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Visco-instability of shear viscoelastic collisional dusty plasma systems

Part of: Collisions in Collisionless Plasmas

Published online by Cambridge University Press:  21 March 2018

M. Mahdavi-Gharavi ,
K. Hajisharifi  and
H. Mehidan
M. Mahdavi-Gharavi
Affiliation:
Department of Physics and Institute for Plasma Research, Kharazmi University, 49 Dr. Mofatteh Avenue, Tehran 15614, Iran
K. Hajisharifi*
Affiliation:
Department of Physics and Institute for Plasma Research, Kharazmi University, 49 Dr. Mofatteh Avenue, Tehran 15614, Iran
H. Mehidan
Affiliation:
Department of Physics and Institute for Plasma Research, Kharazmi University, 49 Dr. Mofatteh Avenue, Tehran 15614, Iran
*
†Email addresses for correspondence: k.hajisharifi@gmail.com, hajisharifi@khu.ac.ir
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Abstract

In this paper, the stability of Newtonian and non-Newtonian viscoelastic collisional shear-velocity dusty plasmas is studied, using the framework of a generalized hydrodynamic (GH) model. Motivated by Banerjee et al.’s work (Banerjee et al., New J. Phys., vol. 12 (12), 2010, p. 123031), employing linear perturbation theory as well as the local approximation method in the inhomogeneous direction, the dispersion relations of the Fourier modes are obtained for Newtonian and non-Newtonian dusty plasma systems in the presence of a dust–neutral friction term. The analysis of the obtained dispersion relation in the non-Newtonian case shows that the inhomogeneous viscosity force depending on the velocity shear profile can be the genesis of a free energy source which leads the shear system to be unstable. Study of the dust–neutral friction effect on the instability of the considered systems using numerical analysis of the dispersion relation in the Newtonian case demonstrates that the maximum growth rate decreases considerably by increasing the collision frequency in the hydrodynamic regime, while this reduction can be neglected in the kinetic regime. Results show a more significant stabilization role of the dust–neutral friction term in the non-Newtonian cases, through decreasing the maximum growth rate at any fixed wavenumber and construction of the instable wavenumber region. The results of the present investigation will greatly contribute to study of the time evolution of viscoelastic laboratory environments with externally applied shear; where in these experiments the dust–neutral friction process can play a considerable role.

Keywords

dusty plasmasplasma instabilitiesstrongly coupled plasmas
Type
Research Article
Information
Journal of Plasma Physics , Volume 84 , Issue 2 , April 2018 , 305840201
Copyright
© Cambridge University Press 2018 

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References

Angelis, U. de 1992 The physics of dusty. Plasmas Phys. Scr. 45 (5), 465.Google Scholar
Banerjee, D., Janaki, M. S., Chakrabarti, N. & Chaudhri, M. 2010 Viscosity gradient-driven instability of ‘shear mode’ in a strongly coupled plasma. New J. Phys. 12 (12), 123031.Google Scholar
El-Awady, E. I. & Djebli, M. 2012 Dust acoustic waves in a collisional strongly coupled dusty plasmas. Astrophys. Space Sci. 342 (1), 105–111.Google Scholar
Frenkel, Y. 1946 Kinetic Theory of Liquids. Clarendon.Google Scholar
Feng, Y., Goree, J. & Liu, B. 2012 Frequency-dependent shear viscosity of a liquid two-dimensional dusty plasma. Phys. Rev. E 85 (6), 066402.CrossRefGoogle ScholarPubMed
Goertz, C. K. 1989 Dusty plasmas in the solar system. Rev. Geophys. 27 (2), 271–292.CrossRefGoogle Scholar
Gruzinov, A.2008 GRB: magnetic fields, cosmic rays, and emission from first principles? arXiv:0803.1182.Google Scholar
Horanyi, M., Houpis, H. L. F. & Mendis, D. A. 1988 Charged dust in the Earth’s magnetosphere. Astrophys. Space Sci. 144 (1–2), 215–229.Google Scholar
Ikezi, H. 1986 Coulomb solid of small particles in plasmas. Phys. Fluids 29 (6), 1764–1766.Google Scholar
Ivlev, A. V., Steinberg, V., Kompaneets, R., Hofner, H., Sidorenko, I. & Morfill, G. E. 2007 Non-Newtonian viscosity of complex-plasma fluids. Phys. Rev. Lett. 98 (14), 145003.CrossRefGoogle ScholarPubMed
Jana, S., Banerjee, D. & Chakrabarti, N. 2015 Stability of an elliptical vortex in a strongly coupled dusty plasma. Phys. Plasmas 22 (8), 083704.Google Scholar
Kaw, P. K. 2001 Collective modes in a strongly coupled dusty plasma. Phys. Plasmas 8 (5), 1870–1878.Google Scholar
Mendis, D. A. & Rosenberg, M. 1994 Cosmic dusty plasma. Annu. Rev. Astron. Astrophys. 32 (1), 419–463.CrossRefGoogle Scholar
Mishra, A., Kaw, P. K. & Sen, A. 2000 Instability of shear waves in an inhomogeneous strongly coupled dusty plasma. Phys. Plasmas 7 (8), 3188–3193.Google Scholar
Nunomura, S., Misava, T., Ohno, N. & Takamura, S. 1999 Instability of dust particles in a Coulomb crystal due to delayed charging. Phys. Rev. Lett. 83 (10), 1970.CrossRefGoogle Scholar
Pesceli, H. L., Rasmussen, J. J. & Thomsen, K. 1984 Nonlinear interaction of convective cells in plasmas. Phys. Rev. Lett. 52 (24), 2148.Google Scholar
Rosenberg, M. & Kalman, G. 1997 Dust acoustic waves in strongly coupled dusty plasmas. Phys. Rev. E 56 (6), 7166.Google Scholar
Steinberg, V., Ivlev, A., Kompaneets, R. & Morfill, G. E. 2008 Shear instability in fluids with a density-dependent viscosity. Phys. Rev. Lett. 100 (25), 254502.Google Scholar
Shukla, P. K. & Mamun, A. A. 2001 Dust-acoustic shocks in a strongly coupled dusty plasma. IEEE Trans. Plasma Sci. 29 (2), 221–225.Google Scholar
Tsytovich, V. N. & Havnes, O. 1993 Charging processes, dispersion properties and anomalous transport in dusty plasma. Comm. Plasma Phys. Control. Fusion 15 (5), 267–280.Google Scholar
Thomas, H., Morfill, G. E., Demmel, V., Goree, J., Feuerbacher, B. & Mohlmann, D. 1994 Plasma crystal: Coulomb crystallization in a dusty plasma. Phys. Rev. Lett. 73 (5), 652.Google Scholar
Ussenov, Y. A., Ramazanov, T. S., Dzhuma Gulova, K. N. & Dosbolayen, M. K. 2014 Application of dust grains and Langmuir probe for plasma diagnostics. Eur. Phys. Lett. 105 (1), 15002.Google Scholar
Whipple, E. C., Northrop, T. G. & Mendis, D. A. 1985 The electrostatics of a dusty plasma. J. Geophys. Res. 90 (A8), 7405–7413.CrossRefGoogle Scholar
Whipple, E. C. 1981 Potentials of surfaces in space. Rep. Prog. Phys. 44 (11), 1197.CrossRefGoogle Scholar