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Dust particles of finite dimensions in complex plasmas: thermodynamics and dust-acoustic wave dispersion

Published online by Cambridge University Press:  30 August 2018

A. E. Davletov Open the ORCID record for A. E. Davletov [Opens in a new window] ,
L. T. Yerimbetova ,
Yu. V. Arkhipov ,
Ye. S. Mukhametkarimov ,
A. Kissan  and
I. M. Tkachenko
A. E. Davletov*
Affiliation:
Department of Physics and Technology, Al-Farabi Kazakh National University, 71 Al-Farabi av., 050040 Almaty, Kazakhstan
L. T. Yerimbetova
Affiliation:
Department of Physics and Technology, Al-Farabi Kazakh National University, 71 Al-Farabi av., 050040 Almaty, Kazakhstan
Yu. V. Arkhipov
Affiliation:
Department of Physics and Technology, Al-Farabi Kazakh National University, 71 Al-Farabi av., 050040 Almaty, Kazakhstan
Ye. S. Mukhametkarimov
Affiliation:
Department of Physics and Technology, Al-Farabi Kazakh National University, 71 Al-Farabi av., 050040 Almaty, Kazakhstan
A. Kissan
Affiliation:
Department of Physics and Technology, Al-Farabi Kazakh National University, 71 Al-Farabi av., 050040 Almaty, Kazakhstan
I. M. Tkachenko
Affiliation:
Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain
*
†Email address for correspondence: [email protected]
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Abstract

Grounded on the premise that dust particles are charged hard balls, the analysis in Davletov et al. (Contrib. Plasma Phys., vol. 56, 2016, 308) provides an original pseudopotential model of intergrain interaction in complex (dusty) plasmas. This accurate model is engaged herein to consistently treat the finite-size effects from the process of dust particle charging to determination of the thermodynamic quantities and the dust-acoustic wave dispersion in the strongly coupled regime. The orbital motion limited approximation is adopted to evaluate an electric charge of dust grains immersed in a neutralizing background of the buffer plasma. To account for finite dimensions of dust particles, the radial distribution function is calculated within the reference hypernetted-chain (RHNC) approximation to demonstrate a well-pronounced short-range order formation at rather large values of the coupling parameter and the packing fraction. The evaluated excess pressure of the dust component is compared to the available theoretical approaches and the simulation data and is then used to predict the dust-acoustic wave (DAW) dispersion in the strongly coupled regime under the assumption that the dust particles charge varies in the course of propagation. In contrast to many previous investigations, it is demonstrated for the first time ever that for DAWs the charge variation of dust particles should necessarily be taken into account while evaluating the dust isothermal compressibility.

Keywords

dusty plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 4 , August 2018 , 905840410
Copyright
© Cambridge University Press 2018 

