Solar-Terrestrial Physics Solar-Terrestrial Physics Solar-Terrestrial Physics 2500-0535 33969 10.12737/stp-54201911 Results of current research Results of current research Results of current research Determination of ULF-wave characteristics most strongly reacting to minor changes of ionospheric electron density in a high-latitude region Determination of ULF-wave characteristics most strongly reacting to minor changes of ionospheric electron density in a high-latitude region Ахметов Олег Иршатович Akhmetov Oleg Irshatovich akhmetov@pgia.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Мингалев Игорь Викторович Mingalev Igor Viktorovich mingalev_i@pgia.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 Мингалев Олег Викторович Mingalev Oleg Viktorovich mingalev_o@pgia.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Суворова Зоя Викторовна Suvorova Zoya Viktorovna suvorova@pgia.ru Белаховский Владимир Борисович Belahovskiy Vladimir Borisovich belakhov@mail.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Черняков Сергей Mихайлович Chernyakov Sergey Mihaylovich smcherniakov@gmail.com Полярный геофизический институт РАН Апатиты Россия Polar Geophysical Institute RAS Apatity Russian Federation Полярный геофизический институт РАН Апатиты Россия Polar Geophysical Institute RAS Apatity Russian Federation Мурманский арктический государственный университет Апатиты Россия Murmansk Arctic State University Apatity Russian Federation Полярный геофизический институт РАН Апатиты Россия Polar Geophysical Institute RAS Apatity Russian Federation Мурманский арктический государственный университет Апатиты Россия Murmansk Arctic State University Apatity Russian Federation Полярный геофизический институт РАН Апатиты Россия Polar Geophysical Institute RAS Apatity Russian Federation Полярный геофизический институт Апатиты Россия Polar Geophysical Institute Apatity Russian Federation Полярный геофизический институт РАН Апатиты Россия Polar Geophysical Institute RAS Apatity Russian Federation 5 4 81 90 https://zh-szf.ru/en/nauka/article/33969/view

In this paper, we use numerical experiment methods to address the problem of determining characteristics of ELF (0.3–3 kHz) electromagnetic waves recorded in the surface layer and providing the maximum amount of information about the Earth–ionosphere waveguide. We have analyzed the effect of the horizontal spatial structure of electron density of the Earth–ionosphere waveguide on propagation of electromagnetic waves. We have identified characteristics that allow us to record them by instrumental methods in conditions of weakly disturbed ionosphere. The density profiles used in numerical experiments have been obtained from data acquired by the Partial Reflection Radar at the Polar Geophysical Institute, located at the radiophysical observatory Tumanny in the Murmansk Region (69.0° N, 35.7° E), and by the IRI2016 model during the March 15, 2013 solar flare and the subsequent magnetic storm on March 17, 2013. The electromagnetic signal propagation model used in this work is the adaptation of gas-hydrodynamic methods to electrodynamic applications. The model is based on the scheme of upwind approximation of spatial derivatives (Godunov’s method with correction of streams). We also use splitting by spatial directions and physical processes. Signal field attenuation due to conductivity and its rotation due to Hall conductivity of the medium are considered in separate splitting steps by analytical formulas.

In this paper, we use numerical experiment methods to address the problem of determining characteristics of ELF (0.3–3 kHz) electromagnetic waves recorded in the surface layer and providing the maximum amount of information about the Earth–ionosphere waveguide. We have analyzed the effect of the horizontal spatial structure of electron density of the Earth–ionosphere waveguide on propagation of electromagnetic waves. We have identified characteristics that allow us to record them by instrumental methods in conditions of weakly disturbed ionosphere. The density profiles used in numerical experiments have been obtained from data acquired by the Partial Reflection Radar at the Polar Geophysical Institute, located at the radiophysical observatory Tumanny in the Murmansk Region (69.0° N, 35.7° E), and by the IRI2016 model during the March 15, 2013 solar flare and the subsequent magnetic storm on March 17, 2013. The electromagnetic signal propagation model used in this work is the adaptation of gas-hydrodynamic methods to electrodynamic applications. The model is based on the scheme of upwind approximation of spatial derivatives (Godunov’s method with correction of streams). We also use splitting by spatial directions and physical processes. Signal field attenuation due to conductivity and its rotation due to Hall conductivity of the medium are considered in separate splitting steps by analytical formulas.

