Revisiting the Booker Quartic Dispersion Relation
Abstract
The Booker quartic is a dispersion relation that is important for propagation / reflection near a spitze. Although it was first developed in the 1930s, with recent interest in computational ray tracing, the quartic has seen a resurgence of use and importance. In The propagation of radio waves, K.G. Budden gives an equation for the Booker quartic in general coordinates that is different than what is given in his previous book, Radio Waves in the Ionosphere. We rederive this formulation following a slightly different approach and note an error in Budden's most recent representation of the formula that manifests in the absence of an extra term. Qualitatively, we show that this term does make a difference in general coordinates but not for the usual convention of propagation in the x - z plane. Our approach involves detailed derivations of his (3.55) and (6.17) which are not included in the text in which we also correct a typographical error in the former. We then proceed to discus the quantitative repercussions of the more serious error.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 13, 2022
- Accession Number
- AD1156773
Entities
People
- Erick M. Smith
Organizations
- United States Naval Research Laboratory