Radio Science Bulletin 325 - June 2008 - URSI

Practical Applicationsof Haselgrove’s Equations forHF SystemsL.J. NickischAbstractJenifer Haselgrove’s 1955 paper, entitled “Ray Theoryand a New Method for Ray Tracing,” has become the classicreference for the application of Hamilton’s equations to theproblem of ionospheric radiowave propagation. Herformulation provides a computationally tractable means foranalyzing radiowave propagation when ionosphericrefraction is a significant effect, as is the case in the highfrequency(HF: 3-30 MHz) band, where shortwavecommunication systems and over-the-horizon (OTH) radarsoperate. The study of HF propagation effects oncommunications and radar systems has formed a substantialportion of my career, and so it is with pleasure that I reviewthe more significant aspects of that work to honor JeniferHaselgrove (now Jenifer Leech) for her very significantcontribution, Haselgrove’s Equations. I discuss the extensionof Haselgrove’s Equations for accurate computation of rayfocusing and ray homing, and the application of Haselgrove’sEquations in HF propagation-channel modeling, simulationof Doppler-spread surface clutter for OTH radar, geolocationof targets for OTH radar, and the mitigation of travelingionospheric disturbances (TIDs) for OTH radar.1. IntroductionSeptember 4, 1984, freshly out of graduate school andon the first day of my new job at Mission ResearchCorporation (MRC) in Santa Barbara, California, I washanded a copy of Budden’s classic reference, Radio Wavesin the Ionosphere [1]. I was told that I was to become anexpert on HF propagation. Assured by my boss that nothinguseful was expected from me for six months, I was free todelve deeply into the study of HF propagation theory, anddevoured “Budden” cover-to-cover. It was there that Ilearned of Jenifer Haselgrove’s derivation of the equationsthat bear her name, Haselgrove’s Equations [2]. As Buddenstates in his book, referring to the problem of ray tracing inslowly varying magnetoionic media, “Haselgrove has shownhow the differential equations for a very general coordinatesystem can be derived from Fermat’s principle of stationarytime.” I was very familiar with Fermat’s principle andvariational calculus from my graduate studies, having appliedit in my dissertation project to a problem in quantum fieldtheory (not to mention countless problems in my graduatelevelclassical-mechanics and field-theory courses).Haselgrove’s Equations are an implementation ofHamilton’s equations, suitable for numerical integration ona computer, which she applied to ionospheric radiowavepropagation [3, 4].I soon acquired the Jones-Stephenson “Raytrace”code [5], the best-known and (at least at the time) mostreadily available computer program applying Haselgrove’sEquations to radiowave propagation in the ionosphere. Icame to know this code intimately, and was soon facile inmodifying it with subroutines of my own creation.The Cold War was still strongly in effect in thosedays, and Mission Research’s role as a think tank includedestimating the effects of nuclear detonations on theionosphere, and the subsequent deleterious effects oncommunication and radar system performance. The firstproject I was assigned was to compute the effect on thesignal strength of HF communication links caused bytraveling ionospheric disturbances (TIDs), driven by acousticgravity waves (AGWs) generated by low-altitude nuclearbursts. This, I was told, could be addressed by tracing a“flux tube” of nearly-separated rays, and computing the rayfocusing (or defocusing) by the change in the cross sectionalarea of the flux tube. However, I soon discovered that in amassive-attack nuclear scenario, the ionosphere couldbecome so convoluted by interfering TIDs that it wasimpossible to accurately calculate the signal strength in thisway. If the flux tube was too large, then the answer wasmerely an average over the large region intercepted by theflux tube. To get more accuracy, one could make the fluxtube smaller, but eventually finite numerical precisionL. J. Nickisch is with NorthWest Research Associates, 301Webster Street, Monterey, CA 93940 USA; Tel: +1 (831)-582-4905; e-mail: LJ@nwra.com.36TheRadio Science Bulletin No 325 (June 2008)