Second-order effects in high-frequency transionospheric propagation

Abstract

Refraction and polarization rotation effects in high-frequency radio waves passing through the ionosphere are commonly used to determine the integrated electron content by applying a first-order ray theory. More detailed analyses show that the distribution of ionization enters the theory in second-order effects. Previously, these second-order effects have been included in the analyses by solving for the propagation paths in model ionospheres, using digital computers and adjusting the model to fit the observations. This paper presents an analytical derivation of the second-order effects, in a form suitable for manual data reduction and including the effects of nonlinear refractive index, ray-path bending, and magnetoionic mode splitting. Application of the equations to ionospheric models shows order of magnitude error reduction as compared with first-order analysis methods. The significance of the results in experiments involving phase-path dispersion and polarization rotation dispersion is discussed. It is proposed that maps of certain parameters of the second-order equations be computed in conjunction with the magnetic field component maps required by the first-order equations, so that manual inclusion of second-order effects may be possible in the analysis of data from beacon satellites.