Wiener-Hopf Analysis of EM-Wave Diffraction by a Finite Plate in Cold Plasma

Abstract

Propagation of electromagnetic (EM) waves play a vital role in communication system. The ultraviolet radiations impinging on earth’s atmosphere ionize a fraction of neutral atmosphere which results into a mixture of charged particles (i.e. ions and electrons) as well as neutral particles. Since the collisions in the region of earth’s atmosphere above 80 km from earth, are very rare, therefore, under such conditions the recombination rate of charged species is very slow resulting a permanent ionized medium, named as ionosphere. A cold plasma may correspond to ionosphere under the presence of earth’s magnetic field where the effect of finite temperature and pressure variations are ignored. The ionosphere of plasma is highly magnetized under earth’s magnetic field; therefore, it can be treated as an anisotropic medium. Also, since the cold plasma can be considered as a model for the ionosphere, it is possible to investigate the diffraction mechanisms of the complex scatterers in the ionosphere such as airplanes or satellites. Measurements based on the artificial satellites moving in the ionosphere around the earth, communicating to earth station are affected drastically as the communicating signals radiated by satellite and diffracted by some obstacle get modified on interaction with ionosphere plasma (cold plasma) and also because of the nature of material of the body i.e. electric and magnetic susceptibilities or impedance. To quantify the results arising due to the effectiveness of cold plasma and nature of the material on the diffraction of electromagnetic waves, some theoretical models have been devised in the present thesis. Thesis is summarized in the order below. Chapter one contains literature survey of previous research study by the researchers, some basic description of plane wave, Fourier transform, cold plasma, analytic continuation, method of stationary phase (an asymptotic method) and a short note on Wiener-Hopf technique for general readers. Chapter two addresses diffraction of electromagnetic plane wave by a finite plate in the cold plasma. Helmholtz equation is derived with the combined use of Maxwell’s equations and electric field components in terms of magnetic field with cold plasma effects. Dirichlet boundary conditions assumed along the plate. Fourier transform is applied on the problem and using the general theory of Wiener-Hopf procedure is used to obtain the Wiener-hopf equation. The required diffracted field is obtained by inverse Fourier transform and then by the method of stationary phase. Graphs are plotted to analyze that how the separated field (diffracted field by finite plate) is affected by physical parameters in the presence and absence of cold plasma. The contents of this chapter are published in Physics of Wave Phenomena 26 (2018) 342-350. Chapter three explores the diffracted electromagnetic plane wave by a finite plate in the cold plasma. Helmholtz equation is derived with the combined use of Maxwell’s equations and electric field components in terms of magnetic field with cold plasma effects. Neumann boundary conditions assumed along the plate. Fourier transform is applied on the problem and using the general theory of Wiener-Hopf procedure is used to obtain the Wiener-Hopf equation. The required diffracted field is obtained by inverse Fourier transform and then by the method of stationary phase. Graphs are plotted to analyze that how the separated field (diffracted field by finite plate) is affected by physical parameters in the presence and absence of cold plasma. The contents of this chapter are published in Plasma Physics Reports 46 (2020) 1-9. Chapter four examines the diffracted electromagnetic plane wave by a finite plate in the cold plasma. Impedance is assumed on upper and lower surface of the plate. Therefore, Leontovich boundary conditions are considered to study the effects of impedance on separated field. Helmholtz equation is derived with the combined use of Maxwell’s equations and electric field components in terms of magnetic field with cold plasma effects. Fourier transform is applied on the problem and using the general theory of Wiener-Hopf procedure is used to obtain the Wiener-Hopf equations. The required diffracted field is obtained by inverse Fourier transform and then by the method of stationary phase. Graphs are plotted to analyze that how the separated field (diffracted field by finite plate) is affected by physical parameters in the presence and absence of cold plasma. Chapter five describes the diffracted electromagnetic plane wave by a symmetric finite plate in the cold plasma. Impedance on upper and lower surface of the plate is taken into an account. Leontovich boundary conditions are used to analyze the effects of impedance on the diffracted field by symmetric plate of finite length. Helmholtz equation is derived with the combined use of Maxwell’s equations and electric field components in terms of magnetic field with cold plasma effects. Fourier transform is applied on the problem and using the general theory of Wiener-Hopf procedure is used to obtain the Wiener-Hopf equations. The required diffracted field is obtained by inverse Fourier transform and then by the method of stationary phase. Graphs are plotted to analyze that how the separated field (diffracted field by finite plate) is affected by physical parameters in the presence and absence of cold plasma. Chapter six presents the diffracted electromagnetic plane wave by a slit of finite width in the cold plasma. Surface Helmholtz equation is derived with the combined use of Maxwell’s equations and electric field components in terms of magnetic field with cold plasma effects. Fourier transform is applied on the problem and using the general theory of Wiener-Hopf procedure is used to obtain the Wiener-Hopf equations. The required diffracted field is obtained by inverse Fourier transform and then by the method of stationary phase. Graphs are plotted to analyze that how the separated field (diffracted field by finite plate) is affected by physical parameters in the presence and absence of cold plasma.