Apatity, Russian Federation
Murmansk Arctic State University
Apatity, Russian Federation
Murmansk Arctic State University
Apatity, Russian Federation
Apatity, Russian Federation
Apatity, Russian Federation
from 01.01.2010 until now
Apatity, Russian Federation
Apatity, Russian Federation
Apatity, Russian Federation
UDK 519.62 Численные методы решения обыкновенных дифференциальных уравнений
In this paper, we examine the features of RSDN-20 signal propagation in a high-latitude Earth–ionosphere waveguide during solar proton events, using computational experiment methods. We have analyzed two proton ground-level enhancement (GLE) events of December 13, 2006 (GLE70) and September 10, 2017 (GLE72). Electron density profiles were constructed using the Global Dynamic Model of Ionosphere (GDMI) and the RUSCOSMICS model, developed at PGI. We present estimated phase and amplitude changes in RSDN-20 signals during precipitation of high-energy protons in the high-latitude region of the Earth–ionosphere waveguide. From the results of computational experiments and the analysis of the electromagnetic signal attenuation based on analytical Maxwell’s equation system solution in magnetized ionospheric plasma, we have found a pattern in the signal attenuation frequency dependence associated simultaneously with the signal reflection height, electron density profiles, and the collision frequency of electrons with neutral particles and ions. We discuss limitations of the computational experiment method and compare simulation results with data from Lovozero and Tuloma observatories.
numerical modeling, radio wave propagation, ionosphere, high latitudes, GLE, VLF, RSDN-20, GDMI
1. Akhmetov O.I., Mingalev I.V., Mingalev O.V., Suvorova Z.V., Belakhovsky V.B., Chernyakov S.M. Determination of the characteristics of INCH waves that react most strongly to minor changes in the electron density of the ionosphere at high latitudes. Solar-Terrestrial Physics. 2019, vol. 5, no. 4, pp. 81-90. DOI:https://doi.org/10.12737/stp-54201911.
2. Akhmetov O.I., Mingalev I.V., Mingalev O.V., Belakhovsky V.B., Suvorova Z.V. Propagation of electromagnetic waves in the region of high latitudes at various states of the ionosphere at frequencies of the RSDN-20 (ALPHA) radionavigation system. Geomagnetism and Aeronomy. 2021a, vol. 61, no. 3, pp. 376-388. DOI:https://doi.org/10.1134/S0016793221030026.
3. Akhmetov O.I., Mingalev I.V., Mingalev O.V., Belakhovsky V.B., Suvorova Z.V. Propagation of electromagnetic waves with frequencies of the Beta time signal service through the ionosphere in different states at high latitudes. Bulletin of the Russian Academy of Sciences: Physics. 2021b, vol. 85, no. 3, pp. 224-229. DOI:https://doi.org/10.3103/S1062873821020039.
4. Akhmetov O.I., Belakhovsky V.B., Mingalev I.V., Mingalev O.V., Larchenko A.V., Suvorova Z.V. About the propagation of RSDN-20 “Alpha” signals in the Earth-ionosphere waveguide during geomagnetic disturbances. Radio Sci. 2023, vol. 58, e2022RS007490. DOI:https://doi.org/10.1029/2022RS007490.
5. Alken P., Thébault E., Beggan C.D., Amit H., Aubert J., Baerenzung J., et al. International Geomagnetic Reference Field: the thirteenth generation. Earth Planets Space. 2021, vol. 73, 49. DOI:https://doi.org/10.1186/s40623-020-01288-x.
6. Clilverd M., Seppälä A., Rodger C., Thomson N., Verronen P., Turunen E., et al. Modeling polar ionospheric effects during the October-November 2003 solar proton events. Radio Sci. 2006, vol. 41, id RS2001. DOI:https://doi.org/10.1029/2005RS003290.
7. Deminov M.G., Shubin V.N., Baidin V.I. Model of the E-layer critical frequency for the auroral region. Geomagnetism and Aeronomy. 2021, vol. 61, no. 5, pp. 713-720. DOI:https://doi.org/10.1134/S0016793221050054.
8. Dowden R.L., Adams C.D.D. Phase and amplitude perturbations on the NWC signal at Dunedin from lightning-induced electron precipitation. J. Geophys. Res.: Space Phys. 1989, vol. 94, iss. A1, pp. 497-503. DOI:https://doi.org/10.1029/JA094iA01p00497.
9. Gavrilov B.G., Ermak V.M., Poklad Yu.V., Ryakhovsky I.A. Estimate of variations in the parameters of the midlatitude lower ionosphere caused by the solar flare of September 10, 2017. Geomagnetism and Aeronomy. 2019, vol. 59, no. 5, pp. 587-592. DOI:https://doi.org/10.1134/S0016793219050049.
