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.
The creation of a spatially extended stable DC complex plasma crystal is a big experimental challenge and a topical area of research in the field of dusty plasmas. In this paper we describe a newly built and commissioned dusty plasma experimental device, DPEx-II, at the Institute for Plasma Research. The device can support the formation of large sized Coulomb crystals in a DC glow discharge plasma. The plasma in this L-shaped table-top glass chamber is produced between a circular anode and a long tray shaped cathode. It is characterized with the help of various electrostatic probes over a rang…
Theoretical Research Institute, Pakistan Academy of Sciences (TRIPAS)（巴基斯坦科学院理论研究所）；School of Natural Sciences (SNS), National University of Sciences and Technology (NUST)（国立科学与技术大学自然科学学院）；Department of Scpace Science, Institute of Space Technology (IST)（太空技术研究院空间科学系）
Nonlinear frequency response analysis is a widely used method for determining system dynamics in the presence of nonlinearities. In dusty plasmas, the plasma-grain interaction (e.g., grain charging fluctuations) can be characterized by a single particle nonlinear response analysis, while grain-grain nonlinear interactions can be determined by a multi-particle nonlinear response analysis. Here, a machine learning-based method to determine the equation of motion in the nonlinear response analysis for dust particles in plasmas is presented. Searching the parameter space in a Bayesian manner allow…
The formation of self-consistent dust crystal and its melting is a well known phenomenon in rf generated plasma but remains challenging in DC glow discharge plasma. Here, we report the melting of a two dimensional dusty plasma crystal, suspended in the cathode sheath of a DC glow discharge plasma. The experiments are carried out in a $Π-$shaped Dusty Plasma Experimental (DPEx) device where a stationary crystal of melamine formaldehyde particles is formed between the confining strips in a background of Argon plasma. The stable structure breaks and leads to a fluid state on reducing the neutral …
Numerical simulations of monolayer dust crystals in an RF complex plasma were performed to examine the crystal structure and quantify the effects of including the collision enhanced ion current in the charging model. A GEC cell similar to a previous experimental work was modeled for a range of RF voltages, using a continuum description for the plasma and a particle description for dust grains. The time history of each dust grain was monitored. The dust charge was computed using both the OML and the collision enhanced charging (CEC) model applicable to the sheath region. The dust model accounte…
A precise theoretical investigation has been made on dust-acoustic (DA) waves (DAWs) in a four components dusty plasma medium having inertial warm adiabatic dust grains and inertialess $q$-distributed electrons as well as isothermal ions and positrons. The nonlinear and dispersive parameters of the nonlinear Schrödinger equation (NLSE), which develops by using reductive perturbations technique, have been used to recognize the stable and unstable parametric regions of the DAWs as well as associated DA rogue waves (DARWs) in the unstable parametric regime of the DAWs. The effects of the light po…
This manuscript, presents a theoretical study of the linear and nonlinear characteristics of acoustic and drift waves in a bounded inhomogenious dusty plasma which has potential applications in space and lab environments. In this analysis, flow of all plasma particles is assumed to be along the axial direction whereas gradients in velocity are considered to be along the radial direction. First we study coupling of dust modified ion acoustic (DMA) and drift (DMD) waves (linear analysis) at fast time when dynamics of dust remain inactive, later formation of nonlinear vortex like structures are e…
A nonlinear Schrödinger equation (NLSE) has been derived by employing reductive perturbation method for investigating the modulational instability of dust-ion-acoustic waves (DIAWs) in a four-component plasma having stationary negatively charged dust grains, inertial warm ions, and inertialess non-thermal electrons and positrons. It is observed that under consideration, the plasma system supports both modulationally stable and unstable domains, which are determined by the sign of the dispersive and nonlinear coefficients of NLSE, of the DIAWs. It is also found that the nonlinearity as well as …
A theoretical study is presented for the propagation of Dust Ion Acoustic Waves in an unmagnetized four-component plasma, consisting of Maxwellian negative ions, cold mobile positive ions, $κ$-distributed electrons and positively charged dust grains. Based on the characteristics of Sagdeev pseudopotential and phase portraits, three types of nonlinear waves are observed --- solitons, double layers and supersolitons. The conditions for the existence of such nonlinear waves are highly sensitive to the plasma parameters. The results obtained in this study may be of wide relevance in the field of s…
The formation and melting of a mono-layered charged dust particle crystal in a DC glow discharge Argon plasma is studied. The nature of the melting/formation process is established as a first order phase transition from the nature of the variations in the Coulomb coupling parameter, the dust temperature, the structural order parameter and from the existence of a hysteresis behavior. Our experimental results are distinctly different from existing theoretical predictions for 2D crystals based on the KTHNY mechanism or the Grain boundary induced melting and indicate a novel mechanism that is akin…
In this paper, we studied the structure and dynamics for a trilayer Yukawa crystal. We firstly studied the optimal lattice structure by comparing lattice interaction energy from different lattice distribution, after that, we did the collective mode calculation and analyzed its eigenvectors, if the lattice structure is stable, all the eigenvalues of the dynamical matrix should be positive.
A theoretical investigation of the modulational instability (MI) of dust-acoustic waves (DAWs) by deriving a nonlinear Schrödinger equation in an electron depleted opposite polarity dusty plasma system containing non-extensive positive ions has been presented. The conditions for MI of DAWs and formation of envelope solitons have been investigated. The sub-extensivity and super-extensivity of positive ions are seen to change the stable and unstable parametric regimes of DAWs. The addition of dust grains causes to change the width of both bright and dark envelope solitons. The findings of this s…
Theoretical investigation of the nonlinear propagation and modulational instability (MI) of the dust acoustic (DA) waves (DAWs) in an unmagnetized electron depleted dusty plasma (containing opposite polarity warm dust grains and non-extensive positive ions) has been made by deriving a nonlinear Schrödinger equation with the help of perturbation method. Two types of mode, namely, fast and slow DA modes, have been found. The criteria for the formation of bright and dark envelope solitons as well as the first-order and second-order rogue waves have been observed. The effects of various dusty plas…
Dust-ion-acoustic (DIA) rogue waves (DIARWs) are investigated in a three components dusty plasma system containing inertialess electrons featuring non-thermal non-extensive distribution as well as inertial warm ions and negative dust grains. A nonlinear Schrödinger equation (NLSE), which governs the conditions of the modulational instability (MI) of DIA waves (DIAWs), is obtained by using the reductive perturbation method. It has been observed from the numerical analysis of NLSE that the plasma system supports both modulationally stable domain in which dispersive and nonlinear coefficients of …
We study the non-linear evolution of the acoustic 'Resonant Drag Instability' (RDI) using numerical simulations. The acoustic RDI is excited in a dust-gas mixture when dust grains stream through gas, interacting with sound waves to cause a linear instability. We study this process in a periodic box by accelerating neutral dust with an external driving force. The instability grows as predicted by linear theory, eventually breaking into turbulence and saturating. As in linear theory, the non-linear behavior is characterized by three regimes - high, intermediate, and low wavenumbers - the boundar…
We investigate, for the first time, the nonlinear evolution of the magnetized "resonant drag instabilities" (RDIs). We explore magnetohydrodynamic (MHD) simulations of gas mixed with (uniform) dust grains subject to Lorentz and drag forces, using the GIZMO code. The magnetized RDIs exhibit fundamentally different behaviour than the purely acoustic RDIs. The dust organizes into coherent structures and the system exhibits strong dust-gas separation. In the linear and early nonlinear regime, the growth rates agree with linear theory and the dust self-organizes into two-dimensional planes or "shee…
