ECE 458 Lecture Notes on Applications of Radiowave Propagation Erhan Kudeki Department of Electrical and Computer Engineering University of Illinois at Urbana-Champaign January 2006 (Edited: Jan. 2010) Copyright c 2010 Reserved — No parts of these notes may be reproduced without permission from the author ! Introduction Apartially-ionizedandelectricallyconductinglayeroftheupperatmospherehelpedguid- ing Marconi’s radio signals across the Atlantic during his historic experiment of 1901. Since the existence of such a layer — the ionosphere —wasnotknownatthetime,the outcome of the experiment, a successful radio contact from Wales to Newfoundland, was abigsurpriseandsparkedanintenseresearchonwavepropagationandthemorphology of the upper atmosphere. Today, in the age of space travel, satellites, and wireless infor- mation networks, radio waves have become an essential element of how we communicate with one another across vast distances. These notes describe the physics and applications of radio waves and radiowave propagation within ionized gases enveloping our planet and solar system. Figure 0.1: Guglielmo Marconi with his receiving apparatus on Signal Hill, St. John’s, Newfoundland in December, 1901. (www3.ns.sympatico.ca/henry.bradford/marconi-newf.html) Acrucialaspectofanionizedgas—aplasma —forradiowavepropagationisthe number density N of its free electrons, which is distributed, in the Earth’s ionosphere, as shown in Figure 0.2. Ionospheric electron density N varies with altitude, latitude, longitude, local time, season, and solar cycle1 and impacts the propagation of ionospheric radiowaves in various ways. Since the response of free electrons to eE forcing depends − on the frequency f of the radiowave field E,thedetailsofionosphericpropagationis frequency dependent. At radio frequencies (see Figure 0.3) less than a critical plasma 111 year periodicity in solar energy output that correlates well with the number of visible sunspots on solar surface. Power flux from the sun maximizes in years with maximum sunspot counts (i.e., during “solar max”). 2 Figure 0.2: Typical height profiles of ionospheric electron density N and atmospheric temperature T ,andthenamesofdifferentatmospheric/ionosphericregions and layers. The actual distributions of N and T are highly variable in time and location and contain random components modeled by statistical meth- ods. Physical models for the average profile of N describe a balance between a solar-flux-dependent photo-ionization rate and a recombinational loss rate which is chemistry dependent. Photo-ionization rate proportional to both neutral gas density and ionizing radiation (EUV, X-ray) maximizes at some intermediate atmospheric height because density decreases and ionizing radi- ation flux from sun increases with increasing height. The wiggles in N-profile are due to different types and rates of recombination processes dominant at different height ranges. The ionosphere “survives the night” at different heights to different extents depending on recombination rates (D-region dis- appears but F-region densities are reduced by only an order of magnitude). 3 Figure 0.3: Radio spectrum and commonly used band names. Each band spans one decade of frequencies — e.g., VHF extends from 30 to c 300 MHz — and one decade of free space wavelength λ = f . (http://www.ntia.doc.gov/osmhome/allochrt.html) frequency f √N the ionosphere becomes opaque2 and incident radiowaves from below p ∝ (or above) suffer total internal reflections. Radiowaves with frequencies larger than fp can penetrate the ionosphere but only with a f/fp dependent phase and group speeds. Hence, the medium is dispersive.Also,spatialvariationsofN and fp make the ionosphere an inhomogeneous propagation medium, causing refractions and the curving of ionospheric ray trajectories. Under the right conditions refracted ionospheric rays will curve back to the ground, establishing so-called “sky-wave” links beyond the horizon like in Marconi’s 1901 experiment. Radiowaves crossing the ionosphere suffer some attenuation or loss because of the collisions of ionospheric free electrons with neutral atoms and molecules. Electron collisions cause wave attenuation since during a collision the electron loses part of its kinetic energy borrowed from the radiowave in an irreversible way. The ionosphere also happens to be an anisotropic propagation medium because of an additional ev B force − × o on electrons, where Bo is the Earth’s DC magnetic field and v the electron velocity. As a consequence of this Lorentz force radiowave propagation speeds depend on the direction of wavenormal kˆ in relation to Bo,and,infact,propagationisonlypossibleforcertain polarizations, depending, again, on kˆ.Finally,electrondensityN in the ionosphere always contains a fluctuating