Institute of Solar-Terrestrial Physics SB RAS
Irkutsk, Russian Federation
Irkutsk, Russian Federation
Ultralow-frequency (ULF) waves play an important role in energy transfer within Earth's magnetosphere due to intensive interaction with the surrounding plasma. Previous works have assumed that these waves are strictly divided by polarization into toroidal, when the magnetic field oscillates in the azimuthal direction, and poloidal, when it oscillates in the radial direction. The former are azimuthally large-scale and are excited by external sources, whereas the latter are small-scale and are generated by internal plasma instabilities. Observations show, however, that waves of mixed polarization often occur, and the nature of this mixing has not been explained. In this paper, we carry out a statistical study and show that the polarization of transverse waves has a normal distribution, and the maximum corresponds to oscillations of the toroidal and poloidal components with the same amplitude. At the same time, the spatial distributions of toroidal and poloidal waves are clearly different, but only lead to a small shift in the position of the distribution maximum. This result suggests that in order to compare the theory with ULF wave observations it is necessary to take into account the processes of polarization change, which can affect wave-particle interactions in the magnetosphere.
magnetosphere, ULF waves, Alfvén waves, polarization
1. Agapitov A.V., Cheremnykh O.K. Polarization of ULF waves in the Earth’s magnetosphere. Kinematics and Physics of Celestial Bodies. 2011, vol. 27, no. 3, pp. 117-123. DOI:https://doi.org/10.3103/S0884591311030020.
2. Agapitov A.V., Cheremnykh O.K. Magnetospheric ULF waves driven by external sources. Adv. Astron. Space Phys. 2013, vol. 3, pp. 12-19.
3. Anderson B.J. Statistical studies of Pc 3-5 pulsations and their relevance for possible source mechanisms of ULF waves. Ann. Geophys. 1993, vol. 11, pp. 128-143.
4. Antonova E.E., Kornilov I.A., Kornilova T.A., Kornilov O.I., Stepanova M.V. Features of auroral breakup obtained using data of ground-based television observations: case study. Ann. Geophys. 2009, vol. 27, pp. 1413-1422. DOI:https://doi.org/10.5194/angeo-27-1413-2009.
5. Chen L., Hasegawa A. Kinetic theory of geomagnetic pulsations: 1. Internal excitations by energetic particles. J. Geophys. Res. 1991, vol. 96, no. A2, pp. 1503-1512. DOI: 10.1029/ 90JA02346.
6. Chi P.J., Le G. Observations of magnetospheric high-m poloidal waves by ST-5 satellites in low Earth orbit during geomagnetically quiet times. J. Geophys. Res.: Space Phys. 2015, vol. 120, pp. 4776-4783. DOI:https://doi.org/10.1002/2015JA021145.
7. Choi J., Lee D.-H. On the persistent poloidal Alfven waves. Geophys. Res. Lett. 2021, vol. 48, e2021GL092945. DOI:https://doi.org/10.1029/2021GL092945.
8. Cummings W.D., O’Sullivan R.J., Coleman Jr. P.J. Standing Alfvén waves in the magnetosphere. J. Geophys. Res. 1969, vol. 74, no. 3, pp. 778-793. DOI:https://doi.org/10.1029/JA074i003p00778.
9. Dai L., Takahashi K., Wygant J.R., Chen L., Bonnell J., Cattell C.A., et al. Excitation of poloidal standing Alfvén waves through drift resonance wave-particle interaction. Geophys. Res. Lett. 2013, vol. 40, pp. 4127-4132. DOI:https://doi.org/10.1002/grl.50800.
10. Dai L., Takahashi K., Lysak R., Wang C., Wygant J.R., Kletzing C., et al. Storm time occurrence and spatial distribution of Pc4 poloidal ULF waves in the inner magnetosphere: A Van Allen Probes statistical study. J. Geophys. Res.: Space Phys. 2015, vol. 120, pp. 4748-4762. DOI:https://doi.org/10.1002/2015JA021134.
11. Golovchanskaya I.V., Kornilov I.A., Kornilova T.A., Kornilov O.I., Kogai T.G. Signatures of Alfvenic field-line resonance in the behavior of preonset auroral arcs. Geomagnetism and Aeronomy. 2018, vol. 58, no. 1, pp. 43-49. DOI:https://doi.org/10.1134/S0016793218010073.
12. Guglielmi A., Lundin R. Ponderomotive upward acceleration of ions by ion cyclotron and Alfvén waves over the polar regions. J. Geophys. Res. 2001, vol. 106, iss. A7, pp. 13219-13236. DOI:https://doi.org/10.1029/2000JA900066.
13. Guglielmi A.V., Troitskaya V.A. Geomagnitnye pulsatsyi i diagnostika magnitosfery [Geomagnetic pulsations and diagnostics of the magnetosphere]. Moscow, Nauka Publ., 1973, 208 p. (In Russian).
