from 01.01.2013 to 01.01.2021
Irkutsk, Irkutsk region, Russian Federation
Irkutsk, Russian Federation
The review considers the current state of the theory of short-period ULF waves in plasma with admixture of heavy ions (ions whose mass significantly exceeds the mass of protons). The presence of heavy ions influences the spectrum and propagation characteristics of waves in Pc1 range. We examine elements of the theory of quasi-parallel and quasi-perpendicular short-period ULF waves. It is usually suggested that quasi-parallel ion-cyclotron waves have a left circular polarization. Quasi-perpendicular ion-ion hybrid waves have linear polarization and can be poloidal and toroidal. We discuss the theory of an equatorial resonator for Pc1 waves and determine its size from the density of heavy ions. In the radial direction, the waves can be locked in the vicinity of the plasmapause or in the region of a local minimum in the density of heavy ions. The equatorial resonator for arbitrary values of the wave vector components is considered. We note that ion-ion hybrid waves, in contrast to Alfvén waves, have a large parallel component of the magnetic field.
Pc1 geomagnetic pulsations, ULF waves, ion-ion hybrid waves, multicomponent plasma, heavy ions
1. Abramowitz M., Stegun I.A. Handbook of mathematical functions with formulas, graphs and mathematical tables. National Bureau of Standarts Applied Mathematics Series. Washington, 1964.
2. Anderson B.J., Erlandson R.E., Zanetti L.J. A statistical study of Pc1-2 magnetic pulsations in the equatorial magnetosphere: 1. Equatorial occurrence distributions. J. Geophys. Res. 1992a, pp. 3075-3088. DOI:https://doi.org/10.1029/91JA02706.
3. Anderson B.J., Erlandson R.E., Zanetti L.J. A statistical study of Pc1-2 magnetic pulsations in the equatorial magnetosphere: 2.Wave properties. J. Geophys. Res. 1992b, vol. 97, no. A3, pp. 3089-3101. DOI:https://doi.org/10.1029/91JA02697.
4. Anderson B.J., Denton R.E., Ho G., Hamilton D.C., Fuselier S.A., Strangeway R.J. Observational test of local proton cyclotron instability in the Earth’s magnetosphere. J. Geophys. Res.: Space Phys. 1996, vol. 101, no. A10, pp. 21527-21543. DOI:https://doi.org/10.1029/96JA01251.
5. Brunelli B.Ye., Namgaladze A.A. Fizika ionosfery [Physics of the Ionosphere]. Moscow, Nauka Publ., 1988, 528 p. (In Russian).
6. Buchsbaum S.J. Ion resonance in a multicomponent plasma. Phys. Rev. Lett. 1960, vol. 5, no. 11, pp. 495-497. DOI: 10.1103/ PhysRevLett.5.495.
7. Chen L., Thorne R.M., Horne R.B. Simulation of EMIC wave excitation in a model magnetosphere including structured high-density plumes. J. Geophys. Res.: Space Phys. 2009, vol. 114, no. A7. DOI:https://doi.org/10.1029/2009JA014204.
8. Cornwall J.M. Cyclotron instabilities and electromagnetic emission in the ultra low frequency and very low frequency ranges. J. Geophys. Res. 1965, vol. 70, no. 1, pp. 61-69. DOI:https://doi.org/10.1029/JZ070i001p00061.
9. Demekhov A.G. Coupling at the atmosphere-ionosphere-magnetosphere interface and resonant phenomena in the ULF Range. Space Sci. Rev. 2012, vol. 168, no. 1, pp. 595-609. DOI:https://doi.org/10.1007/s11214-011-9832-6.
10. Dmitrienko I.S., Mazur V.A. On waveguide propagation of Alfvén waves at the plasmapause. Planetary Space Sci. 1985, vol. 33, no. 5, pp. 471-477. DOI:https://doi.org/10.1016/0032-0633(85) 90092-3.
11. Dmitrienko I.S., Mazur V.A. The spatial structure of quasicircular Alfvén modes of waveguide at the plasmapause - Interpretation of Pc1 pulsations. Planetary Space Sci. 1992, vol. 40, pp. 139-148. DOI:https://doi.org/10.1016/0032-0633(92)90156-I.
