Theoretical Modeling of Both Statistical Characteristics of Scattered Microwaves and Dynamics of ULF EM Wavy Structures in the Ionosphere

**Tech Area / Field**

- PHY-PLS/Plasma Physics/Physics
- PHY-RAW/Radiofrequency Waves/Physics

**Status**

**3** Approved without Funding

**Registration date**

**21.12.2004**

**Leading Institute**

Georgian Technical University, Georgia, Tbilisi

**Collaborators**

- University of Washington / Department of Electrical Engineering, USA, WA, Seattle\nKyushu University / Department of Computer Science and Communication Engineering, Japan, Fukuoka

**Project summary**

The main goals of the project are: generalization of the Kotelnikov–Shannon’s formula (deterministic and random cases) allowing to achieve higher accuracy of reproduction of a signal and highly noise stability; restoration of stochastic signal and fields its partial derivatives on the basis of sampling in discrete points; justification of the obtain formulas for determine class of nonstationary stochastic processes including harmonized processes and, in particular, stationary stochastic processes; analytical calculation and numerical simulation of statistical moments of the angular power spectrum (APS) scattered high–frequency (HF) radiation by randomly inhomogeneous absorptive anisotropic both dispersive (anisotropic collisional magnetoplasma) and non–dispersive layers and investigation of new features of the “effect of compensation”; we expect to reveal new effects due to joint influence of absorption and anisotropy in the low atmosphere taking into account external inhomogeneous magnetic field; investigation of both generation and dynamics of electromagnetic (EM) wavy structures in turbulent ionosphere; creation of new mechanism of ultra–low–frequency (ULF) planetary-scale EM waves generating in different ionospheric layers; self–organization and generation of ULF large–scale solitary vortices in the ionosphere. Technical approach and methodology of investigation of dynamics of both atmospheric disturbances and nonlinear vortex formations, as structural elements of turbulence is based on the development of new algorithms, schemes and methods of solution of set of nonlinear magnetohydrodynamic equations and Maxwell's equations for EM fields. Novelty of this task is the original approach of investigation of the atmospheric disturbances dynamics, particularly consideration of nonlinear vortex formations as structural elements of turbulence. Accumulation and transparence of vortices at different altitude lead to transparence of trapped particles and substantial fluctuations both density and energy. Various waves (slow, fast, gradient) caused due to vortex electric field will be revealed. The reason of generation of these waves in the ionosphere is continuously acting factor – inhomogeneity and curvature of geomagnetic field. These investigations will be carried out on the bases of analytical calculations and numerical calculations of nonlinear dynamic equations. Dynamic of planetary–scale wavy structures will be investigated in the –approximation. Spatial inhomogeneities of both angular velocity of the earth rotation and geomagnetic field for ULF planetary scale EM waves will be taken into account. Novelty of the project is application of new approach–nonmodal mathematical analyses for investigation of interaction between ULF planetary EM wave and local spatial inhomogeneous wind. Two and three–dimensional modeling equations describing dynamics of nonlinear soliton–vortex formations will be obtained. These equations will be solved by means of analytical and numerical methods using PC applying corresponding initial and boundary conditions. At the next stage of this project new features of the evolution of the APS of HF scattered radiation will be investigated in the geometrical optics (GO) and narrow band of angle approximations. Novelty of this project is the search of new effects in a randomly inhomogeneous, absorptive, anisotropic layers of the ionosphere taking into account external inhomogeneous magnetic field; investigation of new features of the “effect of compensation” for different altitudes of the ionosphere, taking into account both external magnetic field and anisotropy of scattered collisional magnetoplasma. Calculations will be carried out for different spatial spectrum of electron concentration fluctuations and phase function. We will find the “angle of compensation” at which oblique illumination of the surface and medium anisotropy completely compensates each other. In this case the center of gravity of the APS does not displace and the spatial spectrum not broadens. Statistical simulation will be carried out by Monte Carlo method. We will expect to give any recommendations of its practical application. Novelty of this project is the investigation of experimentally measured APS of microwaves scattered by turbulent magnetoplasma layer at oblique external magnetic field and oblique illumination of the surface; the source and the receiver are located on the opposite sides with respect to the turbulent layer. Deformation of the APS in a transient regime will be simulated by Monte Carlo method. Restoration of continuous signals (TV signals, radio signals) by means of registration of discrete samplings will be considered too. For this purpose generalized Kotelnikov–Shannon’s formulas will be derived using methods of the