14. Hughes W.J., Southwood D.J. The screening of micropulsation signals by the atmosphere and ionosphere. J. Geophys. Res. 1976, vol. 81, iss. 19, pp. 3234-3240. DOI: 10.1029/ JA081i019p03234.
15. Kletzing C.A., Kurth W.S., Acuna M., MacDowall R.J., Torbert R.B., Averkamp T., et al. The Electric and Magnetic Field Instrument Suite and Integrated Science (EMFISIS) on RBSP. Space Sci. Rev. 2013, vol. 179, pp. 127-181. DOI: 10.1007/ s11214-013-9993-6.
16. Klimushkin D.Yu. Resonators for hydromagnetic waves in the magnetosphere. J. Geophys. Res. 1998, vol. 103, no. A2, pp. 2369-2375. DOI:https://doi.org/10.1029/97JA02193.
17. Klimushkin D.Yu., Leonovich A.S., Mazur V.A. On the propagation of transversally small-scale standing Alfven waves in a three-dimensionally inhomogeneous magnetosphere. J. Geophys. Res. 1995, vol. 100, iss. A6, pp. 9527-9534. DOI:https://doi.org/10.1029/94JA03233.
18. Klimushkin D.Yu., Mager P.N., Glassmeier K.-H. Toroidal and poloidal Alfvén waves with arbitrary azimuthal wave numbers in a finite pressure plasma in the Earth’s magnetosphere. Ann. Geophys. 2004, vol. 22, pp. 267-287. DOI:https://doi.org/10.5194/angeo-22-267-2004.
19. Klimushkin D.Yu., Mager P.N., Chelpanov M.A., Kostarev D.V. Interaction of the long-period ULF waves and charged particle in the magnetosphere: theory and observations (overview). Solar-Terr. Phys. 2021, vol. 7, iss. 4, pp. 33-66. DOI:https://doi.org/10.12737/stp-74202105.
20. Korotova G., Sibeck D., Engebretson M., Wygant J., Thaller S., Spence H., et al. Multipoint spacecraft observations of long-lasting poloidal Pc4 pulsations in the dayside magnetosphere on 1-2 May 2014. Ann. Geophys. 2016, vol. 23, pp. 985-998. DOI:https://doi.org/10.5194/angeo-34-985-2016.
21. Kostarev D.V., Mager P.N., Klimushkin D.Yu. Alfvén wave parallel electric field in the dipole model of the magnetosphere: Gyrokinetic treatment. Journal of Geophysical Research: Space Physics, 2021, vol. 126. e2020JA028611. DOI:https://doi.org/10.1029/2020JA028611.
22. Le G., Chi P.J., Strangeway R.J., Russell C.T., Slavin J.A., Anderson B., et al. MMS observation of field line resonances under disturbed solar wind conditions. Journal of Geophysical Res.: Space Phys. 2021, vol. 126, e2020JA028936. DOI: 10.1029/ 2020JA028936.
23. Leonovich A.S., Mazur V.A. The spatial structure of poloidal Alfven oscillations of an axisymmetric magnetosphere. Planetary and Space Science. 1990, vol. 38, no. 10, pp. 1231-1241. DOI:https://doi.org/10.1016/0032-0633(90)90128-D.
24. Leonovich A.S., Mazur V.A. A theory of transverse small-scale standing Alfvén waves in an axially symmetric magnetosphere. Planetary and Space Science. 1993, vol. 41, iss. 9, pp. 697-717. DOI:https://doi.org/10.1016/0032-0633(93)90055-7.
25. Leonovich A.S., Mazur V.A. Standing Alfvén waves with m>>1 in an axisymmetric magnetosphere excited by a non-stationary source. Ann. Geophys. 1998, vol. 16, pp. 914-920. DOI:https://doi.org/10.1007/s00585-998-0914-z.
26. Leonovich A.S., Mishin V.V. The energy flux of magnetoacoustic waves from the solar wind into the magnetosphere. Geomagnetism and Aeronomy. 1999, vol. 39, no. 2, pp. 182-187.
27. Leonovich A.S., Klimushkin D.Yu., Mager P.N. Experimental evidence for the existence of monochromatic transverse small-scale standing Alfvén waves with spatially dependent polarization. J. Geophys. Res.: Space Phys. 2015, vol. 120, pp. 5443-5454. DOI:https://doi.org/10.1002/2015JA021044.
28. Liu W., Sarris T.E., Li X., Elkington S.R., Ergun R., Angelopoulos V., et al. Electric and magnetic field observations of Pc4 and Pc5 pulsations in the inner magnetosphere: A statistical study. J. Geophys. Res. 2009, vol. 114, A12206. DOI:https://doi.org/10.1029/2009JA014243.
29. Mager P.N., Klimushkin D.Yu. Generation of Alfvén waves by a plasma inhomogeneity moving in the Earth's magnetosphere. Plasma Physics Reports, 2007, vol. 33, no. 5, pp. 391-398. DOI:https://doi.org/10.1134/S1063780X07050042.