12. Engebretson M.J., Peterson W.K., Posch J.L., Klatt M.R., Anderson B.J., Russell C.T., Singer H.J., Arnoldy R.L., Fukunishi H. Observations of two types of Pc1-2 pulsations in the outer dayside magnetosphere. J. Geophys. Res. 2002, vol. 107, no. A12. DOI:https://doi.org/10.1029/2001JA000198.
13. Engebretson M.J., Keiling A., Fornacon K.-H., Cattell C.A., Johnson J.R., Posch J.L., Quick S.R., Glassmeier K.-H., Parks G.K., R’eme H. Cluster observations of Pc1-2 waves and associated ion distributions during the October and November 2003 magnetic storms. Planetary Space Sci. 2007, vol. 55, no. 6, pp. 829-848. DOI:https://doi.org/10.1016/j.pss.2006.03.015.
14. Engebretson M.J., Posch J.L., Westerman A.M., Otto N.J., Slavin J.A., Le G., Strangeway R.J., Lessard M.R. Temporal and spatial characteristics of Pc1 waves observed by ST5. J. Geophys. Res.: Space Phys. 2008, vol. 113, no. A7. DOI:https://doi.org/10.1029/2008JA013145.
15. Farmer W.A., Morales G.J. Propagation of shear Alfvén waves in two-ion species plasmas confined by a nonuniform magnetic field. Phys. Plasmas. 2013, vol. 20, no. 8, p. 082132. DOI:https://doi.org/10.1063/1.4819776.
16. Fedorov E., Mazur N., Pilipenko V., Engebretson M. Interaction of magnetospheric Alfvén waves with the ionosphere in the Pc1 frequency band. J. Geophys. Res.: Space Phys. 2016, vol. 121, no. 1, pp. 321-337. DOI:https://doi.org/10.1002/2015JA021020.
17. Fraser B.J., Nguyen T.S. Is the plasmapause a preferred source region of electromagnetic ion cyclotron waves in the magnetosphere? J. Atmos. Solar-Terr. Phys. 2001, vol. 63, pp. 1225-1247. DOI:https://doi.org/10.1016/S1364-6826(00)00225-X.
18. Fraser B.J., Lotoániu T.M., Singer H.J. Electromagnetic ion cyclotron waves in the magnetosphere. V: Magnetospheric ULF waves: synthesis and new directions. American Geophysical Union (AGU). 2006, pp. 195-212. DOI:https://doi.org/10.1029/169GM13.
19. Gintzburg M.A. Low-frequency waves in the multicomponent plasma. Geomagnetizm i aeronomiya [Geomagnetism and Aeronomy]. 1963, vol. 3, pp.757-761. (In Russian).
20. Glassmeier K.-H., Mager P.N., Klimushkin D.Yu. Concerning ULF pulsations in Mercury’s magnetosphere. Geophys. Res. Lett. 2003, vol. 30, no. 18. DOI:https://doi.org/10.1029/2003GL017175.
21. Glassmeier K.-H., Klimushkin D., Othmer C., Mager. P. ULF waves at Mercury: Earth, the giants, and their little brother compared. Adv. Space Res. 2004, vol. 33, pp. 1875-1883. DOI:https://doi.org/10.1016/j.asr.2003.04.047.
22. Guglielmi A.V. On the nature of hydromagnetic whistlers. Doklady Akademii Nauk SSSR []. 1967, vol. 174, no 7, pp. 1076-1078. (In Russian).
23. Guglielmi A.V. Cyclotron instability of the outer radiation belt protons. Geomagnetizm i aeronomiya [Geomagnetism and Aeronomy]. 1968, vol. 8, no. 7, pp. 412-419. (In Russian).
24. Guglielmi A., Kangas J. Pc1 waves in the system of solar-terrestrial relations: new reflections. J. Atmos. Solar-Terr. Phys. 2007, vol. 69, pp. 1635-1643. DOI:https://doi.org/10.1016/j.jastp.2007.01.015.
25. Guglielmi A.V., Potapov A.S. The effect of heavy ions on the spectrum of oscillations of the magnetosphere. Kosmicheskie issledovaniya [Cosmic Res.]. 2012, vol. 50, pp. 283-291. (In Russian).
26. Guglielmi A.V., Potapov A.S. Problems of the Pc1 magnetospheric wave theory. A review. Solar-Terr. Phys. 2019, vol. 5, no. 3, pp. 87-92. DOI:https://doi.org/10.12737/stp-53201910.
