Mode couplings and resonance instabilities in dust clusters

TL;DR

This study investigates how ion wakefield-induced mode couplings lead to resonance instabilities and melting in small 2D dust clusters within complex plasmas, revealing specific resonance conditions and melting dynamics.

Contribution

It provides a detailed analysis of mode coupling rules, resonance types, and the melting process in dust clusters using N-body simulations, highlighting the role of ion wakefields.

Findings

Mode coupling occurs only between modes with the same m.

Resonances cause discrete instabilities and melting.

Melting follows a two-step process consistent with the Lindemann criterion.

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.