Method of integral equations for dust particles of finite size

  • L.T. Yerimbetova Al Farabi Kazakh National University, Kazakstan, Almaty

Abstract

In this paper we make use of the earlier proposed pseudopotential model of interaction of dusty plasma particles, which correctly takes into account the finite size of the dust particles in the framework of classical plasma electrodynamics in the random-phase approximation. The potential thus constructed differs significantly from the widely used Yukawa (Debye-Hückel) potential at sufficiently large values ​​of the screening parameter, which is explained by the engagement of different boundary conditions at the surface of dust particles. The proposed pseudopotential model is applied to determine the radial distribution functions and the static structural factors of dust particles by the method of integral equations. In particular, the Ornstein-Zernike relation in the hypernetted-chain approximation with the bridge functions for the point-like particles is numerically solved. Since the dimensions of the dust particles are assumed to be finite, the calculations are also carried out within the framework of the combined method of integral equations, which is based on the determination of the correlation functions for the system of hard spheres within the Percus-Yevick equation with further transition to a model of solid charged balls studied within the modified hypernetted-chain approximation. The results show that at high packing fractions, the radial distribution functions and the static structural factors exhibit more significant peaks in comparison with the simple Ornstein-Zernike relation in the hypernetted-chain approximation, which indicates the formation of short-range and long-range orders in the arrangement of dust particles at rather large values of their coupling.

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References
1 V.E. Fortov and G.E. Morfill, Complex and Dusty Plasmas: From Laboratory to Space (CRC Press, Florida, USA, 2010), 440 p.
2 M. Bonitz and N. Horing, P. Ludwig, Introduction to Complex Plasmas (Springer Publishing, New York, 2010), 450 p.
3 S. Khrapak and G. Morfill, Contrib. Plasma Phys. 49, 148-168, (2009).
4 P.K. Shukla and B. Eliasson, Rev. Mod. Phys. 81, 25-44, (2009).
5 V.N. Tsytovich, J. Phys. A: Math. Gen. 39, 4501-4509, (2006).
6 A. Piel, Plasma Phys. Control. Fusion 59, 014001, (2017).
7 C. Dietz and M.H. Thoma, Phys. Rev. E. 94, 033207, (2016).
8 H. Khlert and M. Bonitz, Phys. Rev. Lett. 104, 015001, (2010).
9 P.K. Shukla, Phys. Plasmas 8, 1791-1803, (2001).
10 V.E. Fortov, A.G. Khrapak, S.A. Khrapak, V.I. Molotkov, and O.F. Petrov, Physics-Uspekhi 47, 447-492 (2004).
11 J.Y. Seok, B.C. Koo and H. Hirashita, Astrophys. J. 807, 100-106, (2015).
12 A.V. Fedoseev, G.I. Sukhinin, A.R. Abdirakhmanov, M.K. Dosbolayev and T.S. Ramazanov, Contrib. Plasma Phys. 56, 234-239, (2016).
13 P. Tolias, S. Ratynskaia, M. de Angeli, G. de Temmerman, D. Ripamonti, G. Riva, I. Bykov, A. Shalpegin, L.Vignitchouk, F. Brochard, K. Bystrov, S. Bardin, and A. Litnovsky, Plasma Phys. Control. Fusion 58, 025009, (2016).
14 C. Castaldo, S. Ratynskaia, V. Pericolli, U. de Angelis, K. Rypdal, L. Pieroni, E. Giovannozzi, G. Mad-dalu no, C. Marmolino, A. Rufoloni, A. Tuccillo, M. Kretschmer and G.E. Morfill, Nucl. Fusion 47, L5-L9, (2007).
15 M. Keidar, A. Shashurin, O. Volotskova, M.A. Stepp, P. Srinivasan, A. Sandler and B. Trink, Phys. Plasmas 20, 057101, (2013).
16 R.M. Walk, J.A. Snyder, P. Scrivasan, J. Kirch, S.O. Diaz, F.C. Blanco, A. Shashurin, M. Keidar and A.D. Sandler, J. Pediatr. Surg. 48, 67-73, (2013).
17 R. Yousefi, A.B. Davis, J. Carmona-Reyes, L.S. Matthews, and T.W. Hyde, Phys. Rev. E. 90, 033101, (2014).
18 T.S. Ramazanov, N.Kh. Bastykova, Y.A. Ussenov, S.K. Kodanova, K.N. Dzhumagulova, and M.K. Dosbolayev, Contrib. Plasma Phys. 52, 110-113, (2012).
19 M. Bonitz, C. Henning, and D. Block, Rep. Prog. Phys. 73, 066501, (2010).
20 G. Kalman, P. Hartmann, Z. Donko, K.J. Golden, and S. Kyrkos, Phys. Rev. E. 87, 043103, (2013).
21 S.A. Khrapak and H.M. Thomas, Phys. Rev. E. 91, 033110, (2015).
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23 A.E. Davletov, Yu.V. Arkhipov, and I.M. Tkachenko, Contrib. Plasma Phys. 56, 308 (2016).
24 H. Iyetomi, S. Ogata, and S. Ichimaru, Phys. Rev. A 46, 1051, (1992).
25 W. Daughton, M.S. Murillo, and L. Thode, Phys. Rev. E. 61, 2129, (2000).
26 M.S. Wertheim, Phys. Rev. Lett. 10, 8, 321, (1963).
27 F. Lado Mol. Phys. 31, 1117, (1976).
28 F. Lado, S. Foiles, and N.W. Ashcroft, Phys. Rev. A. 28, 2374, (1983).
29 Y. Rosenfeld, J. Stat. Phys. 42, 437, (1986).
Published
2018-04-02
How to Cite
YERIMBETOVA, L.T.. Method of integral equations for dust particles of finite size. Recent Contributions to Physics (Rec.Contr.Phys.), [S.l.], v. 62, n. 3, p. 40-49, apr. 2018. ISSN 1563-0315. Available at: <http://bph.kaznu.kz/index.php/zhuzhu/article/view/557>. Date accessed: 22 july 2018.

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