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Authors: Settimi, Alessandro 
Title: An in-depth analysis on the Quasi-Longitudinal approximations applied to ionospheric ray-tracing, oblique and vertical sounding, and absorption
Journal: Annals of Geophysics 
Series/Report no.: 1/65 (2022)
Publisher: INGV
Issue Date: 28-Jan-2022
DOI: 10.4401/ag-8728
Keywords: Appleton-Hartree’s formula
Booker’s rule
″Strong″ and ″weak″ Quasi-Longitudinal (QL) conditions
Walker’s approximation
Ionospheric HF ray-tracing, oblique and vertical sounding, and absorption
Subject Classification01. Atmosphere::01.02. Ionosphere::01.02.99. General or miscellaneous
01. Atmosphere::01.02. Ionosphere::01.02.04. Plasma Physics
01. Atmosphere::01.02. Ionosphere::01.02.05. Wave propagation
05. General::05.01. Computational geophysics::05.01.99. General or miscellaneous
05. General::05.01. Computational geophysics::05.01.05. Algorithms and implementation
Abstract: For the phase refraction index of high frequency (HF) waves in the ionospheric medium exists a well-established theory. However, under the Quasi-Longitudinal (QL) conditions, scientific literature presents various formulas that are not equivalent and that, in some cases, give rise to wrong results. In the present study, further consequences of Booker's rule are discussed, illustrating the validity ranges of the above-mentioned approximate formulas; and the different regimes for applying such QL formulas are described, along with the consequences in simulating the ionospheric HF ray-tracing, oblique and vertical sounding, and absorption.
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