Propagation Characteristics of VLF Waves Below a Stratified and Generally Anisotropic Ionosphere


Book Description

The research constitutes one method of formulation for the calculation of very low frequency radio wave propagation characteristics of the earth-ionosphere waveguide. It involves a brief consideration of some general properties of the ionosphere which influence the propagation of VLF (very low frequencies) waves. In the analysis, the waveguide is the area formed by the earth and the lower conducting region of the ionosphere. The propagation characteristics are obtained from the solution of a modal equation which is formulated directly in terms of the reflection coefficients of both the ionosphere and earth. The coupled vacuum mode theory of Poeverlein is extended to include the earth's curvature effects by assuming the ionosphere as a cylindrical stratified medium. The modal equation is solved by an iterative procedure and propagation characteristics are obtained for a variety of ionospheric conditions for different directions of propagation. A comparison of the numerical results is made with different formulations in the literature. (Author).







Propagation of Elf and Vlf Waves Below a Generally Anisotropic Ionosphere


Book Description

The mode analysis of ELF and VLF waves has been generalized to allow arbitrary directions of propagation below a curved stratified ionosphere with a dipping static magnetic field. In the ELF range, the propagation parameters are changed almost linearly with the azimuthal angle phi by varying the direction of propagation from East to West. In the VLF range, the phase velocity exhibits its maximum value for propagation in South and North direction; and minimum values occur for propagation towards West. Also, maximum attenuation rates occur for propagation towards West. Measured interference distances D of the two lowest wave-guide modes have been explained using nighttime ionosphere models which exhibit sharp density gradients in the height range from 80 to 85 km. (Author).




Propagation of Vlf Waves Below an Anisotropic Stratified Ionosphere with a Transverse Static Magnetic Field


Book Description

The surface impedance of a cylindrically stratified anisotropic ionosphere has been computed in the presence of a transverse static magnetic field without requiring explicit representations of the individual cylindrical wave functions in the lower ionospheric layers. The propagation parameters are determined from the usual transcendental modal equation which is solved starting out with an initial real solution dependent on the reactive part of the ionospheric surface impedance. The surface impedance computations are continued below the ionospheric boundary height and the impedance reflected to the ground level by the ionosphere is compared with the ground impedance. The accuracy of the modal equation is shown to be comparable to a few percent uncertainty of the ground impedance for low conductivity ground. The propagation parameters of the first three waveguide modes are calculated for a number of ionosphere models which include the recent D-region models of Deeks. For propagation in the east to west direction, the phase velocity of the second mode is shown to be discontinuous when the real part of the ionospheric reflection coefficient undergoes a sign change. (Author).




Propagation of Elf and Vlf Waves Below an Anisotropic Ionosphere with a Dipping Static Magnetic Field


Book Description

Fields of cylindrically curved ionosphere layers are approximated by exponential functions which consider the increase of the phase velocity and decrease of the attenuation rate with the altitude of the layers. Matrix multiplication techniques are applied to the treatment of multi-layer ionosphere models. The individual ionosphere layers are thin relative to the wavelength and the approximate field representations give in the limits of horizontal and radial static magnetic field results identical to those obtained using more accurate treatments of curvature effects. TM modes in the space between the earth and the ionosphere excite coupled TM and TE modes in the ionosphere layers, the presence of which are considered in an iterative solution of the modal equation. In the ELF range propagation parameters computed for the East to West (EW) and West to East (WE) directions differ most for dip angles of 15 to 30 degrees. In the VLF range propagation parameters may exhibit discontinuities for EW direction. The interference distance D of the two lower-wave guide modes is increased for propagation in the EW direction relative to propagation in WE direction provided that the electron density profiles exhibit sharp density gradients at heights in the range from 80 - 85 km. The desired propagation characteristics could not be produced in the presence of a nondipping static magnetic field or using smoothly varying electron density profiles. (Author).




Characteristics of the Earth-ionosphere Waveguide for VLF Radio Waves


Book Description

The principal results of this technical note are graphical presentations of the attenuation rates, phase velocities, and excitation factors for the dominant modes in the earth-ionosphere waveguide.The frequency range considered is 8 kc/s to 30 kc/s. *The model adopted for the ionosphere has an exponential variation for both the electron density and the collision frequency, and the effect of the earth's magnetic field is considered.Comparison with published experimental data confirms that the minimum attenuation of VLF radio waves in daytime is approximtely at 18 kc/s, while at night it is somewhat lower.The directional dependences of propagation predicted by the theory are also confirmed by experimental data.(Author).




Terrestrial Propagation of Long Electromagnetic Waves


Book Description

Terrestrial Propagation of Long Electromagnetic Waves deals with the propagation of long electromagnetic waves confined principally to the shell between the earth and the ionosphere, known as the terrestrial waveguide. The discussion is limited to steady-state solutions in a waveguide that is uniform in the direction of propagation. Wave propagation is characterized almost exclusively by mode theory. The mathematics are developed only for sources at the ground surface or within the waveguide, including artificial sources as well as lightning discharges. This volume is comprised of nine chapters and begins with an introduction to the fundamental concepts of wave propagation in a planar and curved isotropic waveguide. A number of examples are presented to illustrate the effects of an anisotropic ionosphere. The basic equations are summarized and plane-wave reflection from a dielectric interface is considered, along with the superposition of two obliquely incident plane waves. The properties of waveguide boundaries are implicitly represented by Fresnel reflection coefficients. Subsequent chapters focus on boundaries of the terrestrial guide; lightning discharges as a natural source of extremely-low-frequency and very-low-frequency radiation; and the mode theory for waves in an isotropic spherical shell. This book will be a useful resource for students and practitioners of physics.







A model for propagation of ELF and VLF waves below naturally perturbed ionospheres


Book Description

A terrestrial propagation model is studied where the earth to ionosphere waveguide system is cylindrically stratified, the dip angle of the static magnetic field is assumed to be arbitrary and the waves propagate in East to West or West to East directions at a constant magnetic latitude. The profiles of ionospheric electronic density chosen for the numerical computations are representative of sudden ionospheric disturbances (SID), solar flares, auroral absorption or polar cap absorption (PCA) events. The resulting phase velocity and attenuation rates of ELF and VLF signals are compared with those computed under representative quiet daytime conditions. PCA events (which give the most dramatic effects) cause a lowering of the effective ionosphere; the resulting propagation is nearly isotropic and the phase velocities are decreased at ELF and increased at VLF. The attenuation rates are increased at ELF and also in the lower part of the VLF band. The propagation parameters are affected to a lesser degree by the other events: ionospheric density perturbations at heights below 60 km have more readily discernable effects at ELF, while the changes of the ionospheric density gradient at larger heights are observable at VLF. However, these differences are not uniquely distinguishable from propagation characteristics obtainable under quiet daytime conditions. (Author).




Journal of Research


Book Description