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arXiv · 1107.3980

Dispersion relations for circular single and double dusty plasma chains

D. V. Tkachenko·T. E. Sheridan·V. R. Misko
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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.

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D. V. Tkachenko, T. E. Sheridan, V. R. Misko. 2011-07-20. Dispersion relations for circular single and double dusty plasma chains. https://doi.org/10.1063/1.3651194

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