dorsal/arxiv
View SchemaNonlinear theory of dust lattice mode coupling in dust crystals
| Authors | Ioannis Kourakis, Padma Kant Shukla |
|---|---|
| Categories | |
| ArXiv ID | physics/0410098 |
| URL | https://arxiv.org/abs/physics/0410098 |
Abstract
Quasi-crystals formed by charged mesoscopic dust grains (dust lattices), observed since hardly a decade ago, are an exciting paradigm of a nonlinear chain. In laboratory discharge experiments, these quasi-lattices are formed spontaneously in the sheath region near a negative electrode, usually at a levitated horizontal equilibrium configuration where gravity is balanced by an electric field. It is long known (and experimentally confirmed) that dust-lattices support linear oscillations, in the longitudinal (acoustic mode) as well as in the transverse, in plane (acoustic-) or off-plane (optic-like mode) directions. Either due to the (typically Yukawa type) electrostatic inter-grain interaction forces or to the (intrinsically nonlinear) sheath environment, nonlinearity is expected to play an important role in the dynamics of these lattices. Furthermore, the coupling between the different modes may induce coupled nonlinear modes. Despite this evidence, the elucidation of the nonlinear mechanisms governing dust crystals is in a rather preliminary stage. In this study, we derive a set of (coupled) discrete equations of motion for longitudinal and transverse (out-of-plane) motion in a one dimensional model chain of charged dust grains. In a continuum approximation, i.e. assuming a variation scale which is larger than the lattice constant, one obtains a set of coupled modified Boussinesq-like equations. Different nonlinear solutions of the coupled system are discussed, based on localized travelling wave ansatze and on coupled equations for the envelopes of co-propagating quasi-linear waves.
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"abstract": "Quasi-crystals formed by charged mesoscopic dust grains (dust lattices),\nobserved since hardly a decade ago, are an exciting paradigm of a nonlinear\nchain. In laboratory discharge experiments, these quasi-lattices are formed\nspontaneously in the sheath region near a negative electrode, usually at a\nlevitated horizontal equilibrium configuration where gravity is balanced by an\nelectric field. It is long known (and experimentally confirmed) that\ndust-lattices support linear oscillations, in the longitudinal (acoustic mode)\nas well as in the transverse, in plane (acoustic-) or off-plane (optic-like\nmode) directions. Either due to the (typically Yukawa type) electrostatic\ninter-grain interaction forces or to the (intrinsically nonlinear) sheath\nenvironment, nonlinearity is expected to play an important role in the dynamics\nof these lattices. Furthermore, the coupling between the different modes may\ninduce coupled nonlinear modes. Despite this evidence, the elucidation of the\nnonlinear mechanisms governing dust crystals is in a rather preliminary stage.\nIn this study, we derive a set of (coupled) discrete equations of motion for\nlongitudinal and transverse (out-of-plane) motion in a one dimensional model\nchain of charged dust grains. In a continuum approximation, i.e. assuming a\nvariation scale which is larger than the lattice constant, one obtains a set of\ncoupled modified Boussinesq-like equations. Different nonlinear solutions of\nthe coupled system are discussed, based on localized travelling wave ansatze\nand on coupled equations for the envelopes of co-propagating quasi-linear\nwaves.",
"arxiv_id": "physics/0410098",
"authors": [
"Ioannis Kourakis",
"Padma Kant Shukla"
],
"categories": [
"physics.plasm-ph"
],
"title": "Nonlinear theory of dust lattice mode coupling in dust crystals",
"url": "https://arxiv.org/abs/physics/0410098"
},
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