27. Guglielmi A.V., Potapov A.S. Frequency-modulated ULF waves in near-Earth space. Phys. Usp. 2021, vol. 64, no. 5, pp. 452-467. DOI:https://doi.org/10.3367/UFNe.2020.06.038777.
28. Guglielmi A.V., Troitskaya V.A. Geomagnitnye pulsatsii i diagnostika magnitosfery [Geomagnetic pulsations and diagnostics of the magnetosphere]. Moscow, Nauka Publ., 1973, 208 p. (In Russian).
29. Guglielmi A.V., Potapov A.S., Russell C.T. The ion cyclotron resonator in the magnetosphere. JETP Lett. 2000, vol. 72, no. 6, p. 298-300.
30. Guglielmi A., Kangas J., Potapov A. Quasiperiodic modulation of the Pc1 geomagnetic pulsations: an unsettled problem. J. Geophys. Res. 2001, vol. 106, no. A11, pp. 25847-25855. DOI:https://doi.org/10.1029/2001JA000136.
31. Gurnett D.A., Shawhan S.D., Brice N.M., Smith R.L. Ion cyclotron whistlers. J. Geophys. Res. 1965, vol. 70, no. 7, pp. 1665-1688. DOI:https://doi.org/10.1029/JZ070i007p01665.
32. Horne R.B., Thorne R.M. On the preferred source location for the convective amplification of ion cyclotron waves. J. Geophys. Res.: Space Phys.1993, vol. 98, no. A6, pp. 9233-9247. DOI:https://doi.org/10.1029/92JA02972.
33. Horne R.B., Thorne R.M. Wave heating of He+ by electromagnetic ion cyclotron waves in the magnetosphere: heating near the H+ − He+ bi-ion resonance frequency. J. Geophys. Res.: Space Phys. 1997, vol. 102, no. A6, pp. 11457-11471. DOI:https://doi.org/10.1029/97JA00749.
34. Jacobs J.A., Watanabe T. Micropulsation whistlers. J. Atmos. Terr. Phys. 1964, vol. 26, no. 8, pp. 825-829. DOI: 10.1016/ 0021-9169(64)90180-1.
35. Kazakov Ye.O., Fülöp T. Mode conversion of waves in the ion-cyclotron frequency range in magnetospheric plasmas. Phys. Rev. Lett. 2013, vol. 111 (12), p. 125002. DOI: 10.1103/ PhysRevLett.111.125002.
36. Kennel C.F., Petschek H.E. Limit on stably trapped particle fluxes. J. Geophys. Res. 1966, vol. 71, no. 1, pp. 1-28. DOI:https://doi.org/10.1029/JZ071i001p00001.
37. Kim E.-H., Johnson J.R. Comment on mode conversion of waves in the ion-cyclotron frequency range in magnetospheric plasmas. Phys. Rev. Lett. 2014, no.113, p. 089501.
38. Kim E.-H., Johnson J.R. Full-wave modeling of EMIC waves near the He+ gyrofrequency. Geophys. Res. Lett. 2016, vol. 43, no. 1, pp. 13-21. DOI:https://doi.org/10.1002/2015GL066978.
39. Kim E.-H., Johnson J.R., Lee D.-H. Resonant absorption of ULF waves at Mercury’s magnetosphere. J. Geophys. Res.: Space Phys. 2008, vol. 113, no. A11, DOI:https://doi.org/10.1029/2008 JA013310.
40. Kim E.-H., Johnson J.R., Cairns I.H., Lee D.-H. Waves in Space Plasmas. AIP Conference Proceedings. 2009, vol. 1187, no. 1, pp. 13-20. DOI:https://doi.org/10.1063/1.3273713.
41. Kim E.-H., Johnson J.R., Lee D.-H. ULF wave absorption at Mercury. Geophys. Res. Lett. 2011, vol. 38, no. 16, p. L16111. DOI:https://doi.org/10.1029/2011GL048621.
42. Kim E.-H., Johnson J.R., Lee D.-H., Pyo Y.S. Field-line resonance structures in Mercury’s multi-ion magnetosphere. Earth, Planets and Space. 2013, vol. 65, no. 5, p. 6. DOI:https://doi.org/10.5047/eps.2012.08.004.
