In this paper, we use numerical experiment methods to address the problem of determining characteristics of ULF (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.
ULF wave propagation, numerical simulation, ionosphere
1. Borovsky J.E., Funsten H.O. Role of solar wind turbulence in the coupling of the solar wind to the Earth’s magnetosphere. J. Geophys. Res. 2003, vol. 108, iss. A6, 1246. DOI: 10.1029/2002JA009601.
2. Burlaga L.F. Intermittent turbulence in the solar wind. J. Geophys. Res. 1991, vol. 96, pp. 5847–5851. DOI: 10.1029/ 91JA00087.
3. Chernyshov A.A., Karelsky K.V., Petrosyan A.S. Subgrid-scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas. Physics-Uspekhi. 2014, vol. 57, no. 5, pp. 421‒452. DOI: 10.3367/UFNe.0184.201405a.0457.
4. D’Amicis R., Bruno R., Bavassano B. Geomagnetic activity driven by solar wind turbulence. Adv. Space Res. 2010, vol. 46, iss. 4, pp. 514–520. DOI: 10.1016/j.asr.2009.08.031.
5. Holappa L., Mursula K., Asikainen T. A new method to estimate annual solar wind parameters and contributions of different solar wind structures to geomagnetic activity. J. Geophys. Res.: Space Physics. 2014, vol. 119, pp. 9407–9418. DOI: 10.1002/2014JA020599.
6. Horsthemke W., Lefever R. Noise-Induced Transitions. Theory and Applications in Physics, Chemistry, and Biology. Berlin, Heidelberg, Springer-Verlag, 1984, 322 p. (Springer Series in Synergetics, vol. 15.).
7. Johnson J.R., Wing S. A solar cycle dependence of nonlinearity in magnetospheric activity. J. Geophys. Res. 2005, vol. 110, A04211. DOI: 10.1029/2004JA010638.
8. Kurazhkovskaya N.A., Klain B.I. Effect of geomagnetic activity, solar wind and parameters of interplanetary magnetic field on regularities in intermittency of Pi2 geomagnetic pulsations. Solnechno-zemnaya fizika [Solar-Terrestrial Physics]. 2015, vol. 1, iss. 3, pp. 11‒20. (In Russian). DOI: 10.12737/11551.
9. Livshits I.M., Obridko V.N. Variations of the dipole magnetic moment of the Sun during the solar activity cycle. Astronomy Reports. 2006, vol. 50, iss. 11, pp. 926‒935. DOI: 10.1134/S1063772906110060.
10. Malinetsky G.G., Potapov A.B. Sovremennye problemy nelineinoi dinamiki [Current Problems in Nonlinear Dynamics]. Moscow, Editorial URSS, 2000, 335 p. (In Russian).
11. Marsch E., Tu C.-Y. Intermittency, non-Gaussian statistics and fractal scaling of MHD fluctuations in the solar wind. Nonlin. Processes Geophys. 1997, vol. 4, pp. 101–124.
12. Ohtomo N., Tokiwano K., Tanaka Y, Sumi A., Terach S. Exponential characteristics of power spectral densities caused by chaotic phenomena. J. Phys. Soc. Japan. 1995, vol. 64, no. 4, pp. 1104‒1113.
13. Riazantseva M.O., Zastenker G.N. Intermittency of solar wind density fluctuations and its relation to sharp density changes. Cosmic Res. 2008, vol. 46, no. 1, pp. 1–7. DOI: 10.1134/ S0010952508010012.
14. Schreiber H. On the periodic variations of geomagnetic activity indices Ap and ap. Ann. Geophysicae. 1998, vol. 16, pp. 510–517.
15. Sigeti D.E. Exponential decay of power spectra at high frequency and positive Lyapunov exponents. Physica D. 1995, vol. 82, iss. 1–2, pp. 136‒153. DOI: 10.1016/0167-2789(94)00225-F.
