Solnechno-Zemnaya Fizika Solnechno-Zemnaya Fizika Солнечно-земная физика 2712-9640 100193 10.12737/szf-112202506 Результаты исследований Results of current research Результаты исследований Studying the radial structure of the poloidal Alfvén resonator by the method of phase portraits from Van Allen Probes satellite data Исследование радиальной структуры полоидального альфвеновского резонатора методом «фазовых портретов» по данным спутника Van Allen Probes Власов Александр Александрович Vlasov Aleksandr Aleksandrovich a.vlasov@iszf.irk.ru Институт солнечно-земной физики СО РАН Иркутск Россия Institute of Solar-Terrestrial Physics SB RAS Irkutsk Russian Federation 26 06 2025 26 06 2025 11 2 69 78 25 11 2024 24 03 2025 https://naukaru.ru/en/nauka/article/100193/view

В работе исследована пространственная структура собственных гармоник полоидального альфвеновского резонатора, зарегистрированных спутником RBSP-B 23 октября 2012 г. в 19:12–20:24 UT. Для интерпретации данных использован метод фазовых портретов, представляющих собой совокупность графиков компонент магнитного/ электрического поля колебаний и разности фаз между поперечными компонентами. На основе теоретического описания магнитосферных МГД-волн построено аналитическое решение для собственных мод полоидального альфвеновского резонатора. Показано, что разности фаз отдельных монохроматических гармоник наблюдаемых колебаний имеют квазипериодическую структуру, что позволило подтвердить их резонаторную природу, а аналитически рассчитанные компоненты магнитного поля вдоль траектории движения спутника качественно совпадают с данными спутниковых наблюдений. На основе сопоставления теоретических расчетов структуры поперечных компонент магнитного поля с данными наблюдений выдвинуто предположение, что основной вклад в наблюдаемые колебания вносят вторая и четвертая собственные гармоники полоидального резонатора.

In the paper, we examine the spatial structure of eigenharmonics of the poloidal Alfvén resonator recorded by the RBSP-B satellite on 23 October 2012 at 19:12–20:24 UT. We employ the method of phase portraits, which is a set of plots of magnetic/electric field components of oscillations as well as the phase shift between transverse components, to interpret the data. Based on the theoretical description of magnetospheric MHD waves, an analytical solution for eigenharmonics of the poloidal Alfvén resonator is framed. The phase shift of individual harmonics of the observed oscillations is shown to have a quasi-periodic structure, which allows us to confirm that they have resonator modes, and the magnetic field components analytically calculated along the satellite trajectory qualitatively coincide with the satellite data. From comparison of theoretical calculations of the structure of transverse magnetic field components with observational data, we put forward an assumption that the second and fourth harmonics of the poloidal resonator make the main contribution to the observed oscillations.

 альфвеновские волны полоидальный резонатор УНЧ-волны спутниковые наблюдения Alfvén waves poloidal resonator ULF waves satellite observations Работа была выполнена при поддержке гранта РНФ № 22-77-10032 The work was financially supported by RSF (Grant No. 22-77-10032)