43. Kim E.-H., Johnson J.R., Lee D.-H. Localization of Ultra-Low Frequency Waves in Multi-Ion Plasmas of the Planetary Magnetosphere. J. Astron. Space Sci. 2015a, vol. 32, pp. 289-295. DOI:https://doi.org/10.5140/JASS.2015.32.4.289.
44. Kim E.-H., Johnson J.R., Kim H., Lee D.-H. Inferring magnetospheric heavy ion density using EMIC waves. J. Geophys. Res.: Space Phys. 2015b, vol. 120, no. 8, pp. 6464-6473. DOI:https://doi.org/10.1002/2015JA021092.
45. Kim E.-H., Johnson J.R., Lee D.-H. Electron inertial effects on linearly polarized electromagnetic ion cyclotron waves at Earth’s magnetosphere. J. Geophys. Res.: Space Phys. 2019, vol. 124, no. 4, pp. 2643-2655. DOI:https://doi.org/10.1029/2019JA026532.
46. Klimushkin D.Yu. Method of description of the Alfvén and magnetosonic branches of inhomogeneous plasma oscillations. Plasma Phys. Rep. 1994, vol. 20, pp. 280-286.
47. Klimushkin D.Yu. Resonators for hydromagnetic waves in the magnetosphere. J. Geophys. Res. 1998, vol. 103, pp. 2369-2375. DOI:https://doi.org/10.1029/97JA02193.
48. Klimushkin, D.Yu., Mager P.N. The Alfvén mode gyrokinetic equation in finite-pressure magnetospheric plasma. J. Geophys. Res.: Space Phys. 2015, vol. 120, pp. 4465-4474. DOI:https://doi.org/10.1002/2015JA021045.
49. 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, ap. 267-288. DOI:https://doi.org/10.5194/angeo-22-267-2004.
50. Klimushkin D.Yu., Mager P.N., Glassmeier K.-H. Axisymmetric Alfvén resonances in a multi-component plasma at finite ion gyrofrequency. Ann. Geophys. 2006, vol. 24, pp. 1077-1084. DOI:https://doi.org/10.5194/angeo-24-1077-2006.
51. Klimushkin D.Yu., Mager P.N., Marilovtseva O.S. Parallel structure of Pc1 ULF oscillations in multi-ion magnetospheric plasma at finite ion gyrofrequency. J. Atmos. Solar-Terr. Phys. 2010, vol. 72, no. 18, pp. 1327-1332. DOI: 10.1016/ j.jastp.2010.09.019.
52. Krall N., Trivelpiece A.W. Principles of plasma physics. McGraw-Hill; First Edition, 1973. 674 p.
53. Landau L.D., Lifshits E.M. Kurs teoreticheskoi fiziki. Kvantovaya mekhanika (nerelyativistskaya teoriya) [The course of Theoretical Physics. Quantum Mechanics (nonrelativistic theory)]. Fizmalit. 2004, 800 p. (In Russian).
54. Lee D.-H., Johnson J.R., Kim K., Kim K.-S. Effects of heavy ions on ULF wave resonances near the equatorial region. J. Geophys. Res.: Space Phys. 2008, vol. 113, no. A11. DOI: 10.1029/ 2008JA013088.
55. Leonovich A.S., Mazur V.A. A theory of transverse small-scale standing Alfvén waves in an axially symmetric magnetosphere. Planetary Space Sci. 1993, vol. 41, pp. 697-717. DOI:https://doi.org/10.1016/0032-0633(93)90055-7.
56. Leonovich A.S., Mazur V.A. Magnetospheric resonator for transverse-small-scale standing Alfvén waves. Planetary Space Sci. 1995, vol. 43, pp. 881-883. DOI:https://doi.org/10.1016/0032-0633(94)00206-7.
57. Leonovich A.S., Mazur V.A. A model equation for monochromatic standing Alfvén waves in the axially-symmetric magnetosphere. J. Geophys. Res. 1997, vol. 102, P. 11443-11456. DOI:https://doi.org/10.1029/96JA02523.
58. Leonovich A.S., Mazur V.A. Lineinaya teoriya MGD-kolebanii magnitosfery [Linear theory of MHD-waves of magnetosphere]. Fizmalit. 2016, 480 p. (In Russian).