component δN that varies randomly with position and time and scatters the radiowaves crossing the ionosphere. Scattered signals can be detected and analyzed by radar systems to study the morphology and dynamics of the upper atmosphere. The scattering process also causes a “twinkling effect” — called scintillations —onamplitudesandphasesofradiowavescrossingtheionosphere. The notes here provide an introductory account of the propagation phenomena high- lighted above after a brief review of Maxwell’s equations and their plane wave solutions 2 Plasma frequency fp √80.6N in MKS units as we will derive in Chapter 2. With a maximum value 12 3 ≈ of N 10 m− in the ionosphere, the maximum fp 9 MHz typically. Thus the ionosphere is ∼ ∼ typically opaque for radio frequencies less than 9 MHz. 4 in Chapter 1. Chapter 2 examines ionospheric propagation neglecting the effect of the Earth’s DC magnetic field and focusing on a vertical incidence geometry — dispersion, inhomogeneity, and absorption effects are introduced one at a time and discussed. Chap- ter 3 describes ionospheric the sky-wave links and also includes a discussion of refraction in the lowest layer of the neutral atmosphere, the troposphere.InChapter4wediscuss the tropospheric radio links following a study of radiation and reception properties of antennas. The chapter also includes discussions of antenna noise and radio imaging. The last two chapters are devoted to the most advanced topics of these notes: Chapter 5 de- scribes backscatter research radars used for the study of the lower and upper atmosphere and the ionosphere, whereas the topic covered in Chapter 6 is magnetoionic theory of anisotropic propagation effects in magnetized plasmas. Additional advanced topics in- cluding radiowave scintillations, surface-wave propagation, and the theory of ionospheric incoherent scatter are included as appendices. The notes are intended for an audience familiar with Maxwell’s equations and plane- waves from an introductory electromagnetics course. It is also expected that the student has familiarity with linear system theory (convolution, Fourier transforms, impulse) as well as the theory of random variables (pdf’s, expected values). Required concepts from plasma physics and atmospheric physics will be introduced in a “just-in-time” fashion and no attempt will be made for a complete coverage in those areas. Useful references (available in Engineering Library): 1. Rao, N. N., Elements of Engineering Electromagnetics, 1997, Prentice Hall 2. Bekefi, G. and A. H. Barret, Electromagnetic vibrations, waves, and radiation, 1984, MIT 3. Staelin, D. H., A. W. Morgenthaler, and J. A. Kong, Electromagnetic Waves, 1994, Prentice Hall 4. Collin, R. E., Antennas and radiowave propagation, 1985, McGraw Hill 5. Davies, K., Ionospheric radio, 1990, Peter Peregrinus 6. Yeh, K. C., and C. H. Liu, theory of ionospheric waves, 1972, Academic 7. Kelley, M. C., The Earth’s ionosphere, 1989, Academic 8. Kerr, D. E., Propagation of short radio waves, 1951, McGraw Hill 9. Jordan, E. C. and K. G. Balmain, Electromagnetic waves and radiating systems, 1968, Prentice Hall 10. Ramo, S., J. R., Whinnery, and T. Van Duzer, Fields and waves in communication electronics, 1964, Wiley 11. Burdic, W. S., Radar signal analysis, 1968, Prentice Hall 5 12. Levanon, N, Radar principles, 1988, Wiley-Interscience 13. Ratcliffe, J. A., The magneto-ionic theory, 1962, Cambridge 14. Budden, K. G., Propagation of radio waves, 1985, Cambridge 15. Gurnett, D. A., and A. Bhattacharjee, Introduction to plasma physics, 2005, Cam- bridge 6 Contents 1WavesolutionsofMaxwell’sequations 9 1.1 Electromagnetic fields and Maxwell’s equations . 9 1.2 Plane wave solutions . 11 1.3 Poynting vector . 16 1.4 Wave polarizations and orthogonality . 17 1.5 Non-uniform plane waves . 19 1.6 Plane wave reflection coefficients . 20 2Ionosphericpropagationandverticalsoundings 25 2.1 TEM plane waves in the upper-atmosphere . 25 2.2 Dispersion and group velocity . 30 2.3 Ionospheric dispersion and propagation . 33 2.4 Group delay, group path, and ionospheric TEC . 36 2.5 Phase delay, differential Doppler, and differential TEC . 40 2.6 WKB and full-wave solutions of propagation in inhomogeneous media . 41 2.7 Vertical incidence ionospheric sounding . 50 2.8 Ionospheric absorption . 55 3Radiolinksininhomogeneousmedia 62 3.1 Field solutions in plane stratified media . 62 3.2 Ray tracing in plane stratified media . 66 3.3 Eikonal equation and general ray tracing equations . 72 3.4 Ray tracing in spherical stratified media . 76 3.5 Tropospheric ducting . 83 3.6 Sky-wave links in a plane stratified ionosphere . 86 3.7 Effect of spherical geometry on sky-wave links . 95 3.8 Earth-ionosphere waveguide and ELF propagation . 96 4Radiation,antennas,links,imaging 100 4.1 Radiation