Mode couplings and resonance instabilities in dust clusters

Abstract

The normal modes for three to seven particle two-dimensional (2D) dust clusters in a complex plasma are investigated using an N-body simulation. The ion wakefield downstream of each particle is shown to induce coupling between horizontal and vertical modes. The rules of mode coupling are investigated by classifying the mode eigenvectors employing the Bessel and trigonometric functions indexed by order integers (m, n). It is shown that coupling only occurs between two modes with the same m and that horizontal modes having a higher shear contribution exhibit weaker coupling. Three types of resonances are shown to occur when two coupled modes have the same frequency. Discrete instabilities caused by both the first and third type of resonances are verified and instabilities caused by the third type of resonance are found to induce melting. The melting procedure is observed to go through a two-step process with the solid-liquid transition closely obeying the Lindemann criterion.

Mode couplings and resonance instabilities in finite dust chains

“…In this case, such coupling occurs only between modes having specified symmetries and obeying specific mode coupling rules, similar to the mode coupling seen in polyatomic molecules [1,2]. The instabilities created by the resonance between two coupled modes are discrete, reflecting the discreteness of the normal modes [22,28].…”

“…In this work, the ion wake is modeled employing an adaptation of the widely used point charge model [8,9,[19][20][21][22]. This model assumes the potential around a dust particle levitated in a plasma sheath to be described by a combination of two potentials, one created by the dust particle with charge Q and another by a positive point charge q located a distance l beneath it, representing the ion wake.…”

“…Recently, research on mode couplings has been extended to include two-dimensional (2D) dust clusters both theoretically * ke_qiao@baylor.edu † truell_hyde@baylor.edu [20][21][22]27] and experimentally [28]. Instead of the continuous high-energy-density region observed in the thermal fluctuation spectrum for large crystals, normal mode spectra for dust clusters exhibit a complex coupling pattern between discrete horizontal and vertical modes even when the modes are not in resonance.…”

“…Similar to large crystals, if the resonance instabilities are strong enough, they can induce melting of the cluster with the melting obeying the Lindemann criterion [22]. It is worth noting that although melting and/or the solid-liquid transition is a concept originally defined for large physical systems, it has recently become a topic of increasing interest for finite systems [29,30] and has been observed across a wide variety of systems including electrons in quantum dots [31], ions in traps [32], atomic clusters [33,34], and complex plasmas [35][36][37].…”

“…The ambient ion flow in the plasma sheath, where dust particles are levitated and the resulting ion wake below the particles [15][16][17] can dramatically enhance such coupling mechanisms from second (nonlinear) to first (linear) order [18], allowing detection even at lowamplitude particle displacements. Using a point charge model [8,9,[19][20][21][22] to simulate the ion wake, it has been shown that resonance instability can be triggered when the two coupled wave modes intersect. This phenomenon was recently observed experimentally [18,[23][24][25] in the thermal fluctuation spectrum illustrated by a high-energy-density region at the intersection between the DLWs.…”