59. 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. P. 5443-5454. DOI:https://doi.org/10.1002/2015JA021044.
60. Lessard M.R., Lund E.J., Kim H.M. Pi1B pulsations as a possible driver of Alfvénic aurora at substorm onset. J. Geophys. Res.: Space Phys. 2011, vol. 116, no. A6. DOI: 10.1029/ 2010JA015776.
61. Lotoaniu T.M. Propagation of electromagnetic ion cyclotron wave energy in the magnetosphere. J. Geophys. Res.: Space Phys. 2005, vol. 110, iss. A7. CiteID A07214. DOI: 10.1029/ 2004JA010816.
62. Lundin R., Guglielmi A. Ponderomotive forces in cosmos. Space Sci. Rev. 2006, vol. 127, pp. 1-116. DOI:https://doi.org/10.1007/s11214-006-8314-8.
63. 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:https://doi.org/10.5047/eps. 2012.10.002.
64. 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, pp. 10,796-10,804. DOI:https://doi.org/10.1029/2018GL079596.
65. Mikhailova O.S. On the possibility of localisation of Pc1 waves nearby the ionosphere, taking account of heavy ions in the magnetosphere. Solnechno-zemnaya fizika [Solar-Terrestrial Phys.]. 2011, vol. 19, pp. 83-87. (In Russian).
66. Mikhailova O.S. Studing the structure of ULF oscillations near the plasmapause, given heavy ions in magnetospheric plasma. Solnechno-zemnaya fizika [Solar-Terrestrial Phys.]. 2013, vol. 23, pp. 84-90. (In Russian).
67. Mikhailova O.S. The spatial structure of ULF-waves in the equatorial resonator localized at the plasmapause with the admixture of the heavy ions. J. Atmos. Solar-Terr. Phys. 2014, vol. 108, pp. 10-16. DOI:https://doi.org/10.1016/j.jastp.2013.12.007.
68. Mikhailova O.S., Mager P.N., Klimushkin D.Yu. Two modes of ion-ion hybrid waves in magnetospheric plasma. Plasma Physics and Controlled Fusion. 2020a, vol. 62, no. 2, p. 025026. DOI:https://doi.org/10.1088/1361-6587/ab5b32.
69. 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. 2020b, vol. 62, no. 9, p. 095008. DOI:https://doi.org/10.1088/1361-6587/ab9be9.
70. Mishin V.V., Lunyushkin S.B., Mikhalev A.V., Klibanova Yu.Yu., Tsegmed B., Karavaev Yu.A., Tashchilin A.V., Leonovich L.A., Penskikh Yu.V. Extreme geomagnetic and optical disturbances over Irkutsk during the 2003 November 20 superstorm. J. Atmos. Solar-Terr. Phys. 2018, vol. 181, pp. 68-78. DOI:https://doi.org/10.1016/j.jastp.2018.10.013.
71. Mishin V.V., Tsegmed B., Klibanova Yu.Yu., Kurika-lova M.A. Burst geomagnetic pulsations as indicators of substorm expansion onsets during storms. J. Geophys. Res.: Space Phys. 2020, vol. 125, no. 10. DOI:https://doi.org/10.1029/2020JA 028521.
72. Mithaiwala M., Rudakov L., Ganguli G. Generation of a ULF wave resonator in the magnetosphere by neutral gas release. J. Geophys. Res.: Space Phys. 2007, vol. 112, no. A9, p. A09218. DOI:https://doi.org/10.1029/2007JA012445.
73. Mursula K. Satellite observations of Pc1 pearl waves: The changing paradigm. J. Atmos. Solar-Terr. Phys. 2007, vol. 69, no. 14, pp. 1623-1634. DOI:https://doi.org/10.1016/j.jastp.2007.02.013.
74. Mursula K., Blomberg L.G., Lindqvist P.-A., Marklund G.T., Bräysy T., Rasinkangas R., Tanskanen P. Dispersive Pc1 bursts observed by Freja. Geophys. Res. Lett. 1994, vol. 21, no.17, pp. 1851-1854. DOI:https://doi.org/10.1029/94GL01584.