16. Sigeti D., Horsthemke W. High-frequency power spectra for systems subject to noise. Phys. Rev. A. 1987, vol. 35, no. 5, pp. 2276‒2282. DOI: 10.1103/physreva.35.2276.
17. Sokolov I.V., van der Holst B., Oran R., Downs C., Roussev I.I., Jin M., Manchester IV W.B., Evans R.M., Gombosi T.I. Magnetohydrodynamic waves and coronal heating: unifying empirical and MHD turbulence models. Astrophys. J. 2013, vol. 764, no. 1, 13 p. DOI: 10.1088/0004-637X/764/1/23.
18. Valsakumar M.C., Satyanarayana S.V.M., Sridhar V. Signature of chaos in power spectrum. Pramana ‒ journal of physics. 1997, vol. 48, no. 1, pp. 69‒85. DOI: 10.1007/BF02845623.
19. Veselovsky I.S., Dmitriev A.V., Suvorova A.V. Algebra and statistics of the solar wind. Cosmic Res. 2010, vol. 48, iss. 2, pp. 113‒128. DOI: 10.1134/S0010952510020012.
20. Vӧrӧs Z., Jankovicová D., Kovács P. Scaling and singularity characteristics of solar wind and magnetospheric fluctuations. Nonlin. Processes Geophys. 2002, vol. 9, pp. 149–162.
21. Webb D.F., Crooker N.U., Plunkett S.P., St. Cyr O.C. The solar sources of geoeffective structure. Space Weather. 2001, pp. 123‒141. (AGU Geophys. Monogr., vol. 125). DOI: 10.1029/GM125p0123.
22. Xu F., Borovsky J.E. A new four-plasma categorization scheme for the solar wind. J. Geophys. Res.: Space Phys. 2015, vol. 120, pp. 70–100. DOI: 10.1002/2014JA020412.
23. Yermolaev Yu.I., Nikolaeva N.S., Lodkina I.G., Yermolaev M.Yu. Catalog of large-scale solar wind phenomena during 1976–2000. Cosmic Res. 2009, vol. 47, no. 2, pp. 81–94. DOI: 10.1134/S0010952509020014.
24. Yordanova E., Balogh A., Noullez A., von Steiger R. Turbulence and intermittency in the heliospheric magnetic field in fast and slow solar wind. J. Geophys. Res. 2009, vol. 114, A08101. DOI: 10.1029/2009JA014067.
25. Zotov O.D., Klain B.I. The trigger mode in the dynamics of the magnetosphere. Materialy IV Vserossiskoi konferentsii s mezhdunarodnym uchastiem “Triggernye efecty v geosistemakh” [Proc. of the IV All-Russian Conference with International Participation “Trigger Effects in Geosystems”. (Moscow, June 6–9, 2017)]. Moscow, GEOS Publ., 2017, pp. 442‒449. (In Russian).
26. Zotov O.D., Klain B.I., Kurazhkovskaya N.A. Stochastic resonance in the Earth’s magnetosphere dynamics. Proc. 7th International Conference “Problems of Geocosmos”. St. Petersburg, May 26–30, 2008. St. Petersburg, 2008, pp. 360‒364.
27. Zotov O.D., Klain B.I., Kurazhkovskaya N.A. Peculiarities of the dynamics of the magnetosphere in the solar activity cycle. Materialy 12 mezhdunarodnoi shkoly-konferentsii “Problemy geokosmosa”. [Proc. of the 12th International School Conference “Problems of Geospace”. St. Petersburg, Peterhof, October 8–12, 2018]. St. Petersburg, VVM Publ., 2018, pp. 320–325. (In Russian).
28. URL: www.wdcb.ru (accessed April 16, 2019).
29. URL: http://swdcwww. kugi.kyoto-u.ac.jp/index.html (accessed May 15, 2019).
30. URL: https://omniweb.gsfc.nasa.gov/ow.html (accessed May 15, 2019).