Single to multiple acoustic vortex excitations in the transition to defect-mediated dust acoustic wave turbulence

We experimentally investigate the cooperative excitations in the transition from a self-excited three-dimensional ordered plane wave to a defect-mediated turbulence (DMT) state with multiple unstable defect filaments in a dusty plasma system. It is found that, with increasing effective driving, a single acoustic vortex (AV) with positive or negative helicity winding around a long straight defect filament with small wiggling in the $2+1\mathrm{D}$ (dimensional) space-time space starts to emerge along the center axis of the small dust cluster. The sequential ruptures of the crest surfaces from the cluster boundary followed by their reconnection with adjacent ruptured crest surfaces, or repelling one of the pairwise generated defects out of the boundary, are the key for the single AV generation. Further increasing driving makes the single defect filament exhibit helical excursion in the $2+1\mathrm{D}$ space. The system eventually enters the state with a few short-lived AVs and the DMT state with multiple AVs. The gradual increasing defect filament fluctuations and defect number in the transition to the DMT more strongly distort the nearby waveforms, which leads to the transition from the emergence of distinct sideband peaks to the broadened peaks in the power spectra of temporal dust density fluctuation. For the system with a larger cluster size, the single AV states are skipped in the transition to the DMT state.

Figure 1

Sketch of the experimental setup, similar to our previous experimental setup [27].

Figure 2

(a) and (b) Color-coded plots of $n_d$ on the $xy$, $xt$, and $yt$ planes and defect filaments in the $xyt$ space, showing the transition from the defect-free plane wave state I to the weakly disordered wave state V (DMT state), through state II with a single defect filament exhibiting small amplitude wiggling, state III with a single helical defect filament, and state IV with a single to few chaotic defect filaments. The crosses in (a) label defect locations with null amplitudes and undefined phases. The orange and blue defect filaments (trajectories) in (b) represent the left- and right-handed helicities of the surrounding AVs, respectively. Their corresponding projections on the bottom $xy$ plane are also plotted. In (a) and (b), the panels in the same row share the same spatial and temporal scales.

Figure 3

Stereo waveforms of wave crest surfaces winding around the orange and blue defect filaments in the $xyt$ space, representing the left- and right-handed helicities of states II to V, respectively. Either a left- or right-handed single AV can be spontaneously excited in state II [e.g., (a) and (b), respectively] and state III (not shown). The same spatial and temporal scales are used in plotting for all the waveforms.

Figure 4

(a) Temporal evolution of $n_d\left(t\right)$ at points A and B, located at the dust cluster center and 2 mm from the center, respectively [see their locations on the bottom $xy$ plane of state III in Fig. 2] from states I to V. (b) Waterfall plots of the corresponding averaged power spectra of the local $n_d\left(t\right)$ over a circular area 8 mm in diameter and centered at point A. The defect trajectories determine the surrounding helical waveforms, which modulate dust density and consequently determine how the sharp peaks in the dust density power spectra are broadened.

Figure 5

(a) Temporal evolution of total defect number $N\left(t\right)$ in a circular area 8 mm in diameter and centered at the $xy$ plane, for states II to V. The gray lines indicate the zero level of defect number. (b) Power spectra of $N\left(t\right)$ for states IV and V. (c) Waterfall plots of the power spectra of $X\left(t\right)$ (blue) and $Y\left(t\right)$ (cyan) for states II to V, where ($X,Y$) is the defect location in the $xy$ plane. In state III, the dominant frequency is labeled by $f_d$. The numbers by the gray lines in (b) and (c) indicate the scaling exponents of the descending tails in the power spectra.

Figure 6

(a) Stereo waveforms of the wave crest surfaces around pairwise generated and annihilated defects with opposite helicities in state V. See our previous report [24] for more details. (b) and (c) Generation of the single defect filament by repelling one of the pairwise generated AVs to the cluster boundary, and by rupturing crest surfaces from the cluster boundary followed by crest surfaces reconnection, respectively. The same spatial and temporal scales are used in plotting (b) and (c).