Obliquely propagating dust-density waves

Self-excited dust-density waves are experimentally studied in a dusty plasma under microgravity. Two types of waves are observed: a mode inside the dust volume propagating in the direction of the ion flow and another mode propagating obliquely at the boundary between the dusty plasma and the space charge sheath. The dominance of oblique modes can be described in the frame of a fluid model. It is shown that the results fom the fluid model agree remarkably well with a kinetic electrostatic model of Rosenberg [J. Vac. Sci. Technol. A 14, 631 (1996)]. In the experiment, the instability is quenched by increasing the gas pressure or decreasing the dust density. The critical pressure and dust density are well described by the models.

Figure 1

Side view of the IMPF-K device. The r.f. discharge has segmented electrodes and is operated in push-pull mode between pairs of electrodes. The two ring electrodes are electrically connected.

Figure 2

(Color online) (a) Still image of the dust-density wave. The arrows indicate the different wave propagation directions in regions 1 and 2. The electric field direction is perpendicular to the sheath boundary. (b) Spectral power density $P\left(f\right)$ of the dust density wave. (c) Reconstructed phase fronts of the dust density wave.

Figure 3

(a) Unstable oblique modes at the conditions of Ref. 24. (b) The maximum growth rate is found at $k{\lambda }_{\mathit{De}}\cos \theta \approx 1$.

Figure 4

Comparison of the growth rates predicted by the fluid model (a)–(c) and the kinetic model (d)–(f) for ion beam velocities of $0.3v_B$, $0.7v_B$, and $1.0v_B$. The other parameters are taken from our experiment. The curves are labeled with the propagation angle $\theta =0°-80°$.

Figure 5

Properties of the most unstable wave in the kinetic model as a function of the beam velocity. (a) Wavelength in units of the electron Debye length (squares) and propagation angle (circles). (b) Normalized perpendicular wavenumber $k_x{\lambda }_{\mathit{De}}$ and parallel wavenumber $k_z{\lambda }_{\mathit{De}}$. The dashed line is a fit $\propto v_{i0}^{-1}$. (c) Real frequency and growth rate in units of the dust plasma frequency.

Figure 6

Quenching of the instability by increasing the gas pressure. The different curves are labeled by the normalized ion beam velocity $v_{i0}∕v_B$.

Figure 7

Quenching of the instability by reducing the dust density. The different curves are labeled by the normalized ion beam velocity $v_{i0}∕v_B$.