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).




An Integral-Equation Approach to ELF Propagation in a Non-Stratified Earth-Ionosphere Waveguide


Book Description

This report develops and applies a practical method for analyzing long-wave propagation under conditions where the properties of the earth-ionosphere waveguide change markedly over lateral distances comparable to a wavelength or Fresnel zone. Full-wave solutions are used to describe both the vertical and horizontal dependences of the fields, but certain compromises are made to achieve tractability. The method is thus characterized as quasi-full-wave. Its main limitation is that the equation describing the vertical dependence is assumed to nearly decouple from the equation governing the lateral dependence. The method is valid at any frequency for which waveguide modes describe terrestrial propagation. Nonetheless, its practical utility is probably limited to ELF because the lateral properties of the earth-ionosphere waveguide are usually gradual enough to permit use of the WKB approximation at higher frequencies. To facilitate numerical solution, the lateral equation is transformed into an integral equation that accounts for most full-wave properties, including diffraction around a localized disturbance and reflection from lateral gradients. Numerical solutions based on model disturbances having lateral gradients in the direction of propagation reveal a standing wave pattern in front of the disturbance.










Resonances in the Earth-Ionosphere Cavity


Book Description

This book on electromagnetic resonance phenomena describes a general approach to physical problems, ways to solve them, and properties of the solutions obtained. Attention is given to the discussion and interpretation of formal and experimental data and their links to global atmospheric conditions such as the dynamics of global thunderstorm activity, variations of the effective height of the lower ionosphere, etc. Schumann resonance is related to worldwide thunderstorm activity, and simultaneously, to global properties of the lower ionosphere. Transverse resonance is predominantly a local phenomenon containing information on the local height and conductivity of the lower ionosphere and on nearby thunderstorm activity. Transient events in ELF-VLF radio propagation are also treated. These are natural pulsed radio signals and/or abrupt changes of manmade VLF radio signals. The transients associated with cloud-to-ionosphere discharges (red sprites, blue jets, trolls) are discussed, and clarification of the underlying physical ideas and their practical applications to pioneer results achieved in the field recently are emphasised.













A Simplified Theory of ELF Propagation in Its Earth-Ionosphere Transmission Line and Its Worldwide Application. Supplement


Book Description

The NOSC computer program has confirmed that non-reciprocity in the ELF band is not introduced in the refracting stratum near the bottom of the ionosphere. It is introduced higher up where the direction of phase propagation is almost vertical. It has been determined that the effect of a slightly off-vertical angle for the direction of phase propagation in the ionosphere in the ELF band does in fact cause the non-reciprocity obtained by Pappert and Moler (1974). The electromagnetic reason for this has been identified and is described below. The fact that off-vertical angles of less than a degree for the direction of phase propagation have noticeable effects raises the question of how precisely the stratification of the ionosphere may be assumed to be horizontal.




On the Ionospheric Parameters Which Govern High Latitude ELF Propagation in the Earth-Ionosphere Waveguide


Book Description

An approximate wave solution is obtained for the propagating ELF mode at high latitudes in the Earth-ionosphere waveguide. A simple approximate expression for the complex propagation constant emerges from the solution. The propagation constant depends on four parameters, two altitudes and a scale height associated with each altitude. The lower altitude is the height at which the conduction current parallel to the magnetic field becomes equal to the displacement current. The associated scale height is the local scale height of the parallel conductivity. Under daytime ionospheric conditions, the upper altitude is the height at which the local wave number becomes equal to the reciprocal of the local scale height of the refractive index. The associated scale height is the local scale height of the refractive index. Under the simplest nighttime conditions, the second set of parameters is replaced by the altitude of the E-region bottom and the local wave number just inside the E-region. The relative phase velocity depends, in first approximation, only on the ratio of the two altitudes. The attenuation rate depends on the other two parameters, as well. The two principal attenuation mechanisms are Joule heating by longitudinal currents in the vicinity of the lower altitude and energy leakage of the whistler component of the ELF wave at the upper altitude. (Author).