Modulated transverse off-plane dust-lattice wave packets in hexagonal two-dimensional dusty plasma crystals

Abstract

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.

Instability of ion kinetic waves in a weakly ionized plasma

“…[46] are unaffected because, in that work, the subthermal flow regime was considered. The resulting change in the interaction between dust particles may affect their self-organization and dynamics [51][52][53][54][55][56][57][58][59][60][61][62].…”

The particle-wake interactions in a hexagonal twodimensional dust lattice

“…Then we set the determinant of coefficients of Eqs. (17)(18)(19), it gives the dispersion relation as a third rank polynomial versus 2 ω . In limitation conditions when eliminating the wake ion effect, results of this paper converges to the results of, B. Farokhi et al [17] and S. V. Vladimirov et al [18].…”

“…In fundamental physics the most surprising discovery was the observation of crystal-like structures. Such plasma crystal structures can support longitudinal and transverse vibrational modes, which have been extensively studied in the last years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Dust lattice waves (DLW's) are produced by the oscillations of regularly spaced charged micrometer sized particles suspended in a plasma (plasma crystals), and there have been many publications on experimental and theoretical investigations of the DL modes in one-and twodimensional (1D and 2D) crystals [3][4][5][6][7][8][9][10][11][12][13].…”

Nonlinear theory of longitudinal dust-lattice wave in a magnetic dusty plasma crystal

“…Modulationally unstable wave packets may either collapse in response to external perturbations, or evolve toward an ordered state of localized structure (envelope soliton) formation, due to a mutual balance between dispersion and nonlinearity. This generic mechanism is well known in various physical contexts [10][11][12]15] to be related to phase harmonic generation and energy localization via the formation of localized excitations.…”

“…A wide variety of linear and nonlinear modes in 1D chain and 2D hexagonal lattice are investigated in dusty plasma crystals [6][7][8][9][10][11][12][13][14][15]. Amplitude modulation is a wellknown nonlinear effect dominating waves propagating in nonlinear dispersive media, referring to the slow space and time variation of the wave's amplitude, which may potentially be subjected to modulational instability.…”