Mode coupling and resonance instabilities in quasi-two-dimensional dust clusters in complex plasmas

Small quasi-two-dimensional dust clusters consisting of three to eleven particles are formed in an argon plasma under varying rf power. Their normal modes are investigated through their mode spectra obtained from tracking the particles’ thermal motion. Detailed coupling patterns between their horizontal and vertical modes are detected for particle numbers up to 7 and discrete instabilities are found for dust clusters with particle number $⩾9$, as predicted in previous theory on ion-flow induced mode coupling in small clusters. The instabilities are proven to be induced by resonance between coupled horizontal and vertical normal modes.

Figure 1

(a), (b) Normal mode spectra obtained experimentally for three- and four-particle clusters at rf powers of (a) 2.32 and (b) 1.60 W. Dots represent theoretically calculated mode frequencies. (c), (d) Normal mode spectra obtained from simulation with parameters matching those measured in (a) and (b). (e), (f) Mode eigenvectors for clusters corresponding to (a) and (b), where the horizontal (vertical) modes are shown at the top (bottom). The solid lines shown in (a), (b) and (e), (f) connect coupled modes.

Figure 2

(a) Normal mode spectra for a seven-particle cluster at rf power of 17.2 W. The solid lines shown connect coupled modes. (b) Normal mode spectra obtained from simulation with parameters matching those measured in (a).

Figure 3

(a)–(c) The mode spectra of a nine-particle cluster at rf powers of (a) 11.5, (b) 7.5, and (c) 5.2 W. (d)–(i) The particle trajectories from top and side views for clusters in (a)–(c).

Figure 4

The (a) horizontal and (b) vertical particle trajectories for a nine-particle cluster at rf power of 11.5 W. Displacements from equilibrium positions are magnified by a factor of 5 in order for the trajectories to be seen more clearly. Particle positions as a function of time are indicated by the intensity of the markers, going from light to dark. The time interval between adjacent positions is 0.167 s. Insets in (a) and (b) are the eigenvectors of the excited horizontal and vertical modes, respectively.