10. Gledhill J.A. The effective recombination coefficient of electrons in the ionosphere between 50 and 150 km. Radio Sci. 1986, vol. 21, no. 3, pp. 399-408. DOI:https://doi.org/10.1029/RS021i003p00399.
11. Hargreaves J.K. The upper atmosphere and solar-terrestrial relations: An introduction to the aerospace environment. 1st edition.Van Nostrand Reinhold, 1979, 298 p.
12. Inan U.S., Cummer S.A., Marshall R.A. A survey of ELF and VLF research on lightning-ionosphere interactions and causative discharges. J. Geophys. Res.: Space Phys. 2010, vol. 115, iss. A6, A00E36. DOI:https://doi.org/10.1029/2009JA014775.
13. Knipp D., Ramsay A., Beard E., Boright A., Cade T., Hewins I., et al. The May 1967 great storm and radio disruption event: Extreme space weather and extraordinary responses. Space Weather. 2016, vol. 14, pp. 614-633. DOI:https://doi.org/10.1002/2016sw001423.
14. Korja T., Engels M., Zhamaletdinov A.A., Kovtun A.A., Palshin N.A., Smirnov M. Yu., et al. Crustal conductivity in Fennoscandia - a compilation of a database on crustal conductance in the fennoscandian shield. Earth Planets Space. 2002, vol. 54, no. 5, pp. 535-558. DOI:https://doi.org/10.1186/BF03353044.
15. Lifshits E.M., Pitaevsky L.P. Fizicheskaya kinetika [Physical Kinetics]. Moscow, Nauka Publ., 1979, 527 p. (Landau L.D., Lifshits E.M. Teoreticheskaya fizika. [Theoretical Physics]. Vol. X). (In Russian).
16. Marshall R.A., Wallace T., Turbe M. Finite-difference modeling of very-low-frequency propagation in the earth-ionosphere waveguide. IEEE Trans. Antennas Propag. 2017, vol. 65, no. 12, pp. 7185-7197. DOI:https://doi.org/10.1109/TAP.2017.2758392.
17. Maurchev E.A., Balabin Yu.V. Model complex for the study of cosmic rays. Solar-Terrestrial Physics. 2016, vol. 2, no. 4, pp. 3-10. DOI:https://doi.org/10.12737/24269.
18. Meyer P., Parker E.N., Simpson J.A. Solar cosmic rays of February 1956 and their propagation through interplanetary space. Phys. Rev. 1956, vol. 104, no. 3, pp. 768-783.
19. Mishev A., Velinov P.I.Y. Determination of medium time scale ionization effects at various altitudes in the stratosphere and troposphere during ground level enhancement due to solar cosmic rays on 13.12.2006 (GLE 70). C.R. Acad. Bulg. Sci. 2015, vol. 68, pp. 1427-1432.
20. Perez-Peraza J.A., Márquez-Adame J.C., Caballero-Lopez R.A., Manzano I., Roberto R. Spectra of the two official GLEs of solar cycle 24. Adv. Space Res. 2020, vol. 65, iss. 1, pp. 663-676. DOI:https://doi.org/10.1016/j.asr.2019.10.021.
21. Shubin V.N., Krasheninnikov I.V., Merzly A.M., Reznikov A.E., Yanakov A.T., Tikhonov M.V. Dynamic Model of the High-latitude Ionosphere (DMHI): Certificate of the computer program state registration No. 2021616554 Russian Federation. 22.04.2021; applicant Federal'noe gosudarstvennoe byudzhetnoe uchrezhdenie nauki Institut kosmicheskih issledovanij Rossijskoj akademii nauk [Federal State Budgetary Institution of Science Institute of Space Research of the Russian Academy of Sciences]. 2021.
22. Shubin V.N. Global empirical model of critical frequency of the ionospheric F2-layer for quiet geomagnetic conditions. Geomagnetism and Aeronomy. 2017, vol. 57, no. 4, pp. 414-425. DOI:https://doi.org/10.1134/S0016793217040181.
23. Schunk R., Nagy A. Ionospheres: Physics, Plasma Physics, and Chemistry: 2nd ed. Cambridge, Cambridge University Press, 2009, 355 p. (Cambridge Atmospheric and Space Science Ser.). DOI:https://doi.org/10.1017/CBO9780511635342.
24. Wait J.R., Spies K.P. Characteristics of the Earth-ionosphere waveguide for VLF radio waves. Technical Note 300. Boulder, National Bureau of Standards, 1964, 96 p.
