Moscow, Russian Federation
Borok, Russian Federation
UDK 55 Геология. Геологические и геофизические науки
BISAC SCI042000 Earth Sciences / Meteorology & Climatology
The dynamic spectrum of a whistling atmospheric is a signal of falling tone, and the group delay time of the signal as a function of frequency is formed as a result of propagation of a broadband pulse in a medium (magnetospheric plasma) with a quadratic dispersion law. In this paper, we show that for quadratic dispersion the group velocity is invariant under Galilean transformations. This means that, contrary to expectations, the group velocity is paradoxically independent of the velocity of the medium relative to the observer. A general invariance condition is found in the form of a differential equation. To explain the paradox, we introduce the concept of the dynamic spectrum of Green’s function of the path of propagation of electromagnetic waves from a pulse source (lightning discharge in the case of a whistling atmospheric) in a dispersive medium. We emphasize the importance of taking into account the motion of plasma in the experimental and theoretical study of electromagnetic wave phenomena in near-Earth space.
electromagnetic waves, moving plasma, Earth’s magnetosphere, dispersion, propagation path, Green’s function, dynamic spectrum
1. Frankfurt U.I., Frank A.M. Optika dvizhushchikhcya tel [Optics of Moving Bodies]. Moscow, Nauka Publ., 1972, 212 p. (In Russian).
2. Gershman B.N., Ugarov V.A. Propagation and generation of low-frequency electromagnetic waves in the upper atmosphere. Soviet Physics Uspekhi. 1961, vol. 3, pp. 743-764. DOI:https://doi.org/10.1070/PU1961v003n05ABEH005809.
3. Ginzburg V.L. Rasprostranenie elektromagnitnykh voln v plazme [The Propagation of Electromagnetic Waves in Plasmas]. Moscow, Fizmatgiz Publ., 1960, 552 p. (In Russian). (English edition: Ginzburg V.L. The Propagation of Electromagnetic Waves in Plasmas. Translated from the Russian edition (Moscow, 1960) by J.B. Sykes and R.J. Tayler. Pergamon Press, 1964, 535 p.)
4. Guglielmi A.V. On the group velocity of slow waves in a drifting magnetoactive plasma. Geomagnetism and Aeronomy. 1963, vol. 3, no. 4, pp. 754-757. (In Russian).
5. Guglielmi A.V. The propagation of slow waves in a moving plasma. Ann. Geophys. 1968, vol. 24, no. 3, pp. 761-763.
6. Guglielmi A.V., Pokhotelov O.A. Geoelectromagnetic waves. Bristol and Philadelphia, IOP Publ. Ltd., 1996, 402 p.
7. Kadomtsev B.B. Landau damping and echo in a plasma. Soviet Physics Uspekhi. 1968, vol. 11, pp. 328-337.
8. Landau L.D., Lifshitz E.M. Teoriya polya [Field Theory]. Moscow, Nauka Publ., 1988, 512 p. (In Russian). (English edition: Landau L.D., Lifshitz E.M. The Classical Theory of Fields. Pergamon Press, 1975, 403 p.)
9. Landau L.D., Lifshitz E.M. Kvantovaya mekhanika [Quantum Mechanics]. Moscow, Nauka Publ., 1989, 768 p. (In Russian). (English edition: Landau L.D., Lifshitz E.M. Quantum Mechanics. Non-Relativistic Theory. Pergamon Press, 1977, 674 p.).
10. Likhter Ya.I., Guglielmi A.V., Erukhimov L.M., Mikhailova G.A. Volnovaya diagnostika prizemnoi plazmy [Wave diagnostics of surface plasma]. Moscow, Nauka Publ., 1988, 216 p. (In Russian).
11. Pitaevsky L.P., Lifshitz E.M. Fizicheskaya kinetika [Physical Kinetics] Moscow, Nauka Publ., 1979, 807 p. (In Russian). (English edition: Pitaevsky L.P., Lifshitz E.M. Physical Kinetics. Butterworth-Heinemann, 1981, 625 p.).
12. Storey L.R.O. An investigation of whistling atmospherics. Philosophical Transactions of the Royal Society. 1953, vol. 246, no. 908, pp. 113-141. DOI:https://doi.org/10.1098/rsta.1953.0011.
13. Vainshtein L.A. Propagation of pulses. Soviet Physics Uspekhi. 1976, vol. 19, pp. 189-205. DOI:https://doi.org/10.3367/UFNr. 0118.197602h.0339.
