Highly Resolved Self-Excited Density Waves in a Complex Plasma

Experimental results on self-excited density waves in a complex plasma are presented. An argon plasma is produced in a capacitively coupled rf discharge at a low power and gas pressure. A cloud of microparticles is subjected to effective gravity in the range of 1–4 g by thermophoresis. The cloud is stretched horizontally (width/height $\simeq 45\mathrm{mm}/8\mathrm{mm}$). The critical pressure for the onset of the waves increases with the temperature gradient. The waves are propagating in the direction of the ion drift. The wave frequency, phase velocity, and wavelength are measured, and particle migrations affected by the waves are analyzed at a time scale of $1\mathrm{ms}/\mathrm{\text{frame}}$ and a subpixel space resolution.

Figure 1

Cross section through the setup. The parallel plate discharge is symmetrically driven by two rf electrodes, which have a diameter of 6 cm and are separated by 3 cm. They are surrounded by a ceramic insulator and a grounded ring of 9 cm diameter and 1.3 cm width. The heater, shown only schematically, consists of 8 evenly distributed resistors. The upper electrode is cooled with two $40\times 40\mathrm{mm}$ case fans (omitted in the figure).

Figure 2

Critical pressure for the onset of self-excitations versus the temperature difference between the electrodes. The top axis shows values of the normalized thermophoretic force calculated by using 14 (at a fixed electrode separation $F_{\mathrm{th}}\propto \Delta T$). Fit (solid line): $P/P_0=\sqrt{F_{\mathrm{th}}/mg-1+{ϵ}^2}-ϵ$, $P_0=21\mathrm{Pa}$, $ϵ=0.31$. (Insets) Nonlinear wave pattern corresponding to the particular case of self-excitations discussed in details in the text (red triangle in the plot): (a) Central part of the image. (b) Entire cloud.

Figure 3

(Top) Periodgram of the waves. The plot abscissa corresponds to time, the ordinate to height and the brightness to the renormalized sum of all pixel intensities in a 4.56 mm wide central region [Fig. 2a]. The horizontal dashed lines mark the boundaries of the plot area used for analysis. (Bottom) Histograms of the wave parameters determined from the intensity plot: period, phase velocity, and wavelength.

Figure 4

(a) Resonant particle trajectory (black squares), wave front positions (red dots), and (b) particle velocity. (c) Histogram of velocities of well-resolved particles and the wave speed distribution (red line).

Figure 5

(a) Net force acting on the particles in one phase of the wave as a function of height above the lower electrode: red triangles, well-resolved particles; blue dots, current mean force acting on all traced particles; dashed line, total mean of all traced particles; black diamonds, force-field calculated along the trajectory of the resonant particle. Corresponding error bars are shown atop. (Inset) Renormalized charge distribution of well-resolved particles calculated with Eq. (1). (b) Positions of wave ridges in the same phase taken from Fig. 3 vs height above the lower electrode. Note that the positions of force peaks (a) are shifted backward compared to the maxima of the emission intensity (b).