Solar-Terrestrial Physics Solar-Terrestrial Physics Solar-Terrestrial Physics 2500-0535 100194 10.12737/stp-112202506 Results of current research Results of current research Results of current research Studying the radial structure of the poloidal Alfvén resonator by the method of phase portraits from Van Allen Probes satellite data Studying the radial structure of the poloidal Alfvén resonator by the method of phase portraits from Van Allen Probes satellite data 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 60 68 25 11 2024 24 03 2025 https://zh-szf.ru/en/nauka/article/100194/view

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.

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.

 Alfvén waves poloidal resonator ULF waves satellite observations Alfvén waves poloidal resonator ULF waves satellite observations The work was financially supported by RSF (Grant No. 22-77-10032) The work was financially supported by RSF (Grant No. 22-77-10032)

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. 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. 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. 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. 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. 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. 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. 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. Glassmeier K.H. Magnetometer array observations of a giant pulsation event. J. Geophys. Zeitschrift Geophysik. 1980, vol. 48, no. 3, pp. 127–138. Glassmeier K.H. Magnetometer array observations of a giant pulsation event. J. Geophys. Zeitschrift Geophysik. 1980, vol. 48, no. 3, pp. 127–138. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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., 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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., 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., 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. 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. 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., 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. 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. 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., 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. 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. 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. 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. 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. Paschmann G., Daly P.W. Multi-spacecraft analysis methods revisited. International Space Science Institute. 2008, 100 p. Paschmann G., Daly P.W. Multi-spacecraft analysis methods revisited. International Space Science Institute. 2008, 100 p. 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). 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). 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., Kletzing C., Lysak R., Maggs J., 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., 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. 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). 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).