Dispersion relations for circular single and double dusty plasma chains

TL;DR

This paper derives dispersion relations for particles in dusty plasma rings, revealing mode behaviors and anticrossings in single and double chain configurations with implications for understanding plasma wave dynamics.

Contribution

It introduces analytical dispersion relations for dusty plasma chains in ring geometries, including mode modifications and anticrossings as the radius varies.

Findings

Identification of acoustic and optical modes in single chains

Observation of mode anticrossings at smaller radii

Four-mode dispersion relations in double chains

Abstract

We derive dispersion relations for a system of identical particles confined in a two-dimensional annular harmonic well and which interact through a Yukawa potential, e.g., a dusty plasma ring. When the particles are in a single chain (i.e., a one-dimensional ring) we find a longitudinal acoustic mode and a transverse optical mode which show approximate agreement with the dispersion relation for a straight configuration for large radii of the ring. When the radius decreases, the dispersion relations modify: there appears an anticrossing of the modes near the crossing point resulting in a frequency gap between the lower and upper branches of the modified dispersion relations. For the double chain (i.e., a two-dimensional zigzag configuration) the dispersion relation has four branches: longitudinal acoustic and optical and transverse acoustic and optical.