetic trap under microgravity conditions), we have calculated cluster configurations for particle numbers N = 3 to 30. We have shown that clusters with N ≤ 12 initially remain flat, transitioning to three-dimensional configurations as N increases. For N = 8, we have calculated the configurations of minimal potential energy for all values of α and found the points of configuration transitions. For N = 13 and 23, we discuss the influence of both the shielding and anisotropic parameter on potential energy, cluster size, and shell structure.},

doi = {10.1063/1.4885637},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 9,

volume = 21,

place = {United States},

year = {2014},

month = {9}

}