Вакман Д.Е., Вайнштейн Л.А. Амплитуда, фаза, частота — основные понятия теории колебаний. Успехи физических наук. 1977, т. 123, № 4, с. 657–682. Breneman A.W., Wygant J.R., Tian S., Cattell C.A., Thaller S.A., Goetz K., et al. The Van Allen Probes Electric Field and Waves Instrument: Science Results, Measurements, and Access to Data. Space Sci. Rev. 2022, vol. 218, no. 8, article id. 69. DOI: 10.1007/s11214-022-00934-y. Поляков С.В., Рапопорт В.О. Ионосферный альфвеновский резонатор. Геомагнетизм и аэрономия. 1981, т. 21, № 5, c. 610–614. Chen L., Hasegawa A. A theory of long-period magnetic pulsations: 1. Steady state excitation of field line resonance. J. Geophys. Res. 1974, vol. 79, pp. 1024–1032. Breneman A.W., Wygant J.R., Tian S., et al. The Van Allen Probes electric field and waves instrument: science results, measurements, and access to data. Space Sci. Rev. 2022, vol. 218, no. 8, article id. 69. DOI: 10.1007/s11214-022-00934-y. Cramm R., Glassmeier K.H., Othmer C., Fornacon K.H., Auster H.U., Baumjohann W., Georgescu E. A case study of a radially polarized Pc4 event observed by the Equator-S satellite. Ann. Geophys. 2000, vol. 18, no. 4, pp. 411–415. Chen L., Hasegawa A. A theory of long-period magnetic pulsations: 1. Steady state excitation of field line resonance. J. Geophys. Res. 1974, vol. 79, pp. 1024–1032. Eriksson P.T.I., Walker A.D.M., Stephenson J.A.E. A statistical correlation of Pc5 pulsations and solar wind pressure oscillations. Adv. Space Res. 2006, vol. 38, no. 8, pp. 1763–1771. Cramm R., Glassmeier K.H., Othmer H., et al. A case study of a radially polarized Pc4 event observed by the Equator-S satellite. Ann. Geophys. 2000, vol. 18, no. 4, pp. 411–415. Glassmeier K.H. Magnetometer array observations of a giant pulsation event. J. Geophys. Zeitschrift Geophysik. 1980, vol. 48, no. 3, pp. 127–138. Eriksson P.T.I., Walker A.D.M., Stephenson J.A.E. A statistical correlation of Pc5 pulsations and solar wind pressure oscillations. Adv. Space Res. 2006, vol. 38, no. 8, pp. 1763–1771. Guglielmi A.V., Kangas J., Potapov A.S. Quasiperiodic modulation of the Pc1 geomagnetic pulsations: An unsettled problem. J. Geophys. Res.: Space Phys. 2001, vol. 106, no. A11, pp. 25847–25855. DOI: 10.1029/2001JA000136. Glassmeier K.H. Magnetometer array observations of a giant pulsation event. J. Geophys. Zeitschrift Geophysik. 1980, vol. 48, no. 3, pp. 127–138. Keiling A. Alfvén Waves and Their Roles in the Dynamics of the Earth’s Magnetotail: A Review. Space Sci. Rev. 2009, vol. 142, pp. 73–156. Guglielmi A.V., Kangas J., Potapov A.S. Quasiperiodic modulation of the Pc1 geomagnetic pulsations: An unsettled problem. J. Geophys. Res.: Space Phys. 2001, vol. 106, no. A11, pp. 25847–25855. DOI: 10.1029/2001JA000136. Kim K.-H., Kim G.-J., Kwon H.-J. Distribution of equatorial Alfven velocity in the magnetosphere: A statistical analysis of THEMIS observations. Earth Planets and Space. 2018, vol. 70, no. 1, p. 174. DOI: 10.1186/s40623-018-0947-9. Keiling A. Alfvén Waves and Their Roles in the Dynamics of the Earth’s Magnetotail: A Review. Space Sci. Rev. 2009, vol. 142, pp. 73–156. Klimushkin D.Y., Mager P.N., Glassmeier K.H. Toroidal and poloidal Alfvén waves with arbitrary azimuthal wavenumbers in a finite pressure plasma in the Earth’s magnetosphere. Ann. Geophys. 2004, vol. 22, no. 1, pp. 267–287. DOI: 10.5194/angeo-22-267-2004. Kim K.-H., Kim G.-J., Kwon H.-J. Distribution of equatorial Alfven velocity in the magnetosphere: A statistical analysis of THEMIS observations. Earth Planets and Space. 2018, vol. 70, no. 1, p. 174. DOI: 10.1186/s40623-018-0947-9. Kozlov D.A., Leonovich A.S. Polarization splitting of the Alfvén wave spectrum in a dipole magnetosphere with a rotating plasma. Plasma Physics Rep. 2006, vol. 32, no. 9, pp. 765–774. Klimushkin D.Y., Mager P.N., Glassmeier K.H. Toroidal and poloidal Alfvén waves with arbitrary azimuthal wavenumbers in a finite pressure plasma in the Earth’s magnetosphere. Ann. Geophys. 