Qualitative and Quantitative Analysis of Nonlinear Structures in Space Plasmas

Abstract

The present thesis is focused on the formation and propagation of nonlinear struc tures in space plasmas. The propagation characteristics of nonlinear solitary and pe riodic waves are studied via Korteweg-de Vries (KdV) equation, Zakharov-Kuznetsov (ZK) equation, Kadomtsev-Petviashvili (KP) and modified Kadomtsev-Petviashvili (mKP) equations. The theory of planar dynamical system is utilized for analyzing nonlinear phenomena qualitatively. For the purpose of studying the plasma models quantitatively, Jacobi elliptic functions are used. With the assumption that electrons follow the double spectral index distribution function, the formation of electrostatic ion acoustic periodic waves and solitons with warm ions are shown. The double spectral index distribution successfully reflects the distributions frequently observed in space plasmas. The Korteweg-de Vries (KdV) equation, which characterizes the nonlinear periodic waves with suitable boundary conditions, is derived using the common re ductive perturbation technique. Solitary wave solutions and periodic wave solutions to the KdV equation are discovered by employing a planar dynamical system. It is demonstrated that the propagation properties of nonlinear ion acoustic periodic and solitary structures are affected by modifying the electron population in regions of low and high phase space density. Additionally, a comparison between Maxwellian dis tribution and non-Maxwellian distribution functions is done. Also highlighted is the significance of the current findings in relation to space plasmas. In magnetized two ion component (O-H-e) plasmas with (r, q) distributed electrons, the characteristics of solitary and periodic ion acoustic structures are investigated. It is discovered that in such a plasma, two ion acoustic wave modes, namely the fast and slow modes, can propagate. The well-known reductive perturbation approach is used to obtain the nonlinear Zakharov-Kuznetsov (ZK) equation. The system under investigation admits compressive (hump) and rarefactive (dip) solitary structures as well as periodic wave v solutions, according to the theory of planar dynamical systems. It is found that the physics of the fast and slow modes affect how nonlinear ion acoustic solitary structures behave throughout their propagation. In-depth research is done on the impact of the double spectral indices r and q. It is investigated that changing the distribution func tion’s shape (using these indices) has a significant impact on how nonlinear ion acoustic waves propagate. While the temperature ratio is seen to modify the slow mode, the ratio of heavy to light ion concentration (O/H) is found to change the fast mode. We focused our research on the upper ionosphere, where numerous satellite missions have recorded the presence of non-Maxwellian electrons and bi-ion plasmas. Using kappa distributed two-temperature electrons, while ions are assumed to be Maxwellian, the nonlinear properties of dust acoustic solitary and periodic waves are studied. The nonlinear Kadomtsev-Petviashvili (KP) and modified Kadomtsev-Petviashvili (mKP) equations are derived using the reductive perturbation technique. Study is done on the quantitative and qualitative properties of periodic and solitary compressive and rarefactive wave formations. For the aim of quantitative analysis, the Jacobi elliptic function expansion method is used, and the dynamical system approach is used to study the qualitative behavior. It is observed that at various radii of Saturn’s inner magnetosphere, the amplitude and width of the nonlinear dust acoustic solitary and pe riodic structures vary. When the population of energetic cold electrons is reduced, the solitary structure becomes electrified. Our research is applied to Saturn’s inner mag netosphere, where numerous satellite missions have recorded the presence of negatively charged dust and unevenly distributed two-temperature electrons. The analytical and numerical findings of this thesis are of fundemental importance in nonthermal plasmas to understand the nonlinear solitary structures and cnoidal waves. The results and outcomes further equip us to ascertain the exciting features of nonlinear structures in space plasmas.