Heartbeat instability as auto-oscillation between dim and bright void regimes

We investigated the self-excited as well as optogalvanically stimulated heartbeat instability in RF discharge complex plasma. Three video cameras measured the motion of the microparticles, the plasma emission, and the laser-induced fluorescence simultaneously. Comprehensive studies of the optogalvanic control of the heartbeat instability revealed that the microparticle suspension can be stabilized by a continuous laser, whereas a modulated laser beam induces the void contraction either transiently or resonantly. The resonance occurred when the laser modulation frequency coincided with the frequency of small breathing oscillations of the microparticle suspension, which are known to be a prerequisite to the heartbeat instability. Based on the experimental results we suggest that the void contraction during the instability is caused by an abrupt void transition from the dim to the bright regime [Pikalev et al., Plasma Sources Sci. Technol. 30, 035014 (2021)]. In the bright regime, a time-averaged electric field at the void boundary heats the electrons causing bright plasma emission inside the void. The dim void has much lower electric field at the boundary and exhibits therefore no emission feature associated with it.

Figure 1

Scheme of the experimental setup, (a) side view, (b) top view. The heart of the experiment is the PK-3 Plus chamber [34]. The bottom flange of the chamber can be heated to control the temperature gradient between the electrodes. The cameras observe the microparticle motion and plasma emission. The reference Ar lamp is used to control the wavelength of the tunable laser.

Figure 2

Electronic levels of argon involved in the optogalvanic effect. The laser pumps the transition at 772.38 nm and fluorescence in the 810.37-nm spectral line is observed.

Figure 3

Self-excited heartbeat instability. (a) One of the frames with the velocity field reconstructed using the OpenPIV software [39]. (b) The same frame with superimposed images of (green) the microparticle suspension and (red) the plasma emission captured with the filter with the central wavelength of 750 nm. The dashed lines in plates (a) and (b) depict the areas used for the calculation of the spatiotemporal distributions. (c) Spatiotemporal distributions of the velocity $v_x$ and the plasma emission variations $I_{750}^x$ and $I_{750}^y$ during the self-excited heartbeat instability. The white color in the $v_x$ plot depicts the areas in which no microparticles are present. The black dashed lines depict the temporal position of the frames shown in plates (a) and (b). The microparticle diameter was $2.15\mu \mathrm{m}$, the discharge power was 400 mW. See also Supplemental Material [40].

Figure 4

The horizontal spatiotemporal distributions of the velocities $v_x$ and the plasma emission variations $I_{750}^x$ and $I_{810}^x$ (a) without the laser, (b) with the modulated laser, and (c) with continuous laser. The diameter of the microparticles was $1.95\mu \mathrm{m}$, the discharge power was 500 mW. See also Supplemental Material [40].

Figure 5

Transient optogalvanic heartbeat excitation with the chopper frequency of (a) 1.7 Hz, (b) 19.6 Hz, (c) 44.0 Hz. The microparticle diameter was $1.95\mu \mathrm{m}$, the discharge power was 500 mW. See also Supplemental Material [40].

Figure 6

Transient optogalvanic heartbeat excitation with the attenuated laser beam. The microparticle diameter was $1.95\mu \mathrm{m}$, the discharge power was (a) 250 mW, (b) 350 mW. The bright stripes in the $I_{810}^x$ distribution correspond to the time intervals when the laser was crossing the void through the filters with the following values of the transmission (from the top to the bottom): 0.45, 0.014, 1, 0.12, and 0.19.

Figure 7

Effect of the beam horizontal shift by 10 mm. The microparticle diameter was $2.15\mu \mathrm{m}$, the discharge power was 500 mW.

Figure 8

Stimulation of the heartbeat instability with low laser power. The laser beam was attenuated down to 0.7 mW. The microparticle diameter was $2.15\mu \mathrm{m}$, the discharge power was 350 mW. The laser modulation frequency was (a) 9.8 Hz, (b) 19.5 Hz, (c) 23.9 Hz, (d) 27.3 Hz, and (e) 29.5 Hz. See also Supplemental Material [40].

Figure 9

Horizontally averaged Fourier spectra of $v_x$ and $I_{810}^x$ spatiotemporal distributions shown in (a) Fig. 8; (b) Fig. 8. The laser modulation frequency was (a) 9.8 Hz, (b) 27.3 Hz. Every spectrum is normalized to its maximal value.

Figure 10

Schematic representation of the heartbeat instability cycle. Initially dim void transits to the bright regime. This transition is mediated either by the breathing-oscillations-related mechanism or by the transient optogalvanic effect. The boundary of the bright void becomes unstable and the void collapses due to the electrostatic force prevailing over the ion drag and thermophoretic forces. The dim void recovers due to the outward drift of microparticles.