The study of waves and instabilities in quantum plasmas is of fundamental importance for understanding collective interactions in superdense astrophysical objects, in high intense laser-plasma/solid-matter interactions, in microelectronic devices and metallic nanostructures. In dense quantum plasmas, there are new pressure laws associated with the Fermi-Dirac distribution functions and new quantum forces associated with the quantum Bohm potential and the Bohr magnetization involving electron ½ spin. These forces significantly alter the collective behavior of dense quantum plasmas. This thesis contains six papers, considering several novel collective modes and instabilities at quantum scales. In Paper I, we have used the quantum hydrodynamical (QHD) model for studying the one-dimensional dust-acoustic (DA) waves incorporating the Fermi pressure law and the quantum Bohm potential. The latter modifies the DA wave dispersion relation in a collisional plasma. In Paper II, we have calculated the electrostatic potential of a test charge in an unmagnetized electron-ion quantum plasma. It is found that the Debye-Hückel and oscillatory wake potentials strongly depend upon the Fermi energy at quantum scales. The results can be of interest for explaining the charged particle attraction and repulsion in degenerate quantum plasmas, such as those in semiconductor and microelectronic devices. Paper III presents the parametric study of nonlinear electrostatic waves in two-dimensional collisionless quantum dusty plasmas. A reductive perturbation method has been employed to the QHD equations together with the Poisson equation, obtaining the cylindrical Kadomtsev-Petviashvili (CKP) equations and their stationary localized solutions. We have numerically examined the quantum mechanical and geometrical effects on the profiles of nonplanar quantum dust-ion-acoustic (DIA) and DA solitary waves. The role of static as well as mobile (negatively or positively charged) dust particles on the low-frequency electrostatic waves has also been highlighted for metallic nanostructures. Paper IV introduces the nonlinear properties of the ion-sound waves in a dense electron-ion Fermi magnetoplasma. The computational analysis of the nonlinear system reveals that the Sagdeev-like potential and the ion-sound density excitations are significantly affected by the wave direction cosine and the Mach number at quantum scales. Paper V considers the nonlinear interactions of electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfvén waves in a quantum magnetoplasma. The nonlinear dispersion relations have been analyzed analytically to obtain the growth rates for both the decay and modulational instabilities involving the dispersive IC, LH, and Alfvén waves. In Paper VI, we have identified a new drift-like dissipative instability in a collisional quantum plasma. The modified unstable drift-like mode can cause cross-field anomalous ion-diffusion at quantum scales.

<p>Theoretical studies of dusty plasmas have been performed by focusing attention principally on collective phenomena and on grain motion. This thesis consists of a collection of seven published papers that explore both the collective behavior of a complex plasma system as well as the dynamics of grains in plasmas. In paper 1, a mechanism that explains the energy gain which leads to the self excited grain oscillations is theoretically formulated. The newly developed mechanism explains the observed self excited oscillations through the coupling of plasma sheath fluctuations with the electrostatic force, which holds the dust grain. In paper 2, theoretical and simulation studies have been conducted to study the vertical oscillations of dust grains that are levitated in plasma sheaths, under low pressure conditions. The oscillations were driven either by an external force or by a plasma number density modulation. The proposed model gives a full picture of the dust grains dynamics and is capable of successfully explaining the experimental observations. Paper 3 explores both theoretically and numerically the origin of the nonlinearities that lead to the observed oscillation resonances. The feature of the confining potential well which traps the grain, the influence of an electrode voltage modulation on the trapping well, and hence on the grain dynamics, and the resulting nonlinear resonances are analyzed in detail. The numerical simulations presented successfully reproduce a broad range of dynamical phenomena, including the self excited oscillations, for a range of different parameters. Paper 4 is dedicated to the analysis of the propagation of Dust Acoustic Waves (DAW) in a medium with an equilibrium dust density distribution. It has been theoretically shown that only some harmonics of the dust density distribution will influence the propagation of the DAW, thus modifying its frequency. Paper 5 presents a theoretical and numerical analysis of the excitation of higher harmonics of electrostatic dust cyclotron waves. The instability is driven by the ion and electron currents flowing along the magnetic field. The dispersion relation and the wave instability conditions have been derived, and a detailed numerical analysis has been performed. In Paper 6, we explore theoretically some cross field instabilities of low frequency, long wavelength electrostatic modes in fully and weakly ionized plasmas. It is shown that in a magnetoplasma with a transverse equilibrium dc electric field, the energy associated with the cross field motion of the plasma particles can be coupled to low frequency electrostatic waves. Paper 7 explores the properties and instabilities of low frequency electrostatic waves propagating in a current carrying magnetoplasma with equilibrium density and field aligned ion flow with a transverse gradient. The paper contains previous results as limiting cases, together with additional instabilities related to the equilibrium plasma density distribution. </p>

Theoretical studies of dusty plasmas have been performed by focusing attention principally on collective phenomena and on grain motion. This thesis consists of a collection of seven published papers that explore both the collective behavior of a complex plasma system as well as the dynamics of grains in plasmas. In paper 1, a mechanism that explains the energy gain which leads to the self excited grain oscillations is theoretically formulated. The newly developed mechanism explains the observed self excited oscillations through the coupling of plasma sheath fluctuations with the electrostatic force, which holds the dust grain. In paper 2, theoretical and simulation studies have been conducted to study the vertical oscillations of dust grains that are levitated in plasma sheaths, under low pressure conditions. The oscillations were driven either by an external force or by a plasma number density modulation. The proposed model gives a full picture of the dust grains dynamics and is capable of successfully explaining the experimental observations. Paper 3 explores both theoretically and numerically the origin of the nonlinearities that lead to the observed oscillation resonances. The feature of the confining potential well which traps the grain, the influence of an electrode voltage modulation on the trapping well, and hence on the grain dynamics, and the resulting nonlinear resonances are analyzed in detail. The numerical simulations presented successfully reproduce a broad range of dynamical phenomena, including the self excited oscillations, for a range of different parameters. Paper 4 is dedicated to the analysis of the propagation of Dust Acoustic Waves (DAW) in a medium with an equilibrium dust density distribution. It has been theoretically shown that only some harmonics of the dust density distribution will influence the propagation of the DAW, thus modifying its frequency. Paper 5 presents a theoretical and numerical analysis of the excitation of higher harmonics of electrostatic dust cyclotron waves. The instability is driven by the ion and electron currents flowing along the magnetic field. The dispersion relation and the wave instability conditions have been derived, and a detailed numerical analysis has been performed. In Paper 6, we explore theoretically some cross field instabilities of low frequency, long wavelength electrostatic modes in fully and weakly ionized plasmas. It is shown that in a magnetoplasma with a transverse equilibrium dc electric field, the energy associated with the cross field motion of the plasma particles can be coupled to low frequency electrostatic waves. Paper 7 explores the properties and instabilities of low frequency electrostatic waves propagating in a current carrying magnetoplasma with equilibrium density and field aligned ion flow with a transverse gradient. The paper contains previous results as limiting cases, together with additional instabilities related to the equilibrium plasma density distribution.