Experimental observation of pinned solitons in a flowing dusty plasma

Pinned solitons are a special class of nonlinear solutions created by a supersonically moving object in a fluid. They move with the same velocity as the moving object and thereby remain pinned to the object. A well-known hydrodynamical phenomenon, they have been shown to exist in numerical simulation studies but to date have not been observed experimentally in a plasma. In this paper we report the first experimental excitation of pinned solitons in a dusty (complex) plasma flowing over a charged obstacle. The experiments are performed in a $\mathrm{\Pi }$ shaped dusty plasma experimental (DPEx) device in which a dusty plasma is created in the background of a DC glow discharge Ar plasma using micron sized kaolin dust particles. A biased copper wire creates a potential structure that acts as a stationary charged object over which the dust fluid is made to flow at a highly supersonic speed. Under appropriate conditions nonlinear stationary structures are observed in the laboratory frame that correspond to pinned structures moving with the speed of the obstacle in the frame of the moving fluid. A systematic study is made of the propagation characteristics of these solitons by carefully tuning the flow velocity of the dust fluid by changing the height of the potential structure. It is found that the nature of the pinned solitons changes from a single-humped one to a multihumped one and their amplitudes increase with an increase of the flow velocity of the dust fluid. The experimental findings are then qualitatively compared with the numerical solutions of a model forced Korteweg de Vries (fKdV) equation.

Figure 1

(a) A schematic diagram of the dusty plasma experimental (DPEx) setup. (b) A zoomed view of the tray shaped grounded cathode showing the copper wire (connected with a variable resistance) and two confinement strips.

Figure 2

(a) Illustration of the equilibrium configuration of the dust cloud in the $y\text{−}z$ plane prior to generating the flow. (b) Flow in the dust fluid is initiated from right to left by lowering the potential hill suddenly. The yellow circle represents the location of the copper wire shown in Fig. 1.

Figure 3

(a) A typical experimental image of excitation of single pinned soliton. The dashed vertical line marks the position of the wire, whereas the distance between the two red (solid) vertical lines, placed at distances of 1.5 cm on either side of the wire, is the approximate spatial extent of the potential sheath. (b) Axial profile of compression factor of density perturbation extracted from Fig. 3.

Figure 4

Typical image of excitation of (a) double, (b) four, and (c) many pinned solitons along with the wakes. The yellow dashed line represents the location of the charged object.

Figure 5

Density compression factor of (a) two, (b) four, and (c) many sharp peaks extracted from Figs. 4, 4 and 4. The dashed line represents the location of the wire.

Figure 6

(a) Intensity profile of a three-humped pinned soliton and wakes over time. The dashed lines show that the higher amplitude soliton remains stationary in the laboratory frame, whereas the wakes move along the flow. The dotted line represents the location of the wire. (b) The zoomed view of a portion of Fig. 6 clearly shows that the wakes move from right to left.

Figure 7

Variation of maximum density compression $n_{d\text{max}}/n_{d0}$ with the normalized flow velocity $M$.

Figure 8

Time evolution of (i) single ($B=2.0$, $G=2.0,$ and $v_d=1.5$.) and (ii) three ($B=4$, $G=8,$ and $v_d=2$) pinned solitons obtained numerically by solving the f-KdV equation with $\alpha =2.0$. Solid lines represents the solitonic structure whereas the dashed line represents the source functions. The time is normalized by the inverse of dust plasma frequency.

Figure 9

Time evolution of (a) single ($B=2.0$, $G=2.0,$ and $v_d=1.5$), (b) three ($B=4$, $G=8,$ and $v_d=2.0$), and (c) multiple ($B=6$, $G=20,$ and $v_d=2.2$) pinned solitons obtained by numerically solving the f-KdV equation. Solid lines represent the solitonic structures whereas the dashed lines represents the source function. Time is normalized by the inverse of dust plasma frequency.

Figure 10

Variation of maximum density compression $n_{d\text{max}}/n_{d0}$ obtained from numerical solution with the velocity of source function $v_d$.