Experimental determination of shock speed versus exciter speed in a two-dimensional dusty plasma

Anton Kananovich and J. Goree

Phys. Rev. E 101, 043211 – Published 28 April 2020

Abstract

A shock that is continuously driven by a moving exciter will propagate at a speed that depends on the exciter speed. We obtained this dependence experimentally, in a strongly coupled dusty plasma that was prepared as a single two-dimensional layer of charged microparticles. Attaining this result required an experimental advance, developing a method of driving a shock continuously, which we did using an exciter moving at a constant supersonic speed, analogous to a piston in a cylinder. The resulting compressional pulse was a shock that propagated steadily without weakening, ahead of the moving exciter. We compare our experimental results to an empirical form $M_{shock} = 1 + s M_{exciter}$ , and to the prediction of a recent simulation.

Received 9 May 2019
Revised 24 July 2019
Accepted 16 March 2020

DOI:https://doi.org/10.1103/PhysRevE.101.043211

Physics Subject Headings (PhySH)

Plasma waves Shock waves Shock waves & discontinuities in plasma

Dusty or complex plasma Nonlinear waves Strongly-coupled plasmas

Condensed Matter, Materials & Applied PhysicsFluid DynamicsPlasma Physics

Authors & Affiliations

Anton Kananovich and J. Goree

Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242, USA

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Issue

Vol. 101, Iss. 4 — April 2020

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Images

Figure 1
Experimental setup. A horizontal exciter wire was moved in the positive $x$ direction. Its support structure is drawn to scale, while other features are only sketched schematically. A 2D layer of microparticles was levitated in the upper part of the sheath, sketched as a dashed line, above the powered rf electrode in a vacuum chamber. The sheath had a gentle bowl shape, due to a combination of a strong vertical electric field and a weaker horizontal component, which confined microparticles laterally. The Supplemental Material [8] includes photographs of the chamber, top-view camera, and optics for illuminating the microparticles.
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Figure 2
Pulse evolution. A single pulse, propagating in the $+ x$ direction, was excited by the movement of the wire, which is not seen because it was located above the illumination sheet; its position is marked by a pair of triangles. After the compression started in (a), a sharp leading edge developed in (b) and (c); this shape of the pulse along with its supersonic speed lead us to identify it as a shock. The undisturbed region to the right is a crystalline lattice. To the left of the pulse's peak amplitude, the areal density gradually diminishes to zero. These enhanced-contrast images have been cropped to show only the region of interest, as defined in the Supplemental Material [8], where we also present a video and raw unprocessed images. Examination of the video confirms that microparticles were displaced by the pulse only in the $x$ direction; there was no significant bulk motion in the $y$ direction.
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Figure 3
Areal number density profiles. (a), (b), and (c) correspond to the respective panels of Fig. 2. The sharp leading edge of the pulse's waveform can be seen for example in (b) at $x = 20 mm$ . Using plots like these, it is possible to analyze the shock waveforms' width and amplitude.
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Figure 4
Time series of the position of the pulse's peak, for two runs. The data points are the positions of peak areal density, obtained from experimental images like those in Fig. 2. Linear fits yield the shock speeds, with a small random error.
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Figure 5
Shock speed's dependence on the wire speed. The experimental data points, each representing one run, were obtained as in Fig. 4. Physical units in the left scale are normalized on the right by the sound speed, and likewise for the top scale. The error bars account for the random errors arising in the linear fits as in Fig. 4, but do not account for all sources of error, as discussed in the Supplemental Material [8]. Comparing the experimental data to empirical Eq. (2) yields $M_{shock} = 1 + 0.98 M_{exciter} .$ The dashed curve is Eq. (4) plotted using simulation values [9] for $Γ$ and $κ$ which differ from the experimental values, as explained in the text.
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