(Color online) Sketch of the PK-3 Plus setup (Ref. 1). The powered aluminum electrodes are symmetrically driven by an rf power generator in push–pull mode. They are surrounded by grounded guard rings mounted on the grounded aluminum plate flanges. An insulator ring of high thermal conductivity (alumina) prevents a temperature gradient between the electrodes and the grounded structure. Three electromagnetically driven microparticle dispensers are integrated in each ground shield. The electrode system is surrounded by a quadratic glass cuvette, which provides optical access to the discharge region of .
Dependence of (a) average rms voltage and (b) average rms current on average forward rf power for all studied discharges (see Table I). The dashed lines indicate the general trends and
(Color) Horizontal glow distribution in experiment X. The red curves correspond to the enhanced glow initiating the contraction phase of the heartbeat oscillation. The blue curves show the minimal intensity in the reopening phase of the oscillation. The time-averaged distribution is shown in black. The dashed curves show the intensity deviation from this averaged value. Note that there is a stagnation zone with approximately constant glow intensity located at 14–16 mm from the center (at 0 mm).
Auto-oscillation patterns observed in argon at 9 Pa: (b) and (c) experiment VI with P = 288 mW and (d) experiment VIII with P = 192 mW. (a) A snap-shot of the microparticle cloud. The cross indicates the center of the chamber. The rectangle marks the region used for preparing the time-space plots shown in the bottom panels (b)–(d). In panel (c), three features are indicated by enhanced contrast: (1) the self-excited waves propagating at the cloud edge (Ref. 25), (2) the slowly propagating oscillons (Ref. 14), and (3) the heartbeat oscillations. (b) The six horizontal lines crossing the panel are disturbances caused by short-time voltage pulses. (d) Unstable heartbeat oscillations at low forward rf power.
The oscillation frequency shows a general trend to grow with the rf power: (diamonds) experimental data from Praburam and Goree (Ref. 35) and Samsonov and Goree (Ref. 4) (argon), (half-open circles) experimental data from Mikikian et al. (Ref. 36) (argon), and (circles) given study (argon and neon, monodisperse microparticles). In Refs. 4 and 36, the particles are grown in the discharge. In Ref. 36, the heartbeat frequency is lowered due to failed contractions following a mixed mode oscillation pattern (Ref. 17). The dashed line () is shown as a reference. HB, FM, and GVM stand for “heartbeat mode,” “filamentary mode,” and “great void mode.”
A vertical cross-plane of the dense microparticle cloud of experiment II, Table I. mm (overview camera). The rectangle marks the mm region used to detect the microparticle vibrations and to obtain the oscillation frequencies. The x-position is counted from the left edge of the rectangle. Inserts show (bottom) the time-space plot (see text for the preparation details) and (top) the DFT frequency-wave number spectrum obtained from it. The interparticle separation is .
DFT spectra obtained for (solid line) the time-space plot (Fig. 4), (dotted line) the rms rf voltage, and (dashed line) the rms rf current oscillations, in the phase of stable heartbeat oscillations of experiment VI, Table I.
(Color) Trajectory of an individual particle in experiment IX, Table I. The particle velocity and the “net force” acceleration have been calculated from the tracked particle trajectory. is the damping rate of the Epstein drag force (Ref. 37). Note a well-manifested correlation shown by the net force, accelerating the particle, and dc-current oscillation. The time axis is the same as in Fig. 9.
(Color) Analysis of the lowest frequency experiment in argon performed with 14.9 μm particles experiment IX, Table I. (a) A set of the housekeeping data, (b) a fragment of the time-space plot (12.2 mm × 13.2 s; 26.9 s ≤ t ≤ 40.1 s), (c) Fourier spectrum of the dc current with a fundamental frequency , and (d) Fourier spectrum obtained from the time-space plot giving a frequency-wave number plot with a fundamental frequency . The interparticle separation is . Note a well pronounced correlation between the electrical signal oscillation and the particle oscillation pattern. The gas inside the discharge chamber was refreshed every 60 s during the experiment. The gas refreshments were followed by an increase in pressure, which correlated well with tentative oscillation suppression periods.
The oscillation frequencies of (a) the heartbeat instability and (b) the breathing mode normalized to the dust-plasma frequency vs (rms) discharge voltage normalized to ionization potential. The dashed lines show the mean values: (a) and (b) .
(Color) The onset of the heartbeat instability observed in the experiment IX, Table I. (a) The horizontal position of the particles vs time taken inside a slice of a width across the cloud through the void. The dashed line indicates the geomitric center. (b) The correlation of the “area density” N/S of the cloud with the housekeeping signals. Top to bottom: the area density N/S, the forward rf-power, the dc current, and the pressure. Here, N is the number of the particles inside the rectangle of the size . The time scale is the same as in Fig. 9.
Plasma parameters, forward rf power, and measured fundamental frequencies of the heartbeat experiments. For comparison, we show also the dust plasma frequency f dust and the breathing mode frequency f bm (see Sec. IV D). The estimated dust density n d is also shown (see Sec. III A). The experiments were performed under microgravity conditions on board the ISS in 2006 by Valery Tokarev (16.01.), Pavel Vinogradov (14.08.) and Thomas Reiter (19.08.).
The scaling parameters to the relationships (1).
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