30. Mann I.R., Wright A.N. Finite lifetimes of ideal poloidal Alfvén waves. J. Geophys. Res. 1995, vol. 100, iss. A12, pp. 23677-23686. DOI:https://doi.org/10.1029/95JA02689.
31. Mauk B.H., Fox N.J., Kanekal S.G., Kessel R.L., Sibeck D.G., Ukhorskiy A. Science objectives and rationale for the Radiation Belt Storm Probes mission. Space Sci. Rev. 2013, vol. 179, pp. 3-27. DOI:https://doi.org/10.1007/s11214-012-9908-y.
32. McIlwain C.E. Coordinates for mapping the distribution of magnetically trapped particles. J. Geophys. Res. 1961, vol. 66, iss. 11, pp. 3681-3691. DOI:https://doi.org/10.1029/JZ066i011p03681.
33. Radoski H.R. Highly asymmetric MHD resonances: the guided poloidal mode. J. Geophys. Res. 1967, vol. 72, no. 15, pp. 4026-4027. DOI:https://doi.org/10.1029/JZ072i015p04026.
34. Radoski H.R. A theory of latitude dependent geomagnetic micropulsations: the asymptotic fields. J. Geophys. Res. 1974, vol. 79, pp. 595-613. DOI:https://doi.org/10.1029/JA079i004p00595.
35. Rubtsov A.V., Mikhailova O.S., Mager P.N., Klimushkin D.Yu., Ren J., Zong Q.-G. Multispacecraft observation of the presubstorm long-lasting poloidal ULF wave. Geophys. Res. Lett. 2021, vol. 48, iss. 23, e2021GL096182. DOI: 10.1029/ 2021GL096182.
36. Rubtsov A.V., Nosé M., Matsuoka A., Shinohara I., Miyoshi Y. Polarization and spatial distribution features of Pc4 and Pc5 waves in the magnetosphere. J. Geophys. Res.: Space Phys. 2023a, vol. 128, e2023JA031674. DOI:https://doi.org/10.1029/2023JA031674.
37. Rubtsov A.V., Nosé M., Matsuoka A., Kasahara Y., Kumamoto A., Tsuchiya F., et al. Plasmasphere control of ULF wave distribution at different geomagnetic conditions. J. Geophys. Res.: Space Phys. 2023b, vol. 128, e2023JA031675. DOI:https://doi.org/10.1029/2023JA031675.
38. Samson J.C., Wallis D.D., Hughes T.J., Creutzberg F., Ruohoniemi J.M., Greenwald R.A. Substorm intensifications and field line resonances in the nightside magnetosphere. J. Geophys. Res. 1992, vol. 97, iss. A6, pp. 8495-8518. DOI:https://doi.org/10.1029/91JA03156.
39. Sarris T.E., Wright A.N., Li X. Observations and analysis of Alfvén wave phase mixing in the Earth’s magnetosphere. J. Geophys. Res. 2009, vol. 114, A03218. DOI:https://doi.org/10.1029/2008 JA013606.
40. Takahashi K., Denton R.E., Gallagher D. Toroidal wave frequency at L=6-10: Active Magnetospheric Particle Tracer Explorers/CCE observations and comparison with theoretical model. J. Geophys. Res.: Space Phys. 2002, vol. 107, iss. A2, 1020. DOI:https://doi.org/10.1029/2001JA000197.
41. Takahashi K., Claudepierre S.G., Rankin R., Mann I.R., Smith C.W. Van Allen Probes observation of a fundamental poloidal standing Alfvén wave event related to giant pulsations. J. Geophys. Res.: Space Phys. 2018, vol. 123, iss. 6, pp. 4574-4593. DOI:https://doi.org/10.1029/2017JA025139.
42. Vetoulis G., Chen L. Global structures of Alfvén-ballooning modes in magnetospheric plasmas. Geophys. Res. Lett. 1994, vol. 21, no. 19, pp. 2091-2094. DOI:https://doi.org/10.1029/94GL01703.
43. Wei C., Dai L., Duan S.P., Wang C., Wang Y.X. Multiple satellites observation evidence: High-m poloidal ULF waves with time-varying polarization states. Earth and Planet. Phys. 2019, vol. 3, no. 3, pp. 190-203. DOI:https://doi.org/10.26464/epp2019021.
44. Yamamoto K., Seki K., Matsuoka A., Imajo S., Teramoto M., Kitahara M., et al. A statistical study of the solar wind dependence of multi-harmonic toroidal ULF waves observed by the Arase satellite. J. Geophys. Res.: Space Phys. 2022, vol. 127, e2021JA029840. DOI:https://doi.org/10.1029/2021JA029840.
45. Zolotukhina N.A., Mager P.N., Klimushkin D.Yu. Pc5 waves generated by substorm injection: A case study. Ann. Geophys. 2008, vol. 26, pp. 2053-2059. DOI:https://doi.org/10.5194/angeo-26-2053-2008.