2004, vol. 22, no. 1, pp. 267–287. DOI: 10.5194/angeo-22-267-2004. Kozlov D.A., Leonovich A.S., Vlasov A.A. Determining the radial structure of high-m Alfvén wave by means of the “phase portrait” method. Adv. Space Res. 2024, vol. 73, no. 1, pp. 624–631. Kozlov D.A., Leonovich A.S. Polarization Splitting of the Alfvén wave spectrum in a dipole magnetosphere with a rotating plasma. Plasma Physics Rep. 2006, vol. 32, no. 9, pp. 765–774. Lee D.H., Lysak R.L. Effects of azimuthal asymmetry on ULF waves in the dipole magnetosphere. Geophys. Res. Lett. 1990, vol. 17, no. 1, pp. 53–56. Kozlov D.A., Leonovich A.S., Vlasov A.A. Determining the radial structure of high-m Alfvén wave by means of the “phase portrait” method. Adv. Space Res. 2024, vol. 73, no. 1, pp. 624–631. Leonovich A.S., Mazur V.A. The spatial structure of poloidal Alfvén oscillations of an axisymmetric magnetosphere. Planetary and Space Science. 1990, vol. 43, pp. 1231–1241. DOI: 10.1016/0032-0633(90)90128-D. Lee D.H., Lysak R.L. Effects of azimuthal asymmetry on ULF waves in the dipole magnetosphere. Geophys. Res. Lett. 1990, vol. 17, no. 1, pp. 53–56. Leonovich A.S., Mazur V.A. A theory of transverse small-scale standing Alfven waves in an axially symmetric magnetosphere. Planetary and Space Science. 1993, vol. 41, pp. 697–717. Leonovich A.S., Mazur V.A. The spatial structure of poloidal Alfvén oscillations of an axisymmetric magnetosphere. Planetary and Space Science. 1990, vol. 43, pp. 1231–1241. DOI: 10.1016/ 0032-0633(90)90128-D. Leonovich A.S., Mazur V.A. Magnetospheric resonator for transverse-small-scale standing Alfven waves. Planetary and Space Science. 1995, vol. 43, pp. 881–883. Leonovich A.S., Mazur V.A. A theory of transverse small-scale standing Alfven waves in an axially symmetric magnetosphere. Planetary and Space Science. 1993, vol. 41, pp. 697–717. Leonovich A.S., Mazur V.A. Penetration to the Earth’s surface of standing Alfvén waves excited by external currents in the ionosphere. Ann. Geophys. 1996, vol. 14, pp. 545–556. Leonovich A.S., Mazur V.A. Magnetospheric resonator for transverse-small-scale standing Alfven waves. Planetary and Space Science. 1995, vol. 43, pp. 881–883. Leonovich A.S., Zong Q.-Z., Kozlov D.A., Vlasov A.A. “Phase portraits” of Alfvén waves in magnetospheric plasma. J. Geophys. Res.: Space Phys. 2022, vol. 127, no. 6, p. e2022JA030432. Leonovich A.S., Mazur V.A. Penetration to the Earth’s surface of standing Alfvén waves excited by external currents in the ionosphere. Ann. Geophys. 1996, vol. 14, pp. 545–556. Lysak R.L., Yoshikawa A. Resonant cavities and waveguides in the ionosphere and atmosphere. Magnetospheric ULF Waves: Synthesis and New Directions. Eds. K. Takahashi, P.J. Chi, R.E. Denton, R.L. Lysak. Washington, American Geophysical Union, 2006, vol. 169, pp. 289–306. DOI: 10.1029/169GM19. Leonovich A.S., Zong Q.-Z., Kozlov D.A., et al. “Phase portraits” of Alfvén waves in magnetospheric plasma. J. Geophys. Res.: Space Phys. 2022, vol. 127, no. 6, p. e2022JA030432. Mager P.N., Klimushkin D.Yu. Giant pulsations as modes of a transverse Alfvénic resonator on the plasmapause. Earth, Planets and Space. 2013, vol. 65, pp. 397–409. DOI: 10.5047/eps.2012.10.002. Lysak R.L., Yoshikawa A. Resonant cavities and waveguides in the ionosphere and atmosphere. Magnetospheric ULF Waves: Synthesis and New Directions / Eds. K. Takahashi, P.J. Chi, R.E. Denton, R.L. Lysak. Washington, American Geophysical Union, 2006, vol. 169, pp. 289–306. DOI: 10.1029/169GM19. Mager P.N., Mikhailova O.S., Mager O.V., Klimushkin D.Yu. Eigenmodes of the transverse Alfvénic resonator at the plasmapause: A Van Allen Probes case study. Geophys. Res. Lett. 2018, vol. 45, no. 19, pp. 10796–10804. DOI: 10.1029/2018GL079596. Mager P.N., Klimushkin D.Yu. Giant pulsations as modes of a transverse Alfvénic resonator on the plasmapause. Earth, Planets and Space. 2013, vol. 65, pp. 397–409. DOI: 10.5047/eps.2012.10.002. Mikhailova O.S., Mager P.N., Klimushkin D.Yu. Transverse resonator for ion-ion hybrid waves in dipole magnetospheric plasma. Plasma Physics and Controlled Fusion. 