Plasmas seeded with solid particulates of nanometer to micron sizes (complex plasma systems) are a ubiquitous feature of intergalactic, interstellar and planetary environments but also of plasma processing applications or even fusion devices. Their novel aspects compared with ideal multi-component plasmas stem from (i) the large number of elementary charges residing on the grain surface, (ii) the variability of the charge over mass ratio of the dust component, (iii) the inherent openness and dissipative nature of such systems.   Their statistical description presents a major challenge; On one hand by treating dust grains as point particles new phase space variables must be introduced augmenting the classical Hamiltonian phase space, while the microphysics of interaction between the plasma and the grains will introduce additional coupling between the kinetic equations of each species, apart from the usual fine-grained electromagnetic field coupling. On the other hand complex plasma systems do not always exist in a gaseous state but can also condensate, i.e. form liquid, solid or crystalline states.   In this thesis we study gaseous partially ionized complex plasma systems from the perspective of the Klimontovich technique of second quantization in phase space. Initially, in regimes typical of dust dynamics. Starting from the Klimontovich equations for the exact phase space densities, theory deliverables such as the permittivity, the spectral densities of fluctuations and the collision integrals are implemented either for concrete predictions related to low frequency electrostatic waves or for diagnostic purposes related to the enhancement of the ion density and electrostatic potential fluctuation spectra due to the presence of dust grains. Particular emphasis is put to the comparison of the self-consistent kinetic model with multi-component kinetic models (treating dust as an additional massive charged species) as well as to the importance of the nature of the plasma particle source. Finally, a new kinetic model of complex plasmas (for both constant and fluctuating sources) is formulated. It is valid in regimes typical of ion dynamics, where plasma discreteness can no longer be neglected, and, in contrast to earlier models, does not require relatively large dust densities to be valid. / QC 20120316

<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.