Skip to main content
SpringerLink
Log in

Relevance of the Wigner–Seitz Cell Approximation for the Coulomb Clusters

  • DUSTY PLASMA
  • Published:
Plasma Physics Reports Aims and scope Submit manuscript

Abstract

A molecular dynamics simulation of a system of massive charged particles on a compensating homogeneous background confined by a spherical surface has been carried out. A crystallized cluster is a set of nested spherical shells of almost the same structure and a core. It is shown that cluster melting is a combination of shell and core melting. It is found that the values of the Coulomb coupling parameter Γ corresponding to these two types of melting do not depend on the cluster size. Methods for determining Γ based on the Wigner–Seitz cell model are discussed. It is shown that the estimate based on the root-mean-square deviation of a particle from the center of its cell is unreliable due to the self-diffusion of particles. A relation is proposed that defines Γ in terms of the root-mean-square velocity and acceleration of the particle and does not include the root-mean-square deviation of the particle from its average position. It is shown that this relation is satisfied with high accuracy not only for the crystallized, but also for the liquid state. Thus, it has been demonstrated that the Wigner–Seitz cell model is applicable to the strongly inhomogeneous system under consideration.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.

REFERENCES

  1. W. L. Slattery, G. D. Doolen, and H. E. DeWitt, Phys. Rev. A: At., Mol., Opt. Phys. 21, 2087 (1980). https://doi.org/10.1103/PhysRevA.21.2087

    Article  ADS  Google Scholar 

  2. S. Hamaguchi, R. T. Farouki, and D. H. E. Dubin, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 56, 4671 (1997). https://doi.org/10.1103/PhysRevE.56.4671

    Article  Google Scholar 

  3. Complex and Dusty Plasmas, Ed. by V. E. Fortov and G. E. Morfill (CRC, Boca Raton, FL, 2010).

    Google Scholar 

  4. O. Arp, D. Block, M. Klindworth, and A. Piel, Phys. Plasmas 12, 122102 (2005). https://doi.org/10.1063/1.2147000

  5. O. Arp, D. Block, M. Bonitz, H. Fehske, V. Golubnychiy, S. Kosse, P. Ludwig, A. Melzer, and A. Piel, J. Phys.: Conf. Ser. 11, 234 (2005). https://doi.org/10.1088/1742-6596/11/1/023

    Article  ADS  Google Scholar 

  6. S. Käding and A. Melzer, Phys. Plasmas 13, 090701 (2006). https://doi.org/10.1063/1.2354149

  7. D. Block, S. Käding, A. Melzer, A. Piel, H. Baumgartner, and M. Bonitz, Phys. Plasmas 15, 040701 (2008). https://doi.org/10.1063/1.2903549

  8. O. Arp, D. Block, A. Piel, and A. Melzer. Phys. Rev. Lett. 93, 165004 (2004). https://doi.org/10.1103/PhysRevLett.93.165004

  9. H. Totsuji, T. Ogawa, C. Totsuji, and K. Tsuruta, J. Phys. A: Math. Gen. 39, 4545 (2006). https://doi.org/10.1088/0305-4470/39/17/S36

    Article  ADS  Google Scholar 

  10. S. W. S. Apolinario, J. Albino Aguiar, and F. M. Peeters, Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys. 90, 063113 (2014). https://doi.org/10.1103/PhysRevE.90.063113

  11. D. J. Wineland, J. C. Bergquist, W. M. Itano, J. J. Bollin-ger, and C. H. Manney, Phys. Rev. Lett. 59, 2935 (1987). https://doi.org/10.1103/PhysRevLett.59.2935

    Article  ADS  Google Scholar 

  12. D. H. E. Dubin and T. M. O’Neil, Rev. Mod. Phys. 71, 87 (1999).

    Article  ADS  Google Scholar 

  13. D. I. Zhukhovitskii, V. N. Naumkin, A. I. Khusnulgatin, V. I. Molotkov, and A. M. Lipaev, Phys. Rev. E 96, 043204 (2017). https://doi.org/10.1103/PhysRevE.96.043204

  14. D. A. Baiko, D. G. Yakovlev, H. E. De Witt, and W. L. Slattery, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 61, 1912 (2000). https://doi.org/10.1103/PhysRevE.61.1912

    Article  Google Scholar 

  15. A. I. Chugunov and D. A. Baiko, Phys. A 352, 397 (2005). https://doi.org/10.1016/j.physa.2005.01.005

    Article  Google Scholar 

Download references

Funding

This research is supported by the Russian Science Foundation, Grant no. 20-12-00365.

Author information

Authors and Affiliations

  1. Joint Institute for High Temperatures, Russian Academy of Sciences, 125412, Moscow, Russia

    E. S. Shpil’ko & D. I. Zhukhovitskii

  2. Moscow Institute of Physics and Technology (National Research University), 141701, Dolgoprudny, Moscow oblast, Russia

    E. S. Shpil’ko & D. I. Zhukhovitskii

Authors
  1. E. S. Shpil’ko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. I. Zhukhovitskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. I. Zhukhovitskii.

Ethics declarations

The authors declare that they have no conflicts of interest.

Additional information

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shpil’ko, E.S., Zhukhovitskii, D.I. Relevance of the Wigner–Seitz Cell Approximation for the Coulomb Clusters. Plasma Phys. Rep. 49, 1207–1213 (2023). https://doi.org/10.1134/S1063780X23600937

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1063780X23600937

Keywords:

Search

Navigation