Dynamics of a dust crystal with positive and negative dust (original) (raw)
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The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form φ(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v0. Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse-(shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.
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Effect of polarization force on the propagation of dust acoustic solitary waves
New Journal of Physics, 2010
We report the modifications in the propagation characteristics of dust acoustic solitary waves (DASWs) due to the polarization force acting on micronsize dust particles in a non-uniform plasma. In the small amplitude limit, we derive a K-dV-type equation and show that there is an increase in the amplitude and a reduction in the width of a solitary structure as the polarization force is enhanced for a given Mach number. For arbitrary amplitude waves we employ the Sagdeev potential method and find that the range of Mach numbers where solitary structures can exist becomes narrower in the presence of the polarization interaction. In both limits there exists a critical value of grain size beyond which the DASW cannot propagate.
Physics of Plasmas, 2009
The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. Transverse (off-plane) dust grain oscillatory motion is considered, in the form of a backward propagating wavepacket whose linear and nonlinear characteristics are investigated. An evolution equation is obtained for the slowly varying amplitude of the first (fundamental) harmonic, by making use of a two-dimensional lattice multiple scales technique. An analysis based on the continuum approximation (spatially extended excitations, compated to the lattice spacing) shows that wavepackets will be modulationally stable and that dark-type envelope solitons (density holes) may occur, in the long wavelength region. Evidence is provided of modulational instability and of the occurrence of bright-type envelopes (pulses) at shorter wavelengths. The role of second neighbor interactions is also investigated, and is shown to be rather weak in determining the modulational stability region. The effect of dissipation, assumed negligible in the algebra throughout the article, is briefly discussed.