Solar-Terrestrial Physics

2500-0535

44345

10.12737/stp-74202105

Reviews

Interaction between long-period ULF waves and charged particle in the magnetosphere: theory and observations (overview)

https://orcid.org/0000-0002-3278-6250

Климушкин

Дмитрий Юрьевич

Klimushkin

Dmitri Yur'evich

klimush@iszf.irk.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

https://orcid.org/0000-0002-5450-3397

Магер

Павел Николаевич

Mager

Pavel Nikolaevich

p.mager@iszf.irk.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

Челпанов

Максим Алексеевич

Chelpanov

Maksim Alekseevich

max_chel@iszf.irk.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

Костарев

Данила Владимирович

Kostarev

Danila Vladimirovich

kostarev@iszf.irk.ru

Институт солнечно-земной физики СО РАН Иркутск Россия Institute of Solar-Terrestrial Physics SB RAS Irkutsk Russian Federation

Институт солнечно-земной физики СО РАН Иркутск Россия Institute of Solar Terrestrial Physics SB RAS Irkutsk Russian Federation

Геофизический центр РАН Москва Россия Geophysical Center of the Russian Academy of Sciences Moscow Russian Federation

20 12 2021

7 4 33 66 29 05 2021 24 08 2021

https://zh-szf.ru/en/nauka/article/44345/view

The paper reviews the current state of the problem of interaction between long-period ultra-low-frequency (ULF) waves and high-energy particles. We consider elements of the theory of energy exchange between waves and particles, particle transport across magnetic shells under the influence of the electromagnetic field of a wave, the acceleration of radiation belt particles by both resonant and non-resonant mechanisms. We examine the mechanisms of generation of azimuthally-small-scale ULF waves due to instabilities arising from the wave–particle resonance. The cases of Alfvén, drift-compressional, and drift-mirror waves are analyzed. It is noted that due to the lack of a detailed theory of drift-mirror modes, the possibility of their existence in the magnetosphere cannot be taken as a proven fact. We summarize experimental data on the poloidal and compression ULF waves generated by unstable populations of high-energy particles. We investigate the mechanisms of modulation of energetic particle fluxes by ULF waves and possible observational manifestations of such modulation. Methods of studying the structure of waves across magnetic shells by recording fluxes of resonant particles with a finite Larmor radius are discussed.

ULF waves wave—particle interaction radiation belts plasma instabilities

The reported study was funded by RFBR, Project No. 20-15-50241

Allan W., Poulter E. M., Nielsen E. STARE observations of a Pc5 pulsation with large azimuthal wave number. J. Geophys. Res. 1982, vol. 87, pp. 6163-6172. DOI: 10.1029/ JA087iA08p06163.

Allison H.J., Shprits Y.Y. Local heating of radiation belt electrons to ultra-relativistic energies. Nature Communications. 2020, vol. 11, article id. 4533. DOI: 10.1038/s41467-020-18053-z.

Alperovich L.S., Fedorov E.N. Hydromagnetic Waves in the Magnetosphere and the Ionosphere. Springer, 2007. 426 p. DOI: 10.1007/978-1-4020-6637-5.

Anderson B. J. Statistical studies of Pc3-5 pulsations and their relevance for possible source mechanisms of ULF waves. Ann. Geophys. 1993, vol. 11, pp. 128-143.

Antonsen T.M., Jr. and. Lane B. Kinetic equations for low frequency instabilities in inhomogeneous plasmas. Phys. Fluid. 1980, vol. 23, pp. 1205-1214. DOI: 10.1063/1.863121.

Baddeley L.J., Yeoman T.K., Wright D.M., Davies J.A., Trattner K. J., and Roeder J. L. Morning sector drift-bounce resonance driven ULF waves observed in artificially-induced HF radar backscatter. Ann. Geophys. 2002, vol. 20, pp. 1487-1498. DOI: 10.5194/angeo-20-1487-2002.

Baddeley L.J., Yeoman T.K., Wright D.M., Trattner K.J., Kellet B.J. Statistical study of unstable particle populations in the global ring current and their relation to the generation of high m ULF waves. Ann. Geophys. 2004, vol. 22, pp. 4229-4241. DOI: 10.5194/angeo-22-4229-2004.

Baddeley L.J., Yeoman T.K., Wright D.M., Trattner K.J., Kellet B.J. On the coupling between unstable magnetospheric particle populations and resonant high m ULF wave signatures in the ionosphere. Ann. Geophys. 2005, vol. 23, pp. 567-577. DOI: 10.5194/angeo-23-567-2005.

Baddeley L.J., Lorentzen D.A., Partamies N., Denig M., Pilipenko V.A., Oksavik K., Chen X., Zhang Y. Equatorward propagating auroral arcs driven by ULF wave activity: Multipoint ground- and space-based observations in the dusk sector auroral oval. J. Geophys. Res.: Space Phys. 2017, vol. 122 (5), pp. 5591-5605. DOI: 10.1002/2016JA023427.

10.

Baker D.N. Satellite anomalies due to space storms. Space Storms and Space Weather Hazards. New York, Springer, 2001, pp. 251-284, DOI: 10.1007/978-94-010-0983-6_11.

11.

Baker D.N., Belian R.D., Higbie P.R., Klebesadel R.W., Blake J.B. Deep dielectric charging effects due to high-energy electrons in earth’s outer magnetosphere. J. Electrostatics. 1987, vol. 20(1), pp. 3-19. DOI: 10.1016/0304-3886(87)90082-9.

12.

