ANALYTICAL AND NUMERICAL SIMULATION OF WAVES AND INSTABILITIES IN STRONGLY COMPLEX PLASMA

Abstract

The central objective of this thesis is to examine the fundamental nature of electrostatic wave phenomena in magnetized dusty plasma systems. A detailed understanding of dusty plasma behavior is essential for interpreting a wide range of physical processes occurring in both controlled laboratory experiments and natural space environments. In contrast to ordinary electron–ion plasmas, dusty plasmas contain micron- or submicron-sized solid particles immersed within the plasma, a feature that fundamentally alters the collective dynamics of the system. The presence of these dust grains introduces additional degrees of freedom, leading to richer and more complex wave and instability characteristics. The investigation begins with an exploration of the basic physical principles underlying dusty plasma systems, focusing on the coupled interactions among charged dust particles, electrons, and ions under the influence of an external magnetic field. Particular attention is given to the generation, propagation, and stability of electrostatic waves, as well as to the physical mechanisms responsible for their excitation. Through this approach, the complex nature of electrostatic wave dynamics and instability formation in dusty plasmas is systematically analyzed. The theoretical insights obtained from this study are relevant to a broad spectrum of applications, including plasma-based materials processing, geophysical and atmospheric phenomena, astrophysical systems, microelectronic fabrication, fusion research, and solar wind dynamics. The overarching objective is to elucidate how the interplay between charged dust grains, the surrounding plasma medium, and the magnetic field collectively governs the behavior of electrostatic waves. To achieve these goals, several theoretical frameworks are developed using fundamental plasma fluid description. The governing equations namely the continuity and momentum equations, and Poisson’s equation are employed to derive analytical expressions for wave frequencies and instability growth rates. The dependence of these quantities on key plasma parameter is then examined in detail. Generalised Hydrodynamic Model (GHD) has been used for the description of strongly coupled dust grains as they are in a fluid like state for a wide range of strong coupling parameter. The effects of strong coupling among dust particles on the dispersion characteristics of longitudinal mode and the novel shear mode have been studied. Furthermore, the effect of cylindrical geometry, magnetic field, collissions among dust grains have been analysed. The evolution of Rayleigh Taylor instability (RTI) in a strongly correlated dusty plasma driven by an ion beam has been investigated through Generalized Hydrodynamic( GHD) Model. The instability analysis focuses on effects of beam velocity, beam density, density scale length and strong coupling parameters on the instability growth rate and frequency. The ion beam enhances the pressure imbalance across the interface, thereby driving the RTI, while the viscoelastic response of the strongly coupled medium introduces a stabilizing influence. It has been observed that the growth rate of ion beam driven RTI is suppressed with increasing coupling strength and magnetic field, while the instability grows with higher beam density and velocity enhances the instability, density scale length and beam density. These results provide insight into controlling beam-induced RTI in complex plasmas and are relevant to inertial confinement fusion (ICF), astrophysical dusty plasmas. vi The parallel velocity shear instability (PVSI) or the Kelvin Helmholtz instability is a prominent instability in various astrophysical and laboratory situations. The instability analysis has been done in the linear regime. The combined effect of ion beam and polarisation of dust grains have been studied in the presence of dust charge fluctuation. A theoretical model has been developed to incorporate all this factors. The effect of beam parameters and dust polarisation on the instability has been analysed.