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References

Arkhipov, Y. V., Askaruly, A., Ballester, D., Davletov, A. E., Tkachenko, I. M. & Zwicknagel, G. 2010 Dynamic properties of one-component strongly coupled plasmas: the sum-rule approach. Phys. Rev. E 81, 026402.Google Scholar
Arkhipov, Y. V., Askaruly, A., Davletov, A. E., Dubovtsev, D. Y., Donkó, Z., Hartmann, P., Korolov, I., Conde, L. & Tkachenko, I. M. 2017 Direct determination of dynamic properties of Coulomb and Yukawa classical one-component plasmas. Phys. Rev. Lett. 119, 045001.Google Scholar
Arkhipov, Y. V., Baimbetov, F. B. & Davletov, A. E. 2003 Pseudopotential theory of a partially ionized hydrogen plasma. Contrib. Plasma Phys. 43, 258.Google Scholar
Arkhipov, Y. V., Baimbetov, F. B. & Davletov, A. E. 2005 Ionization equilibrium and equation of state of partially ionized hydrogen plasmas: pseudopotential approach in chemical picture. Phys. Plasmas 12, 082701.Google Scholar
Arkhipov, Y. V., Baimbetov, F. B., Davletov, A. E. & Ramazanov, T. S. 1999 Equilibrium properties of H-plasma. Contrib. Plasma Phys. 39, 495.Google Scholar
Avinash, K., Merlino, R. L. & Shukla, P. K. 2011 Anomalous dust temperature in dusty plasma experiments. Phys. Lett. A 375, 2854.Google Scholar
Bonitz, M., Henning, C. & Block, D. 2010 Complex plasmas: a laboratory for strong correlations. Rep. Prog. Phys. 73, 066501.Google Scholar
Castaldo, C., Ratynskaia, S., Pericoli, V., de Angelis, U., Rypdal, K., Pieroni, L., Giovannozzi, E., Maddaluno, C., Marmolino, C., Rufoloni, A. et al. 2007 Diagnostics of fast dust particles in tokamak edge plasmas. Nucl. Fusion 47, L5.Google Scholar
Daughton, W., Murillo, M. S. & Thode, L. 2000 Empirical bridge function for strongly coupled Yukawa systems. Phys. Rev. E 61, 2129.Google Scholar
Davletov, A. E., Arkhipov, Y. V. & Tkachenko, I. M. 2016 Electric charge of dust particles in a plasma. Contrib. Plasma Phys. 56, 308.Google Scholar
Davletov, A. E., Yerimbetova, L. T., Mukhametkarimov, Y. S. & Ospanova, A. K. 2014 Finite size effects in the static structure factor of dusty plasmas. Phys. Plasmas 21, 073704.Google Scholar
Delzanno, G. L. & Tang, X.-Z. 2015 Comparison of dust charging between Orbital-Motion-Limited theory and Particle-in-Cell simulations. Phys. Plasmas 22, 113703.Google Scholar
Dietz, C. & Thoma, M. H. 2016 Investigation and improvement of three-dimensional plasma crystal analysis. Phys. Rev. E 94, 033207.Google Scholar
Donkó, Z., Kalman, G. J. & Hartmann, P. 2008 Dynamical correlations and collective excitations of Yukawa liquids. J. Phys.: Condens. Matter 20, 413101.Google Scholar
Dzhumagulova, K. N., Masheeva, R. U., Ramazanov, T. S. & Donkó, Z. 2014 Effect of magnetic field on the velocity autocorrelation and the caging of particles in two-dimensional Yukawa liquids. Phys. Rev. E 89, 033104.Google Scholar
Faussurier, G. 2004 Description of strongly coupled Yukawa fluids using the variational modified hypernetted chain approach. Phys. Rev. E 69, 066402.Google Scholar
Fedoseev, A. V., Sukhinin, G. I., Abdirakhmanov, A. R., Dosbolayev, M. K. & Ramazanov, T. S. 2016 Voids in dusty plasma of a stratified DC glow discharge in noble gases. Contrib. Plasma Phys. 56, 234.Google Scholar
Filippov, A. V., Starostin, A. N., Tkachenko, I. M. & Fortov, V. E. 2011 Dust acoustic waves in complex plasmas at elevated pressure. Phys. Lett. A 376, 31.Google Scholar
Filippov, A. V., Starostin, A. N., Tkachenko, I. M., Fortov, V. E., Ballester, D. & Conde, L. 2010 Dust acoustic waves in a nonequilibrium dusty plasma. JETP Lett. 91, 558.Google Scholar
Fisher, R. & Thomas, E. 2010 Measurement of spatially resolved velocity distributions in a dusty plasma. Bull. Am. Phys. Soc. 55 (CP9 37), 79.Google Scholar
Forsberg, M., Brodin, G., Marklund, M., Shukla, P. K. & Moortgat, J. 2006 Nonlinear interactions between gravitational radiation and modified Alfvén modes in astrophysical dusty plasmas. Phys. Rev. D 74, 064014.Google Scholar
Fortov, V. E., Khrapak, A. G., Khrapak, S. A., Molotkov, V. I. & Petrov, O. F. 2004 Dusty plasmas. Phys. Uspekhi 47, 447.Google Scholar
Fortov, V. E. & Morfill, G. E. 2010 Complex and Dusty Plasmas: From Laboratory to Space. CRC Press.Google Scholar