theory of complex variable. This is novelty of the submitted project. Highly effective generalized formula of samplings will be expressed as the infinite stochastic functional series and it can be applied for more exact transfer of continuous signals on various distances. The residual term of this series will be estimated by asymptotical methods. The obtained formulas will have highly speeded of convergence in comparison with the well known Kotelnikov–Shannon’s formula. They will be valid for determine class of nonstationary stochastic processes including harmonized processes and, in particular, stationary stochastic processes. For these purposes functional analyses (matrix analyzed method for functional), the theory of functions of complex variable (the Cauchy residue theory), the theory of the whole functions (asymptotic properties of the whole functions) will be utilized. Expected results are: the dependence of both broadening of the APS and displacement of its center of gravity of multiply scattered EM waves versus: absorption, anisotropy, different orientation of an external magnetic field and different angle of inclination of the line–of–sight with respect to the turbulent plasma layer will be investigated in the ray (–optics) approximation. The source and receiver are located on the opposite sides with respect to the layer. Deformation of the angular spectrum will be considered in a transient zone passing to the depth regime. The angle of compensation at which two asymmetric factors (oblique illumination and medium anisotropy) compensate each other will be found for different layers of the ionosphere. Generalized Kotelnikov–Shennon’s formulae will be obtained for complex variable. They will be submitted as stochastic functional series. The highly effective generalized formula of samplings will be expressed as the infinite series and it can be applied for more exact transfer of continuous signals on various distances. The residual term of this series will be estimated by different asymptotical methods. The obtained formulas will have highly speeded of convergence in comparison with the well known Kotelnikov–Shannon’s formula. They will be valid for deterministic class of nonstationary stochastic processes including harmonized processes and, in particular, for stationary stochastic processes. Physical and mathematical (linear and nonlinear) models of the influence of both ionized components of plasma and geomagnetic field on creation of nonlinear solitary vortices in the ionospheric plasma will be suggested. New mechanism of both generation of ULF planetary-scale EM waves and self organization of nonlinear vortex structures of these waves in different layers of the ionosphere will be submitted. The amplitudes, spatial scales, velocity of propagation and various dynamical characteristics of these structures will be calculated. Dynamic of these large-scale wavy structures will be considered in the - approximation using nonmodal mathematical analyses. This is novelty of submitted project. Linear wavy processes of energy transfer between flows and perturbations, inter-transformation between the waves and modes and other mechanisms will be investigated using nonmodal approximation. The obtained results can be utilized for: diagnostic of parameters of randomly inhomogeneous ionosphere, cosmic and laboratory plasma; modification of remote sensing methods and algorithms; description of X-ray scattering on molecules of thermotropic and liotropic liquid crystals, ultraviolet light scattering by chloroplast. Generalized Kotelnikov–Shannon’s formula will have great practical application in communication systems and can be applied for restoration of continuous signals (TV signals, radio signals) registering by recipient by means of discrete samplings. Compensation effect and other similar effects, which will be revealed by us in different altitudes of the ionosphere, in our point of view, will have great practical application in satellite communications and remote sensing of both artificial and natural plasma inhomogeneities by the translucence methods. Some results will have practical application in medicine, particularly in revealing of the reasons of pathological complications in people by ULF EM precursors caused due to natural hazard (earthquake, volcano, tsunami and other).
The GTU team consists of high qualified physicists and mathematics specialists. They have great experience in physical and mathematical modelling of different problems in linear and nonlinear theory of wave propagation in random media, atmosphere and ionosphere. They have published many papers in refereed scientific journals and proceedings of different international symposiums relating to these problems. Foreign collaborators Professor A. Ishimaru (USA) and Professor M. Tateiba (Japan) are very famous scientists. Their current research includes waves in random media, remote sensing, object detection and imaging in clutter environment, inverse problems, millimeter wave and optical propagation and scattering in the atmosphere and terrain, rough surface scattering and optical diffusion in tissues. Collaboration with Professor A. Ishimaru and Professor M. Tateiba is a great honor for the Georgian team. U.S. and Japanese collaborators and the Georgian Principal Investigator will coordinate the obtained results at regular intervals during the project implementation.