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A simple analytical model of the Coulomb cluster in a cylindrically symmetric parabolic trap

  • Plasma Investigations
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High Temperature Aims and scope

Abstract

A cluster consisting of classical charged particles of the same sign in a cylindrically symmetric parabolic trap is considered in the approximation of a homogeneous distribution of particles over the cluster volume and with neglect of its discrete structure. Simple analytical expressions for the cluster size and potential energy in a trap of arbitrary anisotropy (the ratio of confining forces acting in the radial and axial directions) are obtained. The influence of possible inhomogeneity in the distribution of particles is estimated, and it is established that this factor weakly influences the potential energy of a cluster. The limiting case of a twodimensional cluster is considered. The adopted approximation is valid for clusters with a sufficiently large numbers of particles. Application of the model to relatively small clusters is possible by introducing correction factors into the analytical expressions obtained. These factors are determined based on approximation of the results of numerical simulations.

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References

  1. Thomson, J.J., Electricity and Matter, New York: Charles Scribner’s Sons, 1904.

    MATH  Google Scholar 

  2. Dubin, D.H.E. and O’Neil, T.M., Rev. Mod. Phys., 1999, vol. 71, no. 1, p. 87.

    Article  ADS  Google Scholar 

  3. Davidson, R.C., Physics of Nonneutral Plasmas, London: Imperial College Press, 2001.

    Book  Google Scholar 

  4. Gianetta, R.W. and Ikezi, H., Surf. Sci., 1982, vol. 113, nos. 1–3, p. 405.

    ADS  Google Scholar 

  5. Rousseau, E., Ponarin, D., Hristakos, L., Avenel, O., Varoquaux, E., and Mukharsky, Y., Phys. Rev. B, 2009, vol. 79, p. 045406.

    Article  ADS  Google Scholar 

  6. Ashoori, R.C., Nature (London), 1996, vol. 379, no. 6564, p. 413.

    Article  ADS  Google Scholar 

  7. Golosovsky, M., Saado, Y., and Davidov, D., Phys. Rev. E, 2002, vol. 65, p. 061405.

    Article  ADS  Google Scholar 

  8. Complex and Dusty Plasmas: From Laboratory to Space (Series in Plasma Physics and Fluid Dynamics), Fortov, V.E. and Morfill, G.E., Eds., Boca Raton, Florida, United States: CRC Press, 2009.

  9. Filippov, A., Pylevaya Plazma s vneshnim istochnikom ionizatsii gaza (Dusty Plasma with an External Source of Gas Ionization), Saarbrücken, Germany: Palmarium, 2012.

    Google Scholar 

  10. Andryushin, I.I., Vladimirov, V.I., Deputatova, L.V., Zherebtsov, V.A., Meshakin, V.I., Prudnikov, P.I., and Rykov, V.A., High Temp., 2014, vol. 52, no. 3, p. 337.

    Article  Google Scholar 

  11. Bystrenko, O. and Zagorodny, A., Phys. Rev. E, 2003, vol. 67, p. 066403.

    Article  ADS  Google Scholar 

  12. Khrapak, S.A., Morfill, G.E., Khrapak, A.G., and D’yachkov, L.G., Phys. Plasmas, 2006, vol. 13, no. 5, p. 052114.

    Article  ADS  Google Scholar 

  13. Paul, W., Nobel Lecture, Stockholm, Sweden: Nobel Foundation, 1989.

    Google Scholar 

  14. Lapitskii, D.S., Filinov, V.S., Deputatova, L.V., Vasilyak, L.M., Vladimirov, V.I., and Pecherkin, V.Ya., High Temp., 2015, vol. 53, no. 1, p. 1.

    Article  Google Scholar 

  15. Gilbert, S.L., Bollinger, J.J., and Wineland, D.J., Phys. Rev. Lett., 1988, vol. 60, no. 20, p. 2022.

    Article  ADS  Google Scholar 

  16. Savin, S.F., D’yachkov, L.G., Myasnikov, M.I., Petrov, O.F., Vasiliev, M.M., Fortov, V.E., Kaleri, A.Yu., Borisenko, A.I., and Morfill, G.E., JETP Lett., 2011, vol. 94, no. 7, p. 508.

    Article  ADS  Google Scholar 

  17. Petrov, O.F., Myasnikov, M.I., D’yachkov, L.G., Vasiliev, M.M., Fortov, V.E., Savin, S.F., Kaleri, A.Yu., Borisenko, A.I., and Morfill, G.E., Phys. Rev. E, 2012, vol. 86, p. 036404.