 ELF wave propagation numerical simulation ionosphere ELF wave propagation numerical simulation ionosphere

Akimov V.F., Kalinin Yu.K. Vvedenie v proektirovanie ionosfernykh zagorizontnykh radiolokatorov [Introduction to the Design of Ionospheric Over-the-Horizon Radars]. Moscow, Tekhnosfera Publ., 2017, 492 p. (In Russian). Akimov V.F., Kalinin Yu.K. Vvedenie v proektirovanie ionosfernykh zagorizontnykh radiolokatorov [Introduction to the Design of Ionospheric Over-the-Horizon Radars]. Moscow, Tekhnosfera Publ., 2017, 492 p. (In Russian). Berenger J.-P. A perfectly matched layer for the absorption of electromagnetic waves. J. Computational Phys. 1994, vol. 114, no. 2, pp. 185-200. DOI: 10.1006/jcph.1994.1159. Berenger J.-P. A perfectly matched layer for the absorption of electromagnetic waves. J. Computational Phys. 1994, vol. 114, no. 2, pp. 185-200. DOI: 10.1006/jcph.1994.1159. Bisikalo D.V., Zhilkin A.G., Boyarchuk A.A. Gazodinamika tesnykh dvoinykh zvezd [Gas Dynamics of Close Binary Stars]. Moscow, Fizmatlit Publ. 2013, 632 p. (In Russian). Bisikalo D.V., Zhilkin A.G., Boyarchuk A.A. Gazodinamika tesnykh dvoinykh zvezd [Gas Dynamics of Close Binary Stars]. Moscow, Fizmatlit Publ. 2013, 632 p. (In Russian). Korja T., Engels M., Zhamaletdinov A.A., Kovtun A.A., Palshin N.A., Maxim Yu, et al. Crustal conductivity in Fennoscandia - a compilation of a database on crustal conductance in the Fennoscandian shield. Earth, Planets and Space. 2002, vol. 54, no. 5, pp. 535-558. DOI: 10.1186/BF03353044. Korja T., Engels M., Zhamaletdinov A.A., Kovtun A.A., Palshin N.A., Maxim Yu, et al. Crustal conductivity in Fennoscandia - a compilation of a database on crustal conductance in the Fennoscandian shield. Earth, Planets and Space. 2002, vol. 54, no. 5, pp. 535-558. DOI: 10.1186/BF03353044. Kovenja V.M., Janenko N.N. Metod rasshchepleniya v zadachakh gazovoi dinamiki [Splitting method in problems of gas dynamics]. Novosibirsk, Nauka Publ., 1981, 304 p. (In Russian). Kovenja V.M., Janenko N.N. Metod rasshchepleniya v zadachakh gazovoi dinamiki [Splitting method in problems of gas dynamics]. Novosibirsk, Nauka Publ., 1981, 304 p. (In Russian). Kulikovskij A.G., Pogorelov N.V., Semenov A.Ju. Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii [Mathematical questions in numerical solution of hyperbolic combined equations]. Moscow, Fizmatlit Publ. 2012, 656 p. (In Russian). Kulikovskij A.G., Pogorelov N.V., Semenov A.Ju. Matematicheskie voprosy chislennogo resheniya giperbolicheskikh sistem uravnenii [Mathematical questions in numerical solution of hyperbolic combined equations]. Moscow, Fizmatlit Publ. 2012, 656 p. (In Russian). Liao Z.P., Wong H.L., Yang B.P., Yuan Y.F. A transmitting boundary for transient wave analyses. Scienta Sinica. Ser. A. 1984, vol. 27, no. 10, pp.1063-1076. Liao Z.P., Wong H.L., Yang B.P., Yuan Y.F. A transmitting boundary for transient wave analyses. Scienta Sinica. Ser. A. 1984, vol. 27, no. 10, pp.1063-1076. Mingalev I.V., Mingalev O.V., Akhmetov O.I., Suvorova Z.V. The apparent splitting scheme for Maxwell’s equations. Matematicheskoe modelirovanie [Mathematical Models and Computer Simulations]. Moscow, RAN Publ., 2018, vol. 30, no. 12, pp. 17-38. (In Russian). DOI: 10.31857/S0234087 90001934-1. Mingalev I.V., Mingalev O.V., Akhmetov O.I., Suvorova Z.V. The apparent splitting scheme for Maxwell’s equations. Matematicheskoe modelirovanie [Mathematical Models and Computer Simulations]. Moscow, RAN Publ., 2018, vol. 30, no. 12, pp. 17-38. (In Russian). DOI: 10.31857/S0234087 90001934-1. Mingalev O.V., Mingalev I.V., Melnik M.N., Akhmetov O.I., Ахметов О.