Skip to main content Accessibility help

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

  • A. E. Davletov (a1), L. T. Yerimbetova (a1), Yu. V. Arkhipov (a1), Ye. S. Mukhametkarimov (a1), A. Kissan (a1) and I. M. Tkachenko (a2)...


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.


Corresponding author

Email address for correspondence:


Hide All
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.
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.
Arkhipov, Y. V., Baimbetov, F. B. & Davletov, A. E. 2003 Pseudopotential theory of a partially ionized hydrogen plasma. Contrib. Plasma Phys. 43, 258.
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.
Arkhipov, Y. V., Baimbetov, F. B., Davletov, A. E. & Ramazanov, T. S. 1999 Equilibrium properties of H-plasma. Contrib. Plasma Phys. 39, 495.
Avinash, K., Merlino, R. L. & Shukla, P. K. 2011 Anomalous dust temperature in dusty plasma experiments. Phys. Lett. A 375, 2854.
Bonitz, M., Henning, C. & Block, D. 2010 Complex plasmas: a laboratory for strong correlations. Rep. Prog. Phys. 73, 066501.
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.
Daughton, W., Murillo, M. S. & Thode, L. 2000 Empirical bridge function for strongly coupled Yukawa systems. Phys. Rev. E 61, 2129.
Davletov, A. E., Arkhipov, Y. V. & Tkachenko, I. M. 2016 Electric charge of dust particles in a plasma. Contrib. Plasma Phys. 56, 308.
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.
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.
Dietz, C. & Thoma, M. H. 2016 Investigation and improvement of three-dimensional plasma crystal analysis. Phys. Rev. E 94, 033207.
Donkó, Z., Kalman, G. J. & Hartmann, P. 2008 Dynamical correlations and collective excitations of Yukawa liquids. J. Phys.: Condens. Matter 20, 413101.
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.
Faussurier, G. 2004 Description of strongly coupled Yukawa fluids using the variational modified hypernetted chain approach. Phys. Rev. E 69, 066402.
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.
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.
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.
Fisher, R. & Thomas, E. 2010 Measurement of spatially resolved velocity distributions in a dusty plasma. Bull. Am. Phys. Soc. 55 (CP9 37), 79.
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.
Fortov, V. E., Khrapak, A. G., Khrapak, S. A., Molotkov, V. I. & Petrov, O. F. 2004 Dusty plasmas. Phys. Uspekhi 47, 447.
Fortov, V. E. & Morfill, G. E. 2010 Complex and Dusty Plasmas: From Laboratory to Space. CRC Press.
Hamaguchi, S. & Ohta, H. 2001 Waves in strongly-coupled classical one-component plasmas and Yukawa fluids. Phys. Scr. T89, 127.
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.
Ivlev, A. V. & Morfill, G. 2000 Acoustic modes in a collisional dusty plasma: effect of the charge variation. Phys. Plasmas 7, 1094.
Ivlev, A. V., Samsonov, D., Goree, J., Morfill, G. & Fortov, V. E. 1999 Acoustic modes in a collisional dusty plasma. Phys. Plasmas 6, 741.
Izvekova, Y. N. & Popel, S. I. 2016 Charged dust motion in dust devils on Earth and Mars. Contrib. Plasma Phys. 56, 263.
Kählert, H. & Bonitz, M. 2010 How spherical plasma crystals form. Phys. Rev. Lett. 104, 015001.
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.
Kalman, G. J., Hartmann, P., Donkó, Z. & Rosenberg, M. 2004 Two-dimensional Yukawa liquids: correlation and dynamics. Phys. Rev. Lett. 92, 065001.
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.
Kaw, P. K. 2001 Collective modes in a strongly coupled dusty plasma. Phys. Plasmas 8, 1870.
Kaw, P. K. & Sen, A. 1998 Low frequency modes in strongly coupled dusty plasmas. Phys. Plasmas 5, 3552.
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.
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.
Khrapak, S. & Morfill, G. 2009 Basic processes in complex (dusty) plasmas: charging, interactions, and ion drag force. Contrib. Plasma Phys. 49, 148.