2020, vol. 62, no. 9, p. 095008. DOI: 10.1088/1361-6587/ab9be9. Mager P.N., Mikhailova O.S., Mager O. V., et al. Eigenmodes of the transverse Alfvénic resonator at the plasmapause: A Van Allen Probes case study. Geophys. Res. Lett. 2018, vol. 45, no. 19, pp. 10796–10804. DOI: 10.1029/2018GL079596. Min K., Takahashi K., Ukhorskiy A.Y., Manweiler J.W., Spence H.E., Singer H.J., et al. Second harmonic poloidal waves observed by Van Allen Probes in the dusk-midnight sector. J. Geophys. Res.: Space Phys. 2017, vol. 122, pp. 3013–3039. Mikhailova O.S., Mager P.N., Klimushkin D.Yu. Transverse resonator for ion-ion hybrid waves in dipole magnetospheric plasma. Plasma Physics and Controlled Fusion. 2020, vol. 62, no. 9, p. 095008. DOI: 10.1088/1361-6587/ab9be9. Paschmann G., Daly P.W. Multi-spacecraft analysis methods revisited. International Space Science Institute. 2008, 100 p. Min K., Takahashi K., Ukhorskiy A.Y., et al. Second harmonic poloidal waves observed by Van Allen Probes in the dusk-midnight sector. J. Geophys. Res.: Space Phys. 2017, vol. 122, pp. 3013–3039. Polyakov S.V., Rapoport V.O. Ionosfernyj al’fvenovskij resonator. Geomagnetizm i aeronomiya[Geomagnetism and aeronomy]. 1981, vol. 21, no. 5, pp. 610–614. (In Russian). Paschmann G., Daly P.W. Multi-spacecraft analysis methods revisited. International Space Science Institute. 2008, 100 p. Schumann W.O. Über die strahlungslosen Eigenschwingungen einer leitenden Kugel, die von einer Luftschicht und einer Ionosphärenhülle umgeben ist. Zeitschrift für Naturforschung A. 1952, vol. 7, no. 2, pp. 149–154. DOI: 10.1515/zna-1952-0202. Schumann W.O. Über die strahlungslosen Eigenschwingungen einer leitenden Kugel, die von einer Luftschicht und einer Ionosphärenhülle umgeben ist. Zeitschrift für Naturforschung A. 1952, vol. 7, no. 2, pp. 149–154. DOI: 10.1515/zna-1952-0202. Southwood D.J. Some features of field line resonances in the magnetosphere. Planetary and Space Science. 1974, vol. 22, pp. 483–491. Southwood D.J. Some features of field line resonances in the magnetosphere. Planetary and Space Science. 1974, vol. 22, pp. 483–491. Southwood D.J., Kivelson M.G. Damping standing Alfvén waves in the magnetosphere. J. Geophys. Res. 2001, vol. 106, pp. 10829–10836. Southwood D.J., Kivelson M.G. Damping standing Alfvén waves in the magnetosphere. J. Geophys. Res. 2001, vol. 106, pp. 10829–10836. Stasiewicz K., Bellan P., Chaston C., Kletzing C., Lysak R., Maggs J., et al. Small Scale Alfvénic Structure in the Aurora. Space Sci. Rev. 2000, vol. 92, pp. 423–533. Stasiewicz K., Bellan P., Chaston C., et al. Small Scale Alfvénic Structure in the Aurora. Space Sci. Rev. 2000, vol. 92, pp. 423–533. Takahashi K., Oimatsu S., Nosé M., Min K., Claudepierre S.G., Chan A., et al. Van Allen Probes observations of second-harmonic poloidal standing Alfvén waves. J. Geophys. Res.: Space Phys. 2018, vol. 123, pp. 611–637. Takahashi K., Oimatsu S., Nosé M., et al. Van Allen Probes observations of second-harmonic poloidal standing Alfvén waves. J. Geophys. Res.: Space Phys. 2018, vol. 123, pp. 611–637. Tamao T. Transmission and coupling resonance of hydromagnetic disturbances in the non-uniform Earth’s magnetosphere. Science Reports of Tohoku University. 1965, vol. 17, pp. 43–54. Tamao T. Transmission and coupling resonance of hydromagnetic disturbances in the non-uniform Earth’s magnetosphere. Science Reports of Tohoku University. 1965, vol. 17, pp. 43–54. Vakman D.E., Vajnshtejn L.A. Amplituda, faza, chastota — osnovnye ponyatiya teorii kolebanij. Uspekhi fizicheskih nauk [Advances in the physical sciences]. 1977, vol. 123, no. 4, pp. 657–682. (In Russian).