Hamaguchi, S. & Ohta, H. 2001 Waves in strongly-coupled classical one-component plasmas and Yukawa fluids. Phys. Scr. T89, 127.Google Scholar
Heidemann, R. J., Couëdel, L., Zhdanov, S. K., Sütterlin, K. R., Schwabe, M., Thomas, H. M., Ivlev, A. V., Hagl, T., Morfill, G. E., Fortov, V. E. et al. 2011 Comprehensive experimental study of heartbeat oscillations observed under microgravity conditions in the PK-3 Plus laboratory on board the International Space Station. Phys. Plasmas 18, 053701.Google Scholar
Ivlev, A. V. & Morfill, G. 2000 Acoustic modes in a collisional dusty plasma: effect of the charge variation. Phys. Plasmas 7, 1094.Google Scholar
Ivlev, A. V., Samsonov, D., Goree, J., Morfill, G. & Fortov, V. E. 1999 Acoustic modes in a collisional dusty plasma. Phys. Plasmas 6, 741.Google Scholar
Izvekova, Y. N. & Popel, S. I. 2016 Charged dust motion in dust devils on Earth and Mars. Contrib. Plasma Phys. 56, 263.Google Scholar
Kählert, H. & Bonitz, M. 2010 How spherical plasma crystals form. Phys. Rev. Lett. 104, 015001.Google Scholar
Kalman, G., Hartmann, P., Donkó, Z., Golden, K. I. & Kyrkos, S. 2013 Collective modes in two-dimensional binary Yukawa systems. Phys. Rev. E 87, 043103.Google Scholar
Kalman, G. J., Hartmann, P., Donkó, Z. & Rosenberg, M. 2004 Two-dimensional Yukawa liquids: correlation and dynamics. Phys. Rev. Lett. 92, 065001.Google Scholar
Kang, H. S. & Ree, F. H. 1995 Applications of the perturbative hypernetted-chain equation to the one-component plasma and the one-component charged hard-sphere systems. J. Chem. Phys. 103, 9370.Google Scholar
Kaw, P. K. 2001 Collective modes in a strongly coupled dusty plasma. Phys. Plasmas 8, 1870.Google Scholar
Kaw, P. K. & Sen, A. 1998 Low frequency modes in strongly coupled dusty plasmas. Phys. Plasmas 5, 3552.Google Scholar
Keidar, M., Shashurin, A., Volotskova, O., Stepp, M. A., Srinivasan, P., Sandler, A. & Trink, B. 2013 Cold atmospheric plasma in cancer therapy. Phys. Plasmas 20, 057101.Google Scholar
Kersten, H., Deutsch, H., Stoffels, E., Stoffels, W. W., Kroesen, G. M. W. & Hippler, R. 2001 Micro-disperse particles in plasmas: from disturbing side effects to new applications. Contrib. Plasma Phys. 41, 598.Google Scholar
Khrapak, S. & Morfill, G. 2009 Basic processes in complex (dusty) plasmas: charging, interactions, and ion drag force. Contrib. Plasma Phys. 49, 148.Google Scholar
Khrapak, S. A., Khrapak, A. G., Ivlev, A. V. & Morfill, G. E. 2014 Simple estimation of thermodynamic properties of Yukawa systems. Phys. Rev. E 89, 023102.Google Scholar
Khrapak, S. A. & Morfill, G. 2001 Waves in two-component electron-dust plasma. Phys. Plasmas 8, 2629.Google Scholar
Khrapak, S. A. & Thomas, H. M. 2015a Fluid approach to evaluate sound velocity in Yukawa systems and complex plasmas. Phys. Rev. E 91, 033110.Google Scholar
Khrapak, S. A. & Thomas, H. M. 2015b Practical expressions for the internal energy and pressure of Yukawa fluids. Phys. Rev. E 91, 023108.Google Scholar
Kokura, H., Yoneda, S., Nakamura, K., Mitsuhira, N., Nakamura, M. & Sugai, H. 1999 Diagnostic of surface wave plasma for oxide etching in comparison with inductive RF plasma. Japan J. Appl. Phys. 38, 5256.Google Scholar
Kundrapu, M. & Keidar, M. 2012 Numerical simulation of carbon arc discharge for nanoparticle synthesis. Phys. Plasmas 19, 073510.Google Scholar
Kundu, M., Avinash, K., Sen, A. & Ganesh, R. 2014 On the existence of vapor–liquid phase transition in dusty plasmas. Phys. Plasmas 21, 103705.Google Scholar
Lado, F. 1973 Perturbation correction for the free energy and structure of simple fluids. Phys. Rev. A 8, 2548.Google Scholar
Lado, F. 1976 Charged hard spheres in a uniform neutralizing background using mixed integral equations. Mol. Phys. 31, 1117.Google Scholar
Lado, F. 1982 A local thermodynamic criterion for the reference-hypernetted-chain equation. Phys. Lett. A 89, 196.Google Scholar
Lado, F., Foiles, S. M. & Ashcroft, N. W. 1983 Solutions of the reference-hypernetted-chain equation with minimized free energy. Phys. Rev. A 28, 2374.Google Scholar
Malmrose, M. P., Marscher, A. P., Jorstad, S. G., Nikutta, R. & Elitzur, M. 2011 Emission from hot dust in the infrared spectra of gamma-ray bright blazars. Astrophys. J. 732, 116.Google Scholar
