Twisted Electrostatic Waves and Instabilities in Plasmas

Abstract

The kinetic study of waves and instabilities in multi-component plasmas is carried out to account for finite orbital angular momentum (OAM) states associated with helical wavefronts of the waves. This has its strong relevance for understanding collective modes in space and laser-plasma interaction environments. Multi-component plasma here refers to dusty plasma, two temperature component electron-ion plasma and permeating plasma. The entire thesis is based on five research articles published in international refereed journals, showing various plasma waves and instabilities at different dynamical scales. Chapter 1 introduces the basics of plasma state with its criteria, applications and various characteristics of plasma modes. A literature survey is also made to assess the historical background and current status of the subject. Chapter 2 describes the basic plasma models including the fluid and kinetic approaches to show fluid and statistical behavior of the plasma particles and discusses the properties of planar and non-planar (helical) wavefronts of electrostatic waves. In Chapter 3, the electrostatic twisted dust-acoustic (TDA) and twisted dustion-acoustic (TDIA) waves are studied in a collisionless unmagnetized multi-component dusty plasma, whose constituents are the electrons, singly ionized positive ions, and negatively charged massive dust grains. With this background, the Vlasov-Poisson equations are solved together to derive a generalized dielectric constant by utilizing the Laguerre-Gaussian (LG) perturbed distribution function and electrostatic potential in the paraxial limit. The dispersion and damping rates of TDA and TDIA waves are analyzed with distinct OAM states in a multi-component dusty plasma. Significant modifications in the real wave frequencies and damping rates are shown due to twist parameter and dust concentration effect. It is found that dust concentration enhances the phase speed of the TDIA waves in contrary to TDA waves, whereas the impact of twist parameter reduces xx the frequencies of TDA and TDIA waves. The results are useful to understand the trapping and particle transport owing to wave excitation in laboratory dusty plasmas. In Chapter 4, the study is extended for the investigation of twisted electrostatic waves in an unmagnetized self-gravitating thermal dusty plasma with finite OAM states. The dispersion relation and damping rate of TDA waves are analyzed both analytically and numerically. It is shown that OAM parameter, dust-to-electron temperature ratio and dust self-gravitation effects significantly modify the real wave and Landau damping frequencies. The phase speed of TDA waves is reduced with the variation of twist parameter, dust concentration and dust self-gravitation effects. The relevance of our findings to interstellar dust clouds is discussed in details for micron-sized massive dust grains. Chapter 5 presents the twisted ion-acoustic (TIA) excitations and the existence of kinetic instability with helical wavefronts in a permeating plasma. The latter consists of a solar wind electron-ion plasma that permeates into the target cometary plasma. For this, a Vlasov-Poisson model is used to obtain the explicit expressions for wave dispersion and kinetic instability including the contributions from the orbital angular momentum. It is shown that the existence of instability owes to the exceeding electron speed as compared to the ion-acoustic speed with strong contribution of twist in the wave. Furthermore, it is found that planner ion-acoustic wave propagates as a slow wave in comparison with nonplanar (twisted) wave. Many new features of the twisted dusty plasma modes and associated instabilities are discussed for permeating plasmas in Chapter 6. Existence conditions for damping/growth rates are obtained to show significant modifications in twisted dusty modes as compared to straight propagating dusty modes. Numerically, the instability growth rate with particle streaming and twist effects in the wave potential is significantly xxi affected due to the LG profiles. Relevance of the wave excitations due to penetration of solar wind into cometary clouds or interstellar dusty plasmas is also discussed. In Chapter 7, the electrostatic twisted waves with finite OAM states are studied in a doubly κ-distributed superthermal plasma, containing superthermal hot and cool electrons in addition to positive ions. The modified dispersion relations and growth rate of electrostatic twisted electron-acoustic (TEA) and twisted ion-acoustic (TIA) waves are calculated. For parametric analysis, the impact of hot and cool electron indices (κh) and (κc), twist parameter (η) and hot-to-cool electron density ratio (f) is examined on the profiles of TEA and TIA waves. The threshold conditions for the growth rates of TEA and TIA waves are also analyzed both analytically and numerically. The present results are relevant to Saturn's outer magnetosphere, where two groups of electrons with different finite temperatures follow double κ-distribution functions.