Dynamic collision frequency of Kelbg-pseudopotential-modelled plasmas
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Keywords:
strongly coupled plasma, method of moments with local constraints, sum rule, Nevanlinna function, dynamic collision frequency.Abstract
The simulation data [1,2] on the dynamic collision frequency (DCF) of hydrogen-like plasmas modelled with the Kelbg pseudopotential are treated within the theory of moments with local constraints. Additionally, the correlational sum rule which is the second power frequency moment of the external conductivity real part is taken into account to express the DCF in terms of the Nevanlinna parameter function. The validity of the suggetsed analytic form of the latter is tested against the simulation data, while the sum rules are calculated using the Kelbg potential and the Ornstein-Zernike hypernetted-chain equations.References
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2. Morozov I., Reinholz H., Ropke G., Wierling A. and Zwicknagel G. Molecular dynamics simulations of optical conductivity of dense plasmas
// Phys. Rev. E. – 2005. – Vol. 71. – P. 066408.
3. Arkhipov Yu.V., Askaruly A., Ballester D., Davletov А.Е., Meirkanova G.M., Tkachenko I.M. Collective and static properties of model two
component plasmas // Phys. Rev. E. – 2007. – Vol. 76. – P. 026403(9).
4. Arkhipov, Yu.V., Askaruly, A., Ballester, D., Davletov, A.E., Tkachenko, I.M., Zwicknagel, G. Dynamic properties of one-component stronglyYu.V.Arkhipov et all. International Journal of mathematics and physics 4, №2 (2013)49coupled plasmas: the moment approach // Phys.
Rev. E. – 2010. – Vol. 81. – P. 026402-1–9.5. Tkachenko I.M., rkhipov Yu.V., Askaruly A. The method of moments and its applications inplasma physics. – Germany: Lap Lambert AcademicPublishing. – 2012. –125 р.
6. Adamyan V.M. and Tkachenko I.M. Solution of the Truncated amburger Moment Problem According to M.G. Krein // Operator Theory: Advances and Applications. – 2000. – OT-118. – P. 33.
7. Krein M.G., Nudel'man A.A. The Markov moment problem and extremal problems. –Moscow: Nauka. – 1973. – P. 552.
8. Adamyan V., Alcober J., and Tkachenko I.,Applied Mathematics Research eXpress. – 2003. –Vol. 33. – P. 70.
9. Arkhipov Yu.V., Askaruly A., Davletov А.Е., Tkachenko I.M. Dynamic properties of onecomponent moderately coupled plasmas: the mixed
Lowner-Nevanlinna-Pick approach // Contrib. Plasma Phys. - 2010. – Vol. 50. - P. 69-76.
10. Ichimaru S. Nuclear fusion in dense plasmas // Rev. Mod. Phys. – 1993. – Vol. 65. – P. 255–299.
11. Dubin D.H.E. and O’Neill T.M. Trapped nonneutral plasmas, liquids, and crystals (the thermal equilibrium states) // Rev. Mod. Phys. –
1999. – Vol. 71. – P.87–172.
12. Adamyan V.M., Tkachenko I.M. Truncated Hamburger matrix moment problems with constraints // Proc. Appl. Math. Mech. – 2001. –
Vol. 1. – P. 420-421.
13. Akhiezer N.I., The classical moment problem and some related questions in analysis. – N.Y.: Hafner Publishing Company, 1965.– 253 p.
14. Khargonekar P., Tannenbaum A., Noneuclidian metrics and the robust stabilization of systems with parameter uncertainty, IEEE Trans.
Automat. Contr. – 1985. – Vol. 30. – P. 1005 -1013.
15. Tkachenko I.M., Urrea M., Determination of the adjustable moment model parameter by the minimization of t he Shannon entropy, Z. Angew.
Math. Mech. – 1999. – Vol. 79. – № 3. – P. 789-790.
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Arkhipov, Y. V., Ashikbayeva, A. B., Askaruly, A., & Tkachenko, I. M. (2013). Dynamic collision frequency of Kelbg-pseudopotential-modelled plasmas. International Journal of Mathematics and Physics, 4(2), 44–49. Retrieved from https://ijmph.kaznu.kz/index.php/kaznu/article/view/76
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Theoretical Physics and Plasma Physics
