M.A. Belyansky1, E.Yu. Butyrsky2, V.V. Vasiliev3
1 LLC “NPK MCA”
2,3 VMPI VUNC of the Navy of the N.G. Kuznetsov Naval Academy
1 maxim_belyansky@mail.ru; 2 evgenira88@mail.ru; 3 valeronvazilevs@yandex.ru
The use of the vertical ionospheric sensing method makes it possible to obtain information about ionospheric phenomena of various spatial scales at the receiving point of the radio pulse (from those comparable to the wavelength λ≈50 m, to sizes much larger than the size of the first Fresnel zone, i.e. horizontally comparable to the height of the inner ionosphere ~200 km). This requires the construction of a mathematical model of electromagnetic pulse propagation in the ionosphere and a surface waveguide channel independent of the trajectory.
The presence of such a signal model will make it possible to form a unified structure of processing algorithms that is inextricably linked to signal transformations along the entire trajectory. In this paper, for the tip of the ionospheric layer, its heterogeneity is reduced to linear transformations of the signal over time. Such signal changes are reduced to a multiplicative and additive group of transformations. A Lie algebra is constructed for it.
Belyansky M.A., Butyrsky E.Yu., Vasiliev V.V. A wave packet propagation in ionospheric plasma as transformations induced by a change in the temporal supp of the signal. Radiotekhnika. 2025. V. 89. № 11. P. 89−98. DOI: https://doi.org/10.18127/j00338486-202511-09 (In Russian)
- Djevis K. Radiovolny v ionosfere. M.: Mir.1973. 502 s. (in Russian).
- Radiozondirovanie ionosfery sputnikovymi i nazemnymi ionozondami. Trudy instituta prikladnoj geofiziki im. Fedorova. 2008. Vyp. 87. 212 s. (in Russian).
- Butyrskij E.Ju., Matveev A.V. Matematicheskoe modelirovanie sistem i processov. SPb: Strategija budushhego. 2022. 799 s. (in Russian).
- Vejl' G. Simmetrija. M.: Nauka. 1968. 192 s. (in Russian).
- Butyrskij E.Ju. Matematicheskie modeli gidroakusticheskih signalov i metody ih obrabotki. SPb: Strategija budushhego. 2018. 649 s. (in Russian).
- Ginzburg V.L. Rasprostranenie jelektromagnitnyh voln v plazme. M.: Nauka. 1976. 684 s. (in Russian).
- Budden K.G. Radio waves in the ionosphere. Cambridge: University Press. 1961. 542 p.
- Ibragimov N.H. Gruppy preobrazovanij matematicheskoj fiziki. M.: Nauka. 1983. 28 s. (in Russian).
- Vilenkin N.Ja. Special'nye funkcii i teorija predstavlenij grupp. M.: Nauka. 1965. 587 s. (in Russian).
- Ljeng S. SL(2,R). M.: Mir. 1977. 430 s. (in Russian).
- Butyrskij E.Ju. Modeli signalov, inducirovannye preobrazovaniem vremeni. Nauchnoe priborostroenie. 2011. T. 22. № 1 (in Russian).
- Butyrskij E.Ju. Teoretiko-gruppovoe predstavlenie signalov i perspektivy ego ispol'zovanija. SPb: VMIRJe. 2010. S. 77-87 (in Russian).
- Danilkin N.P., Zabotin Η.A. Novye vidy diagnostiki ionosfernyh parametrov metodom nazemnogo i vneshnego radiozondirovanija. Radiotehnika. 1994. T. 60. № 3. S. 63-74 (in Russian).
- Bowman G.G. Some aspects of large-scale travelling ionospheric disturbance. Planet. Space Sci. 1960. V. 2. P. 829–845.
- Bowman G.G., Dunne G.S., Hainsworth D.W. A relationship between polar magnetic substorms, ionospheric height rises and the occurrence of spread-F. J. Atmos. Terr. Phys. 1987. V. 49. № 2. P. 713–722.
- Dzhaparidze G.A., Mosashvili N.V., Nikolajshvili N.Sh., Sharadze Z.S. Geomagnetizm i ajeronomija. 1989. T. 29. № 2. S. 340-342 (in Russian).
- From W.R., Meehan D.H. Mid-latitude spread-F structure. J. Atmos. Terr. Phys. 1988. V. 50. № 57. P. 629-638.

