Radio Science Bulletin 325 - June 2008 - URSI

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In the December 2008 issue, Part 2 of the testimonialeditions will appear. This will begin with a summary ofmultiple applications of the Haselgrove Equations by James.It will be followed by a historical summary of ray-tracingdevelopment by Bennett. Dyson discusses the impact of theHaselgrove Equations and ray tracing on his career in radioscience.Kimaru discusses a career that began almostsimultaneously with Haselgrove’s, which involved theapplication of her ray-tracing techniques to whistler andother wave propagation in the magnetosphere. The editionis completed with a compilation of applications by Bertel.Please enjoy this tribute to Jenifer Haselgrove and herachievements. In collating and researching for this work,we have been inspired by many of the great minds that havebrought us so far in radio science, but none more thanJenifer Haselgrove and those around her at Cambridge,which led to her famous formulation and her use of one ofmankind’s first computers to solve it. Our hope is that theseeditions draw your attention to those “heady days,” a personwho lived through them, and her achievements. Just asimportantly, it is hoped that it inspires you in your radioscienceendeavors so that someone may write about themwith great respect in the near future.Rod Barnes and Phil WilkinsonCo-Guest Editors,Special Sections Honoring Jenifer HaselgroveE-mail: rbarnes@rri-usa.org, phil@ips.gov.au16TheRadio Science Bulletin No 325 (June 2008)
Ionospheric Ray-TracingEquations and their SolutionChristopher J. ColemanAbstractThe Haselgrove ray-tracing equations are deriveddirectly from Maxwell’s equations. Some methods for theirsolution are discussed. In particular, we look at reducedversions of the equations that allow fast numerical solutionand, in some cases, analytic solution.1. IntroductionIt is now over 50 years since Jenifer Haselgroveintroduced the ray-tracing equations that have becomesynonymous with her name. During this time, her equationshave become a major tool for investigating radiowavepropagation in the ionosphere. In the early days, suchstudies were needed because of the importance of ionosphericpropagation for long-range terrestrial communications. Suchcommunications take place at high frequencies (HF), anduse the fact that radiowaves at HF (3 to 30 MHz) arerefracted back down to the Earth by the ionosphere. However,with the advent of artificial satellites, ionosphericcommunication has become less important. Nevertheless,such communications are still an important tool for themilitary, aid agencies, and remote communities.Furthermore, the introduction of over-the-horizon radar(OTHR) has significantly increased the use of ionosphericpropagation. The extreme demands of over-the-horizonradar have made it necessary to understand ionosphericpropagation at a more refined level, and the Haselgroveequations have played an important part in such studies.Starting with the Haselgrove equations, we reviewsome of the ray-tracing approaches that are available for thestudy of ionospheric propagation. In Section 2, we derivethe Haselgrove equations directly from Maxwell’s equations(together with some basic plasma physics). Derivations ofthe Haselgrove equations tend to use ray optics, in particularthe Hamiltonian equations, as their starting point [1-3].Section 2 attempts to start from a more fundamental position,and to cast the equations as part of a procedure for thesolution of Maxwell’s equations in the high-frequencylimit. In [4], it was found that the Runge-Kutta-Fehlbergnumerical scheme constituted a very efficient means ofsolving the Haselgrove equations, and so we include a briefdescription of this algorithm. Unfortunately, there still existray-tracing applications for which computer solutions tothe Haselgrove equations are not fast enough. A particularcase is the coordinate registration (CR) problem of overthe-horizonradar. In the coordinate-registration problem,fast ray tracing is required to convert the radar range (thetime for the radio signal to travel to the target) into the actualground range. Due to the ever-changing nature of theionosphere, these calculations need to be done in real time.Consequently, in Sections 3 to 5 we look at somesimplifications to the Haselgrove equations that can providethis increased speed. In Section 3, we look at the situationwhere the background magnetic field can be regarded asbeing weak (a good approximation for most HF frequenciesabove 10 MHz). In Section 4, we look at the simplificationthat results when we totally ignore the background magneticfield, an approximation that can be made more respectableby the use of effective wave frequencies. Finally, in Section 5,we consider some first integrals of the ray-tracing equations,and we also consider analytic solutions that can be derivedfrom these first integrals.2. The Haselgrove EquationsFor time-harmonic fields in a vacuum, Maxwell’sequations yield the field equations20 0 0∇×∇× E− ω µ ε E = − jωµJ , (1)where E is the time-harmonic electric field, J is the timeharmoniccurrent density, and ω is the wave frequency.Within the ionospheric plasma, the motion of an electronsatisfiesChristopher J. Coleman is with the School of Electricaland Electronic Engineering, University of Adelaide,Adelaide, SA 5005, Australia;e-mail: ccoleman@eleceng.adelaide.edu.auTheRadio Science Bulletin No 325 (June 2008) 17
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Page 10 and 11: URSI Awards 2008The URSI Board of O
Page 12 and 13: • Compatibility refers to the abi
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Page 36 and 37: Practical Applicationsof Haselgrove
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12. References1. C. Audoin and J. V
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ConferencesCONFERENCE REPORT12TH IN
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URSI CONFERENCE CALENDARURSI cannot
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The Journal of Atmospheric and Sola
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APPLICATION FOR AN URSI RADIOSCIENT
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Radio Science Bulletin 325 - June 2008 - URSI

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