How can I calculate the precise (elliptical) polarization of the downward characteristic (ordinary and extraordinary) waves in ionospheric (magneto-ionic) radio wave propagation?
Input parameters that I want to vary are the azimuth angle, the elevation angle and the orientation of the Earth magnetic field. Other parameters are kept constant. My main interest is in steep elevation angles, typically between 60 and 90 degrees (Near Vertical Incidence Skywave).
First situation I want to calculate is in the Netherlands, where the magnetic field has a dip angle of 67 degrees.
I already replied to your question about what software you could use, so I'll keep this short. To calculate the polarization, first and foremost, you will need a good electron density and magnetic field model. The calculation itself is just a simplification of the Appleton-Hartree equation for the HF case. Ionospheric Radio by Keneth Davies is an excellent reference for the derivation from first principles and goes through a few nice case examples. Ultimately, you'll have a few constants sitting in front of a line integral of the electron density with the magnetic field vector dotted to the signal orientation. I would write out the equation, but Research Gate doesn't have an equation editor in here and the equation itself is pretty simple to find or derive.
If you're not interested in actually developing your own software for this, please see my response to your software question. IONORT is probably your best option, but simpler models exist in VOACAP, ICEPAC, and REC533; however, recent work has shown that these are not particularly good options (https://www.researchgate.net/publication/277974727_Comparison_of_observed_and_predicted_MUF%283000%29F2_in_the_Polar_cap_region_MUF%283000%29F2_in_the_Polar_Cap_Region).
Article Comparison of observed and predicted MUF(3000)F2 in the Pola...
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