Mode couplings and resonance instabilities in finite dust chains

Abstract

Employing a numerical simulation, the normal modes are investigated for finite, one-dimensional horizontal dust chains in complex plasma. Mode couplings induced by the ion flow within the sheath are identified in the mode spectra and the coupling rules are determined. Two types of resonance-induced instabilities are observed, one bidirectional and one unidirectional. Bidirectional instability is found to cause melting of the chain with the melting proceeding via a two-step process which obeys the Lindemann criterion. The relationship between the normal mode spectra observed in finite systems and the wave dispersion relations seen in larger systems was also examined using a dust chain model. For this case, the dispersion relation was obtained through multiplication of the mode spectra matrix by a transition matrix. The resulting dispersion relations exhibit both the general features observed in larger crystals as well as several characteristics unique to finite systems, such as discontinuities and strong energy-density fluctuations.

Dependence of ion wake characteristics on experimental conditions

“…It is known that the point-wake model is not self-consistent and is only a crude approximation. However, the point charge ion wake model has been employed in many studies to model nonreciprocal particle interactions [19,24,[49][50][51][52][53][54][55][56][57][58][59][60][61]. The present results indicate that the pointwake model is inadequate for modeling the dynamic conditions with this power and pressure regime.…”

Existence of both compressional and rarefactive nonlinear solitary waves in a chain of dust particles

“…If l a 1 0  is not satisfied, both k 1 and k 2 are different from equation (5) and equation (6) [39][40][41]. It is difficult to form a string of dust particles experimentally without the wake force [64][65][66][67]. The Yukawa interaction potential may be modified when wake force is considered.…”

Nonlinear mode coupling and internal resonance observed in a dusty plasma

“…Dust particles levitating in the plasma sheath region [3,4] are recognized to exhibit a screened Coulomb interaction [5,6] and are found to form self-organized structures such as chain structures [7,8], monolayer crystals [9,10] and 3D Coulomb balls [5]. The dynamics of the resulting vibrational modes have been studied for these structures, such as the dustlattice (DL) modes produced in a 1D horizontal chain [11][12][13][14], a 2D crystal [15][16][17][18][19][20] and finite clusters [21]. Mode coupling between the longitudinal and vertical transverse DL mode has also been shown to cause instability and melting [16] for 2D plasma crystals [17][18][19][20].…”