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Ray theory formulation and ray tracing method. Application in ionospheric propagation
Language
English
Obiettivo Specifico
2A. Fisica dell'alta atmosfera
Status
Published
JCR Journal
N/A or not JCR
Peer review journal
Yes
Title of the book
Issue/vol(year)
121/ (2014)
Issued date
October 23, 2014
Alternative Location
Subjects
Abstract
This work will lead to ray theory and ray tracing formulation. To deal with this problem the theory of classical geometrical optics is presented, and applications to ionospheric propagation will be described. This provides useful theoretical basis for scientists involved in research on radio propagation in inhomogeneous anisotropic media, especially in a magneto-plasma. Application in high frequencies (HF) radio propagation, radio communication, over-the-horizon-radar (OTHR) coordinate registration and related homing techniques for direction finding of HF wave, all rely on ray tracing computational algorithm. In this theory the formulation of the canonical, or Hamiltonian, equations related to the ray, which allow calculating the wave direction of propagation in a continuous, inhomogeneous and anisotropic medium with minor gradient, will be dealt. At least six Hamilton’s equations will be written both in Cartesian and spherical coordinates in the simplest way. These will be achieved by introducing the refractive surface index equations and the ray surface equations in an appropriate free-dimensional space. By the combination of these equations even the Fermat’s principle will be derived to give more generality to the formulation of ray theory. It will be shown that the canonical equations are dependent on a constant quantity H and the Cartesian coordinates and components of wave vector along the ray path. These quantities respectively indicated as ri(τ), pi(τ) are dependent on the parameter τ, that must increase monotonically along the path. Effectively, the procedure described above is the ray tracing formulation. In ray tracing computational techniques, the most convenient Hamiltonian describing the medium can be adopted, and the simplest way to choose properly H will be discussed. Finally, a system of equations, which can be numerically solved, is generated.
Sponsors
Istituto Nazionale di Geofisica e Vulcanologia (INGV)
References
Bianchi C., (1990). Note sulle interazioni delle onde elettromagnetiche con il plasma ionosferico. Istituto Nazionale di Geofisica, U. O. Aeronomia, Rome, Italy, 149 pages [in Italian].
Bianchi C. and Bianchi S., (2009). Problema generale del ray-tracing nella propagazione ionosferica - formulazione della “ray theory” e metodo del ray tracing. Rapporti Tecnici INGV, 104, 26 pages [in Italian].
Bianchi S., Sciacca U. and Settimi A., (2009). Teoria della propagazione radio nei mezzi disomogenei (Metodo dell’iconale). Quaderni di Geofisica, 75, 14 pages [in Italian].
Bianchi C., Settimi A. and Azzarone A., (2010). IONORT: IONOsphere Ray-Tracing. Programma di ray-tracing nel magnetoplasma ionosferico. Rapporti Tecnici INGV, 161, 20 pages [in Italian].
Budden K. G., (1961). Radio waves in the ionosphere. Cambridge University Press, Cambridge, 688 pages.
Budden K. G. (1988). The Propagation of Radio Waves: The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere. Cambridge University Press, Cambridge, UK, 688 pages.
Davies K., (1990). Ionospheric Radio. Peter Peregrinus Ltd. (ed.) on behalf of the Institution of Electrical Engineers (IET), London, UK, 508 pages.
Felsen L.B. and Marcuvitz N., (1994). Radiation and scattering of waves. IEEE Press Series on Electromagnetic Wave Theory (Book 31), John Wiley & Sons-IEEE Press, New York, USA, 924 pages.
Fowles G. R., (1989). Introduction to modern optic. Dover Books on Physics Series, Dover classics of science and mathematics, Courier Dover Publications, Inc., II edition, New York, USA, 328 pages.
Gorman A. D., (1985). Dispersive wave and caustics. Int. J. Math. & Math. Sci., 8 (1), 93-107, doi: 10.1155/S0161171285000084.
Gorman A. D., (1986). Space-time caustics. Int. J. Math. & Math. Sci., 9 (3), pp. 531-540, doi: 10.1155/S0161171286000662.
