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Attractive interaction between ions inside a quantum plasma structure

Published online by Cambridge University Press:  30 March 2015

Maxim Dvornikov
Maxim Dvornikov*
Affiliation:
Physics Faculty, National Research Tomsk State University, 36 Lenin Ave., 634050 Tomsk, Russia Institute of Physics, University of São Paulo, CP 66318, CEP 05314-970 São Paulo, SP, Brazil Pushkov Institute of Terrestrial Magnetism, Ionosphere and Radiowave Propagation (IZMIRAN), 142190 Troitsk, Moscow, Russia Nonlinear Physics Centre, Research School of Physics and Engineering, Australian National University, 2601 Canberra, ACT, Australia
*
†Email address for correspondence: maxim.dvornikov@usp.br
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Abstract

We construct the model of a quantum spherically symmetric plasma structure based on radial oscillations of ions. We suppose that ions are involved in ion-acoustic plasma oscillations. We find the exact solution of the Schrödinger equation for an ion moving in the self-consistent oscillatory potential of an ion-acoustic wave. The system of ions is secondly quantized and its ground state is constructed. Then, we consider the interaction between ions by the exchange of an acoustic wave. It is shown that this interaction can be attractive. We describe the formation of pairs of ions inside a plasma structure and demonstrate that such a plasmoid can exist in a dense astrophysical medium corresponding to the outer core of a neutron star (NS).

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 3 , June 2015 , 905810327
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Copyright
Copyright © Cambridge University Press 2015 

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References

REFERENCES

Alhaidari, A. D. 2002 Solutions of the nonrelativistic wave equation with position-dependent effective mass. Phys. Rev. A 66, 042116.CrossRefGoogle Scholar
Baiko, D. A. 2009 Coulomb crystals in the magnetic field. Phys. Rev. E 80, 046405.CrossRefGoogle ScholarPubMed
Birkl, G., Kassner, S. and Walther, H. 1992 Multiple-shell structures of laser-cooled 24Mg+ ions in a quadrupole storage ring. Nature 357, 310–313.CrossRefGoogle Scholar
Blokhintsev, D. I. 1964 Quantum Mechanics. Dordrecht: Reidel, pp. 140–141.CrossRefGoogle Scholar
Bonitz, M.et al. 2008 Classical and quantum Coulomb crystals. Phys. Plasmas 15, 055704.CrossRefGoogle Scholar
Bonitz, M., Pehlke, E. and Schoof, T. 2013 Attractive forces between ions in quantum plasmas: failure of linearized quantum hydrodynamics. Phys. Rev. E 87, 033105.CrossRefGoogle Scholar
Braaten, E. and Segel, D. 1993 Neutrino energy loss from the plasma process at all temperatures and densities. Phys. Rev. D 48, 1479–1491.CrossRefGoogle ScholarPubMed
Carstensen, J.et al. 2012 Charging and coupling of a vertically aligned particle pair in the plasma sheath. Phys. Plasmas 19, 033702.CrossRefGoogle Scholar
Chadwick, M. B.et al. 2006 ENDF/B-VII.0: Next generation evaluated nuclear data library for nuclear science and technology. Nucl. Data Sheets 107, 2931–3059.CrossRefGoogle Scholar
Chu, J. H. and I, L. 1994 Direct observation of Coulomb crystals and liquids in strongly coupled rf dusty plasmas. Phys. Rev. Lett. 72 4009–4012.CrossRefGoogle ScholarPubMed
Cohen-Tannoudji, C., Diu, B. and Laloë, F. 1977 Quantum Mechanics, Vol. 2. New York: Wiley, pp. 919–920.Google Scholar
Dawson, J. M. 1959 Nonlinear electron oscillations in a cold plasma. Phys. Rev. 113 383–387.CrossRefGoogle Scholar
Dijkhuis, G. C. 1980 A model for ball lightning. Nature 284, 150–151.CrossRefGoogle Scholar
Dvornikov, M. 2012 Effective attraction between oscillating electrons in a plasmoid via acoustic wave exchange. Proc. R. Soc. A 468, 415–428.CrossRefGoogle Scholar
Dvornikov, M. 2013 Pairing of charged particles in a quantum plasmoid. J. Phys. A: Math. Theor. 46, 045501.CrossRefGoogle Scholar
Dvornikov, M. and Dvornikov, S. 2006 Electron gas oscillations in plasma: theory and applications. In: Advances in Plasma Physics Research, Vol. 5 (ed. Gerard, F.). New York: Nova Science Publishers, pp. 197–212.Google Scholar
Gradshteyn, I. S. and Ryzhik, I. M. 2007 Table of Integrals, Series, and Products, 7th edn.Amsterdam: Elsevier.Google Scholar
Grimes, C. C. and Adams, G. 1979 Evidence for a liquid-to-crystal phase transition in a classical, two-dimensional sheet of electrons. Phys. Rev. Lett. 42 795–798.CrossRefGoogle Scholar
Haas, F. 2011 Quantum Plasmas: An Hydrodynamic Approach. New York: Springer.CrossRefGoogle Scholar
Haensel, P., Potekhin, A. Y. and Yakovlev, D. G. 2007 Neutron Stars I. Equation of State and Structure. New York: Springer, pp. 207–280.CrossRefGoogle Scholar
Hahn, S. L. 2000 Hilbert transform. In: The Transforms and Applications Handbook, 2nd edn. (ed. Poularikas, A. D.). Boca Raton, FL: CRC Press, ch. 7.10.Google Scholar
Heinke, C. O. and Ho, W. C. G. 2010 Direct observation of the cooling of the Cassiopeia a neutron star. Astrophys. J. 719, L167–L171.CrossRefGoogle Scholar
Lifshitz, E. M. and Pitaevskiĭ, L. P. 2010 Physical Kinetics. Burlington, MA: Elsevier, pp. 136–137.Google Scholar
Morfill, G. E. and Ivlev, A. V. 2009 Complex plasmas: an interdisciplinary research field. Rev. Mod. Phys. 81, 1353–1404.CrossRefGoogle Scholar
Nambu, M., Vladimirov, S. V. and Shukla, P. K. 1995 Attractive forces between charged particulates in plasmas. Phys. Lett. A 203, 40–42.CrossRefGoogle Scholar
Onsi, M. and Pearson, J. M. 2002 Equation of state of stellar nuclear matter and the effective nucleon mass. Phys. Rev. C 65, 047302.CrossRefGoogle Scholar
Sagdeev, R. Z. and Galeev, A. A. 1969 Nonlinear Plasma Theory. New York: W. A. Benjamin, Inc., pp. 37–113.Google Scholar
Schmidt, A. G. M. 2007 Time evolution for harmonic oscillators with position-dependent mass. Phys. Scr. 75, 480–483.CrossRefGoogle Scholar
Temme, N. M. 1986 Uniform asymptotic expansion for a class of polynomials biorthogonal on the unit circle. Constr. Approx. 2, 369–376.CrossRefGoogle Scholar
Vlasov, A. A. and Yakovlev, M. A. 1978 Interaction between ions through an intermediate system (neutral gas) and problem of existence of a cluster of particles maintained by its own forces: I. Theor. Math. Phys. 34, 124–130.CrossRefGoogle Scholar
Yakovlev, D. G., Levenfish, K. P. and Shibanov, Yu. A. 1999 Cooling neutron stars and superfluidity in their interiors. Phys.–Usp. 42, 737–778.CrossRefGoogle Scholar
Zelikin, M. I. 2008 Superconductivity of plasma and fireballs. J. Math. Sci. 151, 3473–3496.CrossRefGoogle Scholar