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>This licentiate thesis reports analytical results for the electrostatic response to a test charge moving through dusty plasma. Two particular cases for a slowly moving test charge, namely, grain size distribution and grain charging dynamics are considered. Analytical results for the delayed shielding of a test charge due to dynamical grain charging in dusty plasma are also reported. In the first case, a dusty plasma in thermal equilibrium and with a distribution of grain sizes is considered. A size distribution is assumed which decreases exponentially with the grain mass for large sizes and gives a simple smooth reduction for small sizes. The electrostatic response to a slowly moving test charge, using a second order approximation is found and the effects of collisions are also investigated. It turns out that for this particular size distribution, there is a remarkably simple result that the resulting effective distribution for the electrostatic response is a kappa (generalized Lorentzian) distribution. In the second case, we present an analytical model for the shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging for cases both with and without the collision effects. The response potential is treated as a power series in test charge velocity. Analytical expressions for the response potential are found up to second order in test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. It is concluded that the dynamical charging of the grains in a dusty plasma enhances the shielding of a test charge. To clarify the physics, a separate study is made where the charging is approximated by using a time delay. The resulting potential shows the delayed shielding effect explicitly. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. This kind of work has relevance both in space and astrophysical plasmas.</p>

This licentiate thesis reports analytical results for the electrostatic response to a test charge moving through dusty plasma. Two particular cases for a slowly moving test charge, namely, grain size distribution and grain charging dynamics are considered. Analytical results for the delayed shielding of a test charge due to dynamical grain charging in dusty plasma are also reported. In the first case, a dusty plasma in thermal equilibrium and with a distribution of grain sizes is considered. A size distribution is assumed which decreases exponentially with the grain mass for large sizes and gives a simple smooth reduction for small sizes. The electrostatic response to a slowly moving test charge, using a second order approximation is found and the effects of collisions are also investigated. It turns out that for this particular size distribution, there is a remarkably simple result that the resulting effective distribution for the electrostatic response is a kappa (generalized Lorentzian) distribution. In the second case, we present an analytical model for the shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging for cases both with and without the collision effects. The response potential is treated as a power series in test charge velocity. Analytical expressions for the response potential are found up to second order in test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. It is concluded that the dynamical charging of the grains in a dusty plasma enhances the shielding of a test charge. To clarify the physics, a separate study is made where the charging is approximated by using a time delay. The resulting potential shows the delayed shielding effect explicitly. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. This kind of work has relevance both in space and astrophysical plasmas. / QC 20101220

This doctoral thesis reports analytical and numerical results for the electrostatic response of a dusty plasma to a moving test charge. Two important physical aspects of dusty plasmas, namely grain size distribution and grain charging dynamics were taken into account. In the first case, a dusty plasma in thermal equilibrium and with a distribution of grain sizes is considered. A size distribution is assumed which decreases exponentially with the grain mass for large sizes and gives a simple smooth reduction for small sizes. The electrostatic response to a slowly moving test charge, using a second order approximation is found and the effects of collisions are also investigated. It turns out that for this particular size distribution, there is a remarkably simple result that the resulting effective distribution for the electrostatic response is a kappa (generalized Lorentzian) distribution. In the second case, we present an analytical model for the shielding of a slowly moving test charge in a dusty plasma with dynamical grain charging for cases both with and without the collision effects. The response potential is treated as a power series in test charge velocity. Analytical expressions for the response potential are found up to second order in test charge velocity. The first-order dynamical charging term is shown to be the consequence of the delay in the shielding due to the dynamics of the charging process. It is concluded that the dynamical charging of the grains in a dusty plasma enhances the shielding of a test charge. To clarify the physics, a separate study is made where the charging is approximated by using a time delay. The resulting potential shows the delayed shielding effect explicitly. The terms in the potential that depend on the charging dynamics involve a spatial shift given by the test charge velocity and the charging time. The wake potential of a fast moving test charge in the case of grain charging dynamics was also found. It was observed that the grain charging dynamics leads to a spatial damping and a phase shift in the potential response. Finally, combining these two physical aspects, generalized results for the electrostatic potential were found incorporating the terms from both grain size distribution and grain charging dynamics. The generalized results contain the previous work where these two effects were studied separately and which can now be found as special limiting cases. This kind of work has relevance both in space and astrophysical plasmas. / QC 20100920