Haselgrove J., (1955). Ray theory and a new method of ray tracing. Conference on the Physics of the Ionosphere, Proc. Phys. Soc. London, 23, 355-364.
Kelso J. M., (1964). Radio ray propagation in the ionosphere. McGraw-Hill electronic sciences series, McGraw Hill Book Company, Inc., New York, 408 pages.
Kelso J. M., (1968). Ray tracing in the ionosphere. Radio Sci., 3 (1), 1-12, Accession Number: WOS:A1968A402200002.
Jones R. M. and Stephenson J. J., (1975). A versatile three-dimensional ray tracing computer program for radio waves in the ionosphere. OT Report, 75-76, U. S. Department of Commerce, Office of Telecommunication, U. S. Government Printing Office, Washington, USA, 185 pages.
Weinberg S., (1962). Eikonal Method in Magnetohydrodynamics. Phys. Rev., 126 (6), 1899-1909, doi: 0.1103/PhysRev.126.1899.
Bianchi C. and Bianchi S., (2009). Problema generale del ray-tracing nella propagazione ionosferica - formulazione della “ray theory” e metodo del ray tracing. Rapporti Tecnici INGV, 104, 26 pages [in Italian].
Bianchi S., Sciacca U. and Settimi A., (2009). Teoria della propagazione radio nei mezzi disomogenei (Metodo dell’iconale). Quaderni di Geofisica, 75, 14 pages [in Italian].
Bianchi C., Settimi A. and Azzarone A., (2010). IONORT: IONOsphere Ray-Tracing. Programma di ray-tracing nel magnetoplasma ionosferico. Rapporti Tecnici INGV, 161, 20 pages [in Italian].
Budden K. G., (1961). Radio waves in the ionosphere. Cambridge University Press, Cambridge, 688 pages.
Budden K. G. (1988). The Propagation of Radio Waves: The Theory of Radio Waves of Low Power in the Ionosphere and Magnetosphere. Cambridge University Press, Cambridge, UK, 688 pages.
Davies K., (1990). Ionospheric Radio. Peter Peregrinus Ltd. (ed.) on behalf of the Institution of Electrical Engineers (IET), London, UK, 508 pages.
Felsen L.B. and Marcuvitz N., (1994). Radiation and scattering of waves. IEEE Press Series on Electromagnetic Wave Theory (Book 31), John Wiley & Sons-IEEE Press, New York, USA, 924 pages.
Fowles G. R., (1989). Introduction to modern optic. Dover Books on Physics Series, Dover classics of science and mathematics, Courier Dover Publications, Inc., II edition, New York, USA, 328 pages.
Gorman A. D., (1985). Dispersive wave and caustics. Int. J. Math. & Math. Sci., 8 (1), 93-107, doi: 10.1155/S0161171285000084.
Gorman A. D., (1986). Space-time caustics. Int. J. Math. & Math. Sci., 9 (3), pp. 531-540, doi: 10.1155/S0161171286000662.
Haselgrove J., (1955). Ray theory and a new method of ray tracing. Conference on the Physics of the Ionosphere, Proc. Phys. Soc. London, 23, 355-364.
Kelso J. M., (1964). Radio ray propagation in the ionosphere. McGraw-Hill electronic sciences series, McGraw Hill Book Company, Inc., New York, 408 pages.
Kelso J. M., (1968). Ray tracing in the ionosphere. Radio Sci., 3 (1), 1-12, Accession Number: WOS:A1968A402200002.
Jones R. M. and Stephenson J. J., (1975). A versatile three-dimensional ray tracing computer program for radio waves in the ionosphere. OT Report, 75-76, U. S. Department of Commerce, Office of Telecommunication, U. S. Government Printing Office, Washington, USA, 185 pages.
Weinberg S., (1962). Eikonal Method in Magnetohydrodynamics. Phys. Rev., 126 (6), 1899-1909, doi: 0.1103/PhysRev.126.1899.
Commentary On
C. Bianchi, S. Bianchi, “Problema generale del ray-tracing nella propagazione ionosferica - formulazione della “ray theory” e metodo del ray tracing”, Quaderni di Geofisica 104, pp. 21 (2009).
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