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.
Khrapak, S. A. & Morfill, G. 2001 Waves in two-component electron-dust plasma. Phys. Plasmas 8, 2629.
Khrapak, S. A. & Thomas, H. M. 2015a Fluid approach to evaluate sound velocity in Yukawa systems and complex plasmas. Phys. Rev. E 91, 033110.
Khrapak, S. A. & Thomas, H. M. 2015b Practical expressions for the internal energy and pressure of Yukawa fluids. Phys. Rev. E 91, 023108.
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.
Kundrapu, M. & Keidar, M. 2012 Numerical simulation of carbon arc discharge for nanoparticle synthesis. Phys. Plasmas 19, 073510.
Kundu, M., Avinash, K., Sen, A. & Ganesh, R. 2014 On the existence of vapor–liquid phase transition in dusty plasmas. Phys. Plasmas 21, 103705.
Lado, F. 1973 Perturbation correction for the free energy and structure of simple fluids. Phys. Rev. A 8, 2548.
Lado, F. 1976 Charged hard spheres in a uniform neutralizing background using mixed integral equations. Mol. Phys. 31, 1117.
Lado, F. 1982 A local thermodynamic criterion for the reference-hypernetted-chain equation. Phys. Lett. A 89, 196.
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.
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.
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.
Meijer, E. J. & Frenkel, D. 1991 Melting line of Yukawa system by computer simulation. J. Chem. Phys. 94, 2269.
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.
Murillo, M. S. 1998 Static local field correction description of acoustic waves in strongly coupling dusty plasmas. Phys. Plasmas 5, 3116.
Ohta, H. & Hamaguchi, S. 2000 Wave dispersion relations in Yukawa fluids. Phys. Rev. Lett. 84, 6026.
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.
Ott, T., Bonitz, M., Stanton, L. G. & Murillo, M. S. 2014 Coupling strength in Coulomb and Yukawa one-component plasmas. Phys. Plasmas 21, 113704.
Piel, A. 2017 Plasma crystals: experiments and simulation. Plasma Phys. Control. Fusion 59, 014001.
Quinn, R. A. & Goree, J. 2000 Single-particle Langevin model of particle temperature in dusty plasmas. Phys. Rev.  E 61, 3033.
Rosenberg, M. & Kalman, G. 1997 Dust acoustic waves in strongly coupled dusty plasmas. Phys. Rev. E 56, 7166.
Rosenfeld, Y. 1986 Comments on the variational modified-hypernetted-chain theory for simple fluids. J. Stat. Phys. 42, 437.
Rosenfeld, Y. & Ashcroft, N. 1979 Theory of simple classical fluids: universality in the short-range structure. Phys. Rev. A 20, 1208.
Seok, J. Y., Koo, B.-C. & Hirashita, H. 2015 Dust cooling in supernova remnants in the large Magellanic cloud. Astrophys. J. 807, 100.
Shukla, P. K. & Eliasson, B. 2009 Fundamentals of dust-plasma interactions. Rev. Mod. Phys. 81, 25.
Szetsen, L., Hsiu-Feng, C. & Chien-Ju, C. 2007 Spectroscopic study of carbonaceous dust particles grown in benzene plasma. J. Appl. Phys. 101, 113303.
Tang, X.-Z. & Delzanno, G. L. 2014 Orbital-motion-limited theory of dust charging and plasma response. Phys. Plasmas 21, 123708.
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.
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.
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.
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.
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.
Wertheim, M. S. 1963 Exact solution of the Percus–Yevick integral equation for hard spheres. Phys. Rev. Lett. 10, 321.
Whipple, E. C. 1981 Potentials of surfaces in space. Rep. Prog. Phys. 44, 1197.
Xie, B. S. & Yu, M. Y. 2000a Dust acoustic waves in strongly coupled dissipative plasmas. Phys. Rev. E 62, 8501.
Xie, B. S. & Yu, M. Y. 2000b Dust-acoustic waves in strongly coupled plasmas with variable dust charge. Phys. Plasmas 7, 3137.
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.
MathJax is a JavaScript display engine for mathematics. For more information see



Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed