Extremely Low Frequency (ELF) Propagation Formulas for Dipole Sources Radiating in a Spherical Earth-Ionosphere Waveguide


Book Description

Extremely low frequency (ELF) propagation formulas are derived for dipole sources radiating in a spherical earth-ionosphere waveguide. In these formulas, the earth and ionosphere boundaries are modeled as scalar surface impedances. The spherical waveguide formulas are applied to predict the electromagnetic fields produced by vertical and horizontal electric dipoles (located on the surface of the earth) at antipodal ranges for several frequencies and propagation conditions. These results are used to establish the maximum ranges of validity of ELF propagation formulas that are based on the earth-flattening approximation. Numerous derivations are given in the appendices.




A Parametric Study of Extremely-Low-Frequency (ELF) Propagation Under Anisotropic, Diffuse Ionospheres


Book Description

The report presents results of a numerical study of EM propagation under diffuse anistropic ionospheres at the extremely low frequencies of 45 Hz and 75 Hz. Waveguide mode parameters are presented under both day and night ambient conditions for several values of ground conductivity as a function of geomagnetic flux density, dip angle, and direction of propagation. (Author).




Propagation of Low Frequency Electromagnetic Waves in the Earth Ionosphere Waveguide


Book Description

The report gives a concise review of the present state of research on the propagation of very low frequency (VLF) and extremely low frequency (ELF) waves in the surface waveguide. Calculated values of refraction and damping coefficients, taking neutral particles into account, are given for both the lower ionosphere (D region), and the outer ionosphere, to heights of 3000 to 6000 km. Various theoretical formulas for the field in a waveguide, derived both rigorously and by asymptotic methods, are subjected to analysis, and the theoretical results are compared with most of the experimental data to be found in the literature. Almost all of the world's available information is used (255 names). The book has 54 illustrations and 13 tables.




VLF and ELF Propagation During Sudden Ionospheric Disturbances


Book Description

The study presents the results of a theoretical analysis of the propagation of electromagnetic waves in the very-low-frequency (VLF) and extremely-low-frequency (ELF) ranges in the earth-ionosphere cavity during solar flares. The calculations, which are based upon nominal models of ambient conditions and solar-flare x-ray fluxes and spectra, result in mode-attenuation coefficients which are in good general agreement with observations. The propagation is enhanced relative to ambient conditions at ELF and upper VLF frequencies but is degraded in the lower VLF range. This general behavior is quite insensitive to the details of the assumed x-ray spectrum, the main requirement being a sufficient concentration of x-ray energy in the 1 - 8 A wavelength band. This class of spectrum tends to cause a moderate lowering of the D-region accompanied by an increase in the height gradient of conductivity in the reflection region; this in turn causes the observed phenomena at ELF and VLF during sudden ionospheric disturbances. (Author).




The Role of Energetic Particle Precipitation in Extremely Low Frequency (ELF) Propagation Anomalies


Book Description

The purpose of the present report is to present further work on the influence of precipitating energetic particles on ELF propagation. The effort principally involves the effects of solar particle events in enhancing the conductivities of the earth's ionosphere wave guide. Calculations have been made of the sensitivity of the ELF signal strength to changes in the conductivities over the transmitter that may occur during SPE conditions. In order to be able to calculate more accurately the changes in ELF signal strength associated with solar particle events and other disturbed conditions at twilight, new electron density data measured in the 4 August 1972 event have been used to provide increased knowledge of twilight behavior which will lead to improvements in ion chemistry modelling. The effects of the charge deposition in the polar caps on the earth's electric fields and current systems have been modeled. More realistic ambient electron and ion density daytime profiles have been proposed to provide accurate baseline signal strength calculations.




Propagation of ELF Waves Generated by an HF Ionospheric Heater in the Earth's Plasma Environment


Book Description

Electromagnetic waves in the Extremely Low Frequency range (ELF, 30-3000 Hz) have broad application in physics and engineering such as ionospheric and underground remote sensing and global submarine communications. Additionally, ELF waves can resonantly interact with energetic electrons, an important process that results in the removal of trapped electrons from the radiation belts. ELF waves can be generated by lightning discharges and by natural processes in the Earth's magnetosphere. However, it is extremely difficult to generate ELF waves artificially due to their long wavelengths. In this work, the High Frequency Active Auroral Research Program (HAARP) transmitter array is used to generate ELF waves. The HAARP array generates ELF waves by heating the lower ionosphere with a powerful (3.6 MW) high frequency (2.75-10 MHz) beam. The heating is modulated at an ELF frequency resulting in modulation of the natural auroral electrojet current, which in turn radiates at the ELF frequency. For four years, a set of experiments was conducted in which ELF signals generated by HAARP were detected by the DEMETER satellite at an altitude of 670 km. In addition to observations, the distribution of ELF power is examined with several modeling techniques to explain the observed features. In the experiments and modeling, three distinct regions of ELF radiation are identified. Region 1, the most important region, is a column of radiation propagating upward into space with a horizontal extent of about the size of the heated region (50-100 km) and average field strengths of 100-150 uV/m at 2 kHz. In Region 2, which can extend up to 300 km laterally from HAARP, it is believed that the waves reach the satellite by propagating directly from the source in the ionosphere without reflection from the ground. In contrast, in Region 3, which can extend to 1000 km from HAARP, the generated waves first propagate in the Earth-ionosphere waveguide and partially leak through the ionosphere to be detected on the spacecraft. During the nighttime, the intense column of radiation (Region 1) is displaced by about 100 km horizontally to the south from the HAARP field line. During the daytime, there is no substantial north-south displacement from the HAARP field line. A horizontally homogeneous full-wave model is used to facilitate the physical understanding of the wave propagation. The model accurately predicts the extents of the three regions during daytime and nighttime conditions as well as the location of Region 1 during daytime. However, during the nighttime the model predicts that the column should be up to 100 km north of the HAARP field line. It is proposed that the displacement in observations during the nighttime is caused by a horizontal electron density gradient within the main ionospheric trough. Using ray tracing simulations, we estimate that the gradient of this trough should be an order of magnitude change over a latitude range of 3-5 degrees. It is also demonstrated that the main ionospheric trough is an important parameter of the medium above HAARP not only for ELF observations but also for other types of experiments too. It is found to occur over HAARP during the nighttime in at least 50% of our cases. The first satellite observations of one-hop and two-hop ELF waves generated via HF heating are reported. Among the important new understandings is the fact that daytime is preferential for this type of ELF generation and propagation to the conjugate region. The signal during the daytime is observed almost two times more often than during the nighttime, and triggered emissions are observed only in the daytime. We also find that the region with the strongest signal is displaced about 300 km toward the equator, and the signal is overall higher toward the equator than toward the pole. It is hypothesized that this can be the result of plasmapause guiding. Another important result is the fact that one/two-hop signals are observed over a long range of distances (> 1000 km) and over a wide range of L-shells, although always with roughly constant time delay. This observation suggests that the propagation in the magnetosphere is within the narrow range of L-shells or within a duct, and wide range in the observations is the result of ELF wave backscattering from the ionosphere.




Elf Propagation


Book Description

A simple surface propagation model is commonly used to estimate the effects of ionospheric disturbances on extremely low frequency (ELF) propagation, Though often adequate, one shortcoming of the model is its failure to allow for excitation by the broad-side component of a horizontal dipole. That excitation can be quite significant in a sporadic-E environment, when the modal polarization can contain a substantial mixture of TE component. In this study a beginning is made on ELF propagation model development which allows for broadside excitation as well as a systematic allowance for height gain effects. The development is for a flat earth with a laterally homogeneous, cylindrically symmetric disturbance centered over the transmitter. The method utilizes normal-mode decomposition. Matching equations at the boundary of the disturbance are developed by evaluating height gain integrals, and it is shown that this method is tantamount to simply matching the ground vertical electric and azimuthal magnetic fields at the boundary. Results for a sporadic-E type environment indicate substantial departures from the surface propagation model and WKB predictions.




Generalized ELF Propagation


Book Description

Research in marine electromagnetics requires computation of the propagation characteristics of the extremely low frequency (ELF) electromagnetic radiation arising from an alternating current source embedded in a conducting medium. This paper considers two cases of ELF propagation: in offshore and in-shore locations. The paper outlines a technique which generalizes the solution of Maxwell's equations to an arbitrary number of layers, and which can be extended to a sloping sea bed. The scheme includes solving the parallel layer situation followed by solving a Fredholm integral equation to produce the solution in the sloping layer. The solution for any arbitrary region outside of the sloping layer is then determined by evaluation of an integral. Some computational methods for solving the Fredholm equation are also analyzed, focusing on iterative procedures that provide reasonable computational effectiveness.




ELF Propagation in a Non-Stratified Earth-Ionosphere Waveguide


Book Description

This report analyzes extremely low-frequency (ELF) propagation under conditions where the properties of the earth-ionosphere waveguide change markedly over transverse distances comparable with the width of a Fresnel zone. An integral equation formulation is presented that can be used to obtain numerical results for most types of daytime ionospheric disturbances. Approximate solutions are given for ionospheric disturbances of the type that would occur in single-burst nuclear environments. These fullwave results are compared with results calculated from the widely used two-dimensional WKB approximation, which neglects transverse ionospheric gradients. It is shown that this WKB approximation gives good results for burst-heights above about 100 km, but that fullwave theory that accounts for transverse gradients must be used for lower burst altitudes. For these lower burst-heights, the WKB method seriously overstates the propagation anomaly caused by an on-path burst and understates the anomaly caused by an off-path burst. (Author).