    Article  ADS  Google Scholar 

  18. Rafac, R., Schiffer, J.P., Hangst, J.S., Dubin, D.H.E., and Wales, D.J., Proc. Natl. Acad. Sci. USA, 1991, vol. 88, no. 2, p. 483.

    Article  ADS  Google Scholar 

  19. Hasse, R.W. and Avilov, V.V., Phys. Rev. A, 1991, vol. 44, no. 7, p. 4506.

    Article  ADS  Google Scholar 

  20. Totsuji, H., Kishimoto, T., Totsuji, C., and Tsuruta, K., Phys. Rev. Lett., 2002, vol. 88, p. 125002.

    Article  ADS  Google Scholar 

  21. Schiffer, J.P., Phys. Rev. Lett., 2002, vol. 88, p. 205003.

    Article  ADS  Google Scholar 

  22. Bedanov, V.M. and Peeters, F.M., Phys. Rev. B, 1994, vol. 49, no. 4, p. 2667.

    Article  ADS  Google Scholar 

  23. Nelissen, K., Matulis, A., Partoens, B., Kong, M., and Peeters, F.M., Phys. Rev. E, 2006, vol. 73, p. 016607.

    Article  ADS  Google Scholar 

  24. Rancova, O., Anisimovas, E., and Varanavicius, T., Phys. Rev. E, 2011, vol. 83, p. 036409.

    Article  ADS  Google Scholar 

  25. Dubin, D.H.E., Phys. Rev. A, 2013, vol. 88, p. 013403.

    Article  ADS  Google Scholar 

  26. Schiffer, J.P., Phys. Rev. Lett., 1993, vol. 70, no. 6, p. 818.

    Article  ADS  Google Scholar 

  27. Dubin, D.H.E., Phys. Rev. Lett., 1993, vol. 71, no. 17, p. 2753.

    Article  ADS  Google Scholar 

  28. Cornelissens, Y.G., Partoens, B., and Peters, F.M., Physica E (Amsterdam), 2000, vol. 8, no. 4, p. 314.

    Article  ADS  Google Scholar 

  29. Kamimura, T., Suga, Y., and Ishihara, O., Phys. Plasmas, 2007, vol. 14, p. 123706.

    Article  ADS  Google Scholar 

  30. Apolinario, S.W.S., Partoens, B., and Peeters, F.M., Phys. Rev. B, 2008, vol. 77, p. 035321.

    Article  ADS  Google Scholar 

  31. Hyde, T.W., Kong, J., and Matthews, L.S., Phys. Rev. E, 2013, vol. 87, p. 053106.

    Article  ADS  Google Scholar 

  32. D’yachkov, L.G., Myasnikov, M.I., Petrov, O.F., Hyde, T.W., Kong, J., and Matthews, L., Phys. Plasmas, 2014, vol. 21, p. 093702.

    Article  ADS  Google Scholar 

  33. Turner, L., Phys. Fluids, 1987, vol. 30, no. 10, p. 3196.

    Article  ADS  MATH  Google Scholar 

  34. Landau, L.D. and Lifshitz, E.M., Course of Theoretical Physics: Volume 2. The Classical Theory of Fields, Oxford: Butterworth–Heinemann, 1991.

    Google Scholar 

  35. Antonov, V.A., Nikiforov, I.I., and Kholshevnikov, K.V., Elementy teorii gravitatsionnogo potentsiala i nekotorye sluchai ego yavnogo vyrazheniya (Elements of the Theory of the Gravitational Potential and Some Cases of Its Explicit Expression), St. Petersburg: St. Petersburg State University, 2008.

    Google Scholar 

  36. Calvo, F. and Yurtsever, E., Eur. Phys. J. D, 2007, vol. 44, no. 1, p. 81.

    Article  ADS  Google Scholar 

  37. D’yachkov, L.G., Tech. Phys. Lett., 2015, vol. 41, no. 6, p. 602.

    Article  ADS  Google Scholar 

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Authors and Affiliations

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

    L. G. D’yachkov

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  1. L. G. D’yachkov
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Correspondence to L. G. D’yachkov.

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Original Russian Text © L.G. D’yachkov, 2015, published in Teplofizika Vysokikh Temperatur, 2015, Vol. 53, No. 5, pp. 649–657.

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D’yachkov, L.G. A simple analytical model of the Coulomb cluster in a cylindrically symmetric parabolic trap. High Temp 53, 613–621 (2015). https://doi.org/10.1134/S0018151X15050107

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