Viscosity of two-dimensional strongly coupled dusty plasma modified by a perpendicular magnetic field

Yan Feng, Wei Lin, and M. S. Murillo

Phys. Rev. E 96, 053208 – Published 28 November 2017

Abstract

Transport properties of two-dimensional (2D) strongly coupled dusty plasmas have been investigated in detail, but never for viscosity with a strong perpendicular magnetic field; here, we examine this scenario using Langevin dynamics simulations of 2D liquids with a binary Yukawa interparticle interaction. The shear viscosity $η$ of 2D liquid dusty plasma is estimated from the simulation data using the Green-Kubo relation, which is the integration of the shear stress autocorrelation function. It is found that, when a perpendicular magnetic field is applied, the shear viscosity of 2D liquid dusty plasma is modified substantially. When the magnetic field is increased, its viscosity increases at low temperatures, while at high temperatures its viscosity diminishes. It is determined that these different variational trends of $η$ arise from the different behaviors of the kinetic and potential parts of the shear stress under external magnetic fields.

Received 24 August 2017

DOI:https://doi.org/10.1103/PhysRevE.96.053208

Physics Subject Headings (PhySH)

Dusty or complex plasma Plasma crystals Strongly-coupled plasmas

Plasma Physics

Authors & Affiliations

Yan Feng^* and Wei Lin

Center for Soft Condensed Matter Physics and Interdisciplinary Research, College of Physics, Optoelectronics and Energy, Soochow University, Suzhou 215006, China

M. S. Murillo

Department of Computational Mathematics, Science and Engineering, Michigan State University, East Lansing, Michigan 48824, USA

^*fengyan@suda.edu.cn

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Vol. 96, Iss. 5 — November 2017

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Images

Figure 1
(a) The shear stress autocorrelation function (SACF) and (b) its time integral for cold 2D liquid dusty plasma with the condition $Γ = 200$ and $κ = 2$ under different perpendicular magnetic fields. With a higher magnetic field (higher $β$ ), the decay of SACF is slower, so that its time integral is larger. From the Green-Kubo relation, the viscosity is obtained as the time integral of the SACF, while the upper limit of the integral is chosen as the first zero point of the SACF [20], labeled $t_{I}$ . The resulting value of the viscosity is the first maximum of the time integral of the SACF in (b), where three viscosity values are shown by arrows.
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Figure 2
The shear viscosity of cold 2D liquid dusty plasma with the condition $Γ = 200$ and $κ = 2$ under different perpendicular magnetic fields. The viscosity of cold 2D liquid dusty plasma, from simulation data using the Green-Kubo method, increases with the magnetic field. For each $β$ value, there are four independent data points obtained from four independent runs, and the scatter of these data would correspond to the error bar.
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Figure 3
(a) The SACF and (b) its time integral for hot 2D liquid dusty plasma with the condition $Γ = 8$ and $κ = 2$ under different perpendicular magnetic fields. With a higher magnetic field or $β$ value, the decay of the SACF is quicker, so that its time integral (viscosity) is smaller.
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Figure 4
The SACF and its time integral for 2D liquid dusty plasma at intermediate temperatures, with $κ = 2$ while (a, c) $Γ = 20$ and (b, d) $Γ = 30$ , respectively. In (c) and (d), as $β$ increases from 0, the time integral of the SACF decreases substantially at first, and then for $β$ greater than about 0.5, the integral of the SACF increases gradually.
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Figure 5
Three components of the SACF $[C_{s}^{KK} (t)$ , $C_{s}^{PP} (t)$ , $C_{s}^{KP} (t)]$ for 2D liquid dusty plasma at various temperatures, with $κ = 2$ while (a–c) $Γ = 8$ , (d–f) $Γ = 20$ , (g–i) $Γ = 30$ , and (j–l) $Γ = 200$ , respectively. In the hot 2D liquid dusty plasma, the self-correlation function of the kinetic part $C_{s}^{KK}$ (a) is dominant in the three components, while in the cold 2D liquid dusty plasma, the self-correlation function of the potential part $C_{s}^{PP}$ (k) plays a leading role. In the intermediate temperature range, $C_{s}^{KK}$ and $C_{s}^{PP}$ have comparable magnitude levels. The cross-correlation $C_{s}^{KP}$ is always the smallest, for all temperature ranges. Here, the legend for the curves is the same as in Figs. 3 and 4.
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Figure 6
Frequencies of the ripples in $C_{s}^{KK}$ and $C_{s}^{PP}$ for the conditions of (a) $Γ = 8$ and (b) $Γ = 200$ , while $κ = 2$ . These frequencies are obtained from the times when the first ripple peak occurs in the curves for either $C_{s}^{KK}$ or $C_{s}^{PP}$ . From data fitting, we obtain the analytical expressions for these frequencies, which are ${ω_{peak}^{KK}}^{2} = 0.13 ω_{c}^{2} + 0.00088 ω_{pd}^{2}$ and ${ω_{peak}^{PP}}^{2} = 0.02 ω_{c}^{2} + 0.0077 ω_{pd}^{2}$ for $Γ = 8$ and ${ω_{peak}^{KK}}^{2} = 0.1 ω_{c}^{2} + 0.023 ω_{pd}^{2}$ and ${ω_{peak}^{P P}}^{2} = 0.039 ω_{c}^{2} + 0.005 ω_{pd}^{2}$ for $Γ = 200$ . Insets: Illustrations that the ratios of these two frequencies are both close to 2.
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