И., Suvorova Z.V. New method of the Vlasov-Maxwell system numerical integration. Matematicheskoe modelirovanie [Mathematical Models and Computer Simulations]. Moscow, RAN Publ. 2018, vol. 30, no. 10, pp. 21-43. (In Russian). DOI: 10.31857/S023408790001919-4. Mingalev O.V., Mingalev I.V., Melnik M.N., Akhmetov O.I., Ahmetov O.I., Suvorova Z.V. New method of the Vlasov-Maxwell system numerical integration. Matematicheskoe modelirovanie [Mathematical Models and Computer Simulations]. Moscow, RAN Publ. 2018, vol. 30, no. 10, pp. 21-43. (In Russian). DOI: 10.31857/S023408790001919-4. Mur G. Absorbing boundary conditions for the finite-difference approximation of the time domain electromagnetic field equations. IEEE Electromagnetic Compatibility, 1981, vol. 23, no. 4, pp. 277-382. DOI: 10.1109/TEMC.1981.303970. Mur G. Absorbing boundary conditions for the finite-difference approximation of the time domain electromagnetic field equations. IEEE Electromagnetic Compatibility, 1981, vol. 23, no. 4, pp. 277-382. DOI: 10.1109/TEMC.1981.303970. Pilgaev S.V., Akhmetov O.I., Filatov M.V., Fedorenko Ju.V. The universal device of data synchronization by the GPS receiver. Pribory i tekhnika eksperimenta [Instruments and Experimental Techniques]. Moscow, RAN Publ. 2008, no. 3, pp. 175-176. (In Russian). Pilgaev S.V., Akhmetov O.I., Filatov M.V., Fedorenko Ju.V. The universal device of data synchronization by the GPS receiver. Pribory i tekhnika eksperimenta [Instruments and Experimental Techniques]. Moscow, RAN Publ. 2008, no. 3, pp. 175-176. (In Russian). Tereshhenko V.D., Vasilyev E.B., Ovchinnikov N.A., Popov A.A. The middle wave radar of Polar geophysical institute for the lower ionosphere research. Tehnika i metodika geofizicheskogo jeksperimenta [Technology and Methods of Geophysical Experiment], Apatity, Kola Science Center RAS, 2003, pp. 37-46. (In Russian). Tereshhenko V.D., Vasilyev E.B., Ovchinnikov N.A., Popov A.A. The middle wave radar of Polar geophysical institute for the lower ionosphere research. Tehnika i metodika geofizicheskogo jeksperimenta [Technology and Methods of Geophysical Experiment], Apatity, Kola Science Center RAS, 2003, pp. 37-46. (In Russian). Voskresenskii D.I., Stepanenko V.I., Filippov V.S. Ustroi stva SVCh i antenny. Proektirovanie fazirovannykh antennykh reshetok [Microwave oven devices and antennas. Designing of the phased antenna lattices]. Moscow, Radiotehnika Publ. 2012, 744 p. (In Russian). Voskresenskii D.I., Stepanenko V.I., Filippov V.S. Ustroi stva SVCh i antenny. Proektirovanie fazirovannykh antennykh reshetok [Microwave oven devices and antennas. Designing of the phased antenna lattices]. Moscow, Radiotehnika Publ. 2012, 744 p. (In Russian). Yee Kane. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation, 1966, vol. 14, pp. 302-307. DOI: 10.1109/TAP.1966.1138693. Yee Kane. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation, 1966, vol. 14, pp. 302-307. DOI: 10.1109/TAP.1966.1138693.