The Klimontovich description of complex plasma systems : Low frequency electrostatic modes, spectral densities of fluctuations and collision integrals

Sammanfattning: 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.