THEORETICAL MODELLING OF ELECTROSTATIC WAVES IN A MAGNETIZED DUSTY PLASMA

Abstract

The main aim of the thesis is to understand the intrinsic behaviour of electrostatic waves in a magnetized dusty plasma. It is crucial to learn about the behaviour of dusty plasmas in order to better understand both laboratory and space plasmas. Dusty plasmas are distinguished from other forms of plasmas in various astronomical and laboratory contexts by the presence of solid particles inside the plasma medium. The incorporation of these dust grains increases complexities in the system and sheds new light on the behaviour of waves and instabilities. The first step in our investigation is to identify the fundamental ideas that govern dusty plasmas, including the complex interactions that occur between charged dust particles, electrons, and ions in a magnetized plasma. We examine the propagation of electrostatic waves and instabilities within a plasma as well as the mechanisms that generate these waves, delving into the complex nature of electrostatic waves and instabilities. The results of these studies have numerous applications in a variety of domains, including materials processing, geophysical phenomena, astrophysics, microelectronics, fusion science, and the solar wind. The main goal of our research is to understand the intricate interactions that take place between charged dust particles, the plasma environment, and the magnetic field to collectively influence the characteristics of electrostatic waves. In this thesis, different theoretical models have been developed with the help of the basic equations i.e., the Vlasov Equation, the Equation of Continuity and Motion and Poisson’s Equation to govern the behaviour of waves and instabilities. With the help of these equations, the expressions of frequency and the growth rate have been discovered and the effect of these have been analyzed on different plasma parameters like the gyroradius parameter, temperature, and relative density ratio etc. These studies advance our knowledge of electrostatic waves and instabilities in a magnetized dusty plasma by providing important information regarding the way these waves include charged particle movement, wave-particle interactions, and the overall equilibrium of these systems. The waves and instabilities used in our work are Lower Hybrid Waves (LHWs), Electrostatic Ion Cyclotron Waves (EICWs) and Inhomogeneous Energy Density Driven Instability (IEDDI). LHWs are electrostatic low-frequency plasma waves due to the longitudinal oscillation of ions in a magnetized plasma and these waves can be studied in tokamak plasmas, and lunar dusty plasma and have recently received significant attention for vi Anshu, Delhi Technological University affecting the current drive at a very high density. The EICWs are one of the fundamental modes when the plasma is magnetized, and the electrons drift along magnetic field lines. The EIC is a field-aligned current-driven instability with one of the lowest threshold drift velocities among current-driven instabilities and these waves have applications in space plasma. A flow of energy from one region to another region can enable the mode to grow, giving rise to instability. This is the physical mechanism underlying the IEDDI and this instability can be used to explain a wide range of experiments in Earth’s Ionosphere and other space applications. Further studies on these waves and instabilities have been done in collisionless and collisional plasma. Collisions increase the interactions between charged particles and dust particles, changing the dispersion relation of the waves and exhibiting distinct characteristics. Moreover, these waves can be studied in the presence of the transverse direct current electric field. This electric field changes the dispersion characteristics of waves and the wave behaviour can be studied with different plasma parameters. Numerous analytical methods, including fluid theory and kinetic theory, have been used to study these waves. The two approaches possess unique mathematical equations guiding the behaviour of the waves. Additionally, using electron or ion beams can be used to induce the excitation of waves and instabilities. From fusion science to space plasma, it is essential to comprehend the physics of beam-plasma interactions. These systems have numerous uses, such as particle acceleration, diagnostics and plasma heating. The investigation of electrostatic waves in magnetized dusty plasmas and the analysis of the impacts of various plasma parameters on wave dispersion characteristics are the main objectives of the present work. Our analytical model and the results from numerical calculations would help in understanding the experimental results from several leading groups worldwide.