75. Mursula K., Bräysy T., Niskala K., Marklund G.T., Bräysy T., Rasinkangas R., Tanskanen P. Pc1 pearls revisited: Structured electromagnetic ion cyclotron waves on Polar satellite and on ground. J. Geophys. Res.: Space Phys. 2001, vol. 106, no. A12, pp. 29543-29553. DOI:https://doi.org/10.1029/2000JA003044.
76. Obayashi T. Hydromagnetic whistlers. J. Geophys. Res. 1965, vol. 70, no. 5, pp. 1069-1078. DOI:https://doi.org/10.1029/JZ070i005p01069.
77. Polyakov A.R. The structure of equidistant-frequency groups in the oscillation spectra of the dayside magnetosphere. J. Atmos. Solar-Terr. Phys. 2019, vol. 189, pp. 44-51. DOI:https://doi.org/10.1016/j.jastp.2019.04.008.
78. Rauch J.L., Roux A. Ray tracing of ULF waves in a multicomponent magnetospheric plasma: Consequences for the generation mechanism of ion cyclotron waves. J. Geophys. Res. 1982, vol. 87, no. A10, pp. 8191-8198. DOI:https://doi.org/10.1029/JA087iA 10p08191.
79. Smith R.L., Brice N. Propagation in multicomponent plasmas. J. Geophys. Res. 1964, vol. 69, no. 23, pp. 5029-5040. DOI:https://doi.org/10.1029/JZ069i023p05029.
80. Southwood D.J., Saunders M.A. Curvature coupling of slow and Alfvén MHD waves in a magnetotail field configuration. Planetary Space Sci. 1985, vol. 33, pp. 127-134. DOI: 10.1016/ 0032-0633(85)90149-7.
81. Sucksdorff E. Occurrences of rapid micropulsations at Sodankylä during 1932 to 1935. Terrestrial Magnetism and Atmospheric Electricity. 1936, vol. 41, no. 4, pp. 337-344. DOI:https://doi.org/10.1029/TE041i004p00337.
82. Swanson D.G. Plasma Waves. 2nd Edition. Bristol: IOP, 2003. DOI:https://doi.org/10.1201/b15744.
83. Takahashi K., Denton R.E., Anderson R.R., Hughes W.J. Mass density inferred from toroidal wave frequencies and its comparison to electron density. J. Geophys. Res.: Space Phys. 2006, vol. 111, iss. A1. CiteID A01201. DOI:https://doi.org/10.1029/2005JA011286.
84. Tamao T. Magnetosphere-ionosphere interaction through hydromagnetic waves. Achievements of the International Magnetospheric Study (IMS). 1984, pp. 427-435. (ESA Special Publication, vol. 217).
85. Usanova M.E., Drozdov A., Orlova K., et al. Effect of EMIC waves on relativistic and ultrarelativistic electron populations: Ground-based and Van Allen Probes observations. Geophys. Res. Lett. 2014, vol. 41, no. 5, pp. 1375-1381. DOI:https://doi.org/10.1002/2013GL059024.
86. Yahnin A.G., Yahnina T.A., Frey H.U. Subauroral proton spots visualize the Pc1 source. J. Geophys. Res.: Space Phys. 2007, vol. 112, no. A10. DOI:https://doi.org/10.1029/2007JA012501.
87. Yang B., Zong Q.-G., Wang Y.F., Fu Y., Song P., Fu H.S., Korth A., Tian T., Reme H. Cluster observations of simultaneous resonant interactions of ULF waves with energetic electrons and thermal ion species in the inner magnetosphere. J. Geophys. Res.: Space Phys. 2010, vol. 115, no. A2, DOI:https://doi.org/10.1029/2009JA014542.
88. Yeoman T.K., James M., Mager P.N., Klimushkin D.Yu. SuperDARN observations of high-m ULF waves with curved phase fronts and their interpretation in terms of transverse resonator theory. J. Geophys. Res. 2012, vol. 117, p. A06231. DOI: 10.1029/ 2012JA017668.
89. Young D.T., Perraut S., Roux A., Villedary C., Gendrin R., Korth A., Kremser G., Jones D. Wave-particle interactions near ωHe+ observed on GEOS 1 and 2: 1. Propagation of ion cyclotron waves in He+-rich plasma. J. Geophys. Res.: Space Phys. 1981, vol. 86, no. A8, pp. 6755-6772. DOI:https://doi.org/10.1029/JA086iA08p06755.
