MF and HF propagation characteristics of ionospheric ducts

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The propagation of MF and HF radio waves along ionospheric ducts is studied in detail by developing a waveguide model of the ducts and determining power levels of ducted echoes. The Earth's magnetic field is included, making the propagation medium anisotropic, and influencing the ray paths through field curvature. Electron density gradients, along and transverse to the field lines are considered, and both circular and elliptical duct cross-sections are treated. Propagation characteristics of the ducts are determined by ray tracing using Haselgrove's equations. Comparison with analytical solutions for simple waveguides is used to elucidate the effects of field line curvature and focussing. Distributions of returned echo power have been calculated for ducts with various cross-sections and different depletions in electron density. It is found that field aligned ducts with diameters of the order of several kilometers behave as effective waveguides for both direct and conjugate ducting modes. However, the percentage depletion required for guiding is higher than previous calculations using simplified theory. The field line curvature causes most power distributions to be shifted upwards from the duct centre. It also causes ducting to be confined to the upper boundary of ducts, especially if they are elongated in the vertical direction. The variation of power across a duct can be quite complicated and distinctive. For direct ducting, there is a clear relationship between the total integrated power across a duct and the electron density gradient and propagation frequency.