Mamun, A. A., Shukla, P. K. & Farid, T. 2000 Low-frequency electrostatic dust-modes in a strongly coupled dusty plasma with dust charge fluctuations. Phys. Plasmas 7, 2329.Google Scholar
Meijer, E. J. & Frenkel, D. 1991 Melting line of Yukawa system by computer simulation. J. Chem. Phys. 94, 2269.Google Scholar
Momot, A. I., Zagorodny, A. G. & Orel, I. S. 2017 Interaction force between two finite-size charged particles in weakly ionized plasma. Phys. Rev. E 95, 013212.Google Scholar
Murillo, M. S. 1998 Static local field correction description of acoustic waves in strongly coupling dusty plasmas. Phys. Plasmas 5, 3116.Google Scholar
Ohta, H. & Hamaguchi, S. 2000 Wave dispersion relations in Yukawa fluids. Phys. Rev. Lett. 84, 6026.Google Scholar
Ostrikov, K. N., Vladimirov, S. V., Yu, M. Y. & Morfill, G. E. 2000 Dust-acoustic wave instabilities in collisional plasmas. Phys. Rev. E 61, 4315.Google Scholar
Ott, T., Bonitz, M., Stanton, L. G. & Murillo, M. S. 2014 Coupling strength in Coulomb and Yukawa one-component plasmas. Phys. Plasmas 21, 113704.Google Scholar
Piel, A. 2017 Plasma crystals: experiments and simulation. Plasma Phys. Control. Fusion 59, 014001.Google Scholar
Quinn, R. A. & Goree, J. 2000 Single-particle Langevin model of particle temperature in dusty plasmas. Phys. Rev.  E 61, 3033.Google Scholar
Rosenberg, M. & Kalman, G. 1997 Dust acoustic waves in strongly coupled dusty plasmas. Phys. Rev. E 56, 7166.Google Scholar
Rosenfeld, Y. 1986 Comments on the variational modified-hypernetted-chain theory for simple fluids. J. Stat. Phys. 42, 437.Google Scholar
Rosenfeld, Y. & Ashcroft, N. 1979 Theory of simple classical fluids: universality in the short-range structure. Phys. Rev. A 20, 1208.Google Scholar
Seok, J. Y., Koo, B.-C. & Hirashita, H. 2015 Dust cooling in supernova remnants in the large Magellanic cloud. Astrophys. J. 807, 100.Google Scholar
Shukla, P. K. & Eliasson, B. 2009 Fundamentals of dust-plasma interactions. Rev. Mod. Phys. 81, 25.Google Scholar
Szetsen, L., Hsiu-Feng, C. & Chien-Ju, C. 2007 Spectroscopic study of carbonaceous dust particles grown in benzene plasma. J. Appl. Phys. 101, 113303.Google Scholar
Tang, X.-Z. & Delzanno, G. L. 2014 Orbital-motion-limited theory of dust charging and plasma response. Phys. Plasmas 21, 123708.Google Scholar
Tejero, C. F., Lutsko, J. F., Colot, J. L. & Baus, M. 1992 Thermodynamic properties of the fluid, fcc, and bcc phases of monodisperse charge-stabilized colloidal suspensions within the Yukawa model. Phys. Rev. A 46, 3373.Google Scholar
Tolias, P., Ratynskaia, S., De Angeli, M., De Temmerman, G., Ripamonti, D., Riva, G., Bykov, I., Shalpegin, A., Vignitchouk, L., Brochard, F. et al. 2016 Dust remobilization in fusion plasmas under steady state conditions. Plasma Phys. Control. Fusion 58, 025009.Google Scholar
Tolias, P., Ratynskaia, S. & De Angelis, U. 2014 Soft mean spherical approximation for dusty plasma liquids: one-component Yukawa systems with plasma shielding. Phys. Rev. E 90, 053101.Google Scholar
Vaulina, O. S., Vladimirov, S. V., Petrov, O. F. & Fortov, V. E. 2002 Criteria for phase-transitions in Yukawa systems (dusty plasma). AIP Conf. Proc. 649, 471.Google Scholar
Walk, R. M., Snyder, J. A., Scrinivasan, P., Kirch, J., Diaz, S. O., Blanco, F. C., Shashurin, A., Keidar, M. & Sandler, A. D. 2013 Cold atmospheric plasma for the ablative treatment of neuroblastoma. J. Pediatr. Surg. 48, 67.Google Scholar
Wertheim, M. S. 1963 Exact solution of the Percus–Yevick integral equation for hard spheres. Phys. Rev. Lett. 10, 321.Google Scholar
Whipple, E. C. 1981 Potentials of surfaces in space. Rep. Prog. Phys. 44, 1197.Google Scholar
Xie, B. S. & Yu, M. Y. 2000a Dust acoustic waves in strongly coupled dissipative plasmas. Phys. Rev. E 62, 8501.Google Scholar
Xie, B. S. & Yu, M. Y. 2000b Dust-acoustic waves in strongly coupled plasmas with variable dust charge. Phys. Plasmas 7, 3137.Google Scholar
Yazdi, A., Ivlev, A., Khrapak, S., Thomas, H., Morfill, G. E., Löwen, H., Wysocki, A. & Sperl, M. 2014 Glass-transition properties of Yukawa potentials: from charged point particles to hard spheres. Phys. Rev. E 89, 063105.Google Scholar