Baker D.N., Pulkkinen T.I., Li X., Kanekal S.G., Ogilvie K.W., Lepping R.P., Blake J.B., Callis L.B., Rostoker G., Singer H.J., Reeves G.D. A strong CME-related magnetic cloud interaction with the Earth’s magnetosphere: ISTP observations of rapid relativistic electron acceleration on May 15, 1997. Geophys. Res. Lett. 1998, vol. 25 (15), pp. 2975-2978. DOI: 10.1029/98GL01134.

13.

Baker D.N., Hoxie V., Zhao H., Jaynes A.N., Kanekal S., Li X., Elkington S. Multiyear measurements of radiation belt electrons: acceleration, transport, and loss. J. Geophys. Res.: Space Phys. 2019. Vol. 124, no. 4. P. 2588-2602. DOI: 10.1029/2018JA026259.

14.

Barfield J.N., Pherron R.L. Statistical characteristics of storm-associated Pc 5 micropulsations observed at the synchronous equatorial orbit. J. Geophys. Res. 1972, vol. 77, pp. 4720-4733. DOI: 10.1029/JA077i025p04720.

15.

Beharrell M., Kavanagh A.J., Honary F. On the origin of high-m magnetospheric waves. J. Geophys. Res.: Space Phys. 2010, 115 (A2), p. A02201. DOI: 10.1029/2009JA014709.

16.

Brizard A.J., Chan A.A. Relativistic bounce-averaged quasilinear diffusion equation for low-frequency electromagnetic fluctuations. Physics of Plasmas. 2001, vol. 8, pp. 4762-4771. DOI: 10.1063/1.1408623.

17.

Catto P.J., Tang W.M., Baldwin D.E. Generalized gyrokinetics. Plasma Physics. 1981, vol. 23, pp. 639-650. DOI: 10.1088/0032-1028/23/7/005.

18.

Chelpanov M.A., Mager P.N., Klimushkin D.Yu., Berngardt O.I., Mager O.V. Experimental evidence of drift compressional waves in the magnetosphere: An Ekaterinburg coherent decameter radar case study. J. Geophys. Res.: Space Phys. 2016, vol. 121, pp. 1315-1326. DOI: 10.1002/2015JA022155.

19.

Chelpanov M.A., Mager O.V., Mager P.N., Klimushkin D.Yu., and Berngardt O.I. Properties of frequency distribution of Pc5-range pulsations observed with the Ekaterinburg decameter radar in the nightside ionosphere. J. Atmos. Solar-Terr. Phys. 2018, vol. 167, pp. 177-183. DOI: 10.1016/j.jastp.2017.12.002.

20.

Chelpanov M.A., Mager P.N., Klimushkin D.Yu., Mager O.V. Observing magnetospheric waves propagating in the direction of electron drift with Ekaterinburg Decameter Coherent Radar. Solar-Terr. Phys. 2019, vol. 5, pp. 51-57. DOI: 10.12737/stp-51201907.

21.

Chen L., Cowley S.C. On field line resonances of hydromagnetic Alfvén waves in dipole magnetic field. Geophys. Res. Lett. 1989, vol. 16, pp. 895-897. DOI: 10.1029/GL016i008p00895.

22.

Chen L., Hasegawa A. A theory of long period magnetic pulsation. 1: Steady state excitation of a field line resonance. J. Geophys. Res. 1974, vol. 79, pp. 1024-1032. DOI: 10.1029/JA079i007p01024.

23.

Chen L., Hasegawa A. Kinetic theory of geomagnetic pulsations: 1. Internal excitations by energetic particles. J. Geophys. Res. 1991, vol. 96, pp. 1503-1512. DOI: 10.1029/90JA02346.

24.

Chen L., Hasegawa A. Kinetic theory of geomagnetic pulsations: 2. Ion flux modulations by transverse waves. J. Geophys. Res. 1994, vol. 99, pp. 179-182. DOI: 10.1029/93JA02774.

25.

Cheng C.Z., Lin C.S. Eigenmode analysis of compressional waves in the magnetosphere. Geophys. Res. Lett. 1987, vol. 14 (8), pp. 884-887. DOI: 10.1029/GL014i008p00884.

26.

Cheng C.Z., Qian Q. Theory of ballooning-mirror instabilities for anisotropic pressure plasmas in the magnetosphere. J. Geophys. Res. 1994, vol. 99 (A6), pp. 11193-11209. DOI: 10.1029/94JA00657.

27.

Cheremnykh O.K., Parnowski A.S. The theory of ballooning perturbations in the inner magnetosphere of the Earth. Adv. Space Res. 2004, vol. 33, pp. 769-773. DOI: 10.1016/S0273-1177(03)00642-2.

28.

Chisham G., Orr D., Yeoman T.K. Observations of a giant pulsation across an extended array of ground magnetometers and on auroral radar. Planet. Space Sci. 1992, vol. 40, pp. 953-964. DOI: 10.1016/0032-0633(92)90135-B.

29.

Choi J., Lee D.-H. On the persistent poloidal Alfvén waves. Geophys. Res. Lett. 2021, vol. 48 (12), pp. e2021GL092945. DOI: 10.1029/2021GL092945.

30.

Claudepierre S.G., Mann I.R., Takahashi K., Fennell J.F., Hudson M.K., Blake J.B., et al. Van Allen Probes observation of localized drift resonance between poloidal mode ultra-low frequency waves and 60 keV electrons. Geophys. Res. Lett. 2013, vol. 40, pp. 4491-4497. DOI: 10.1002/grl.50901.

31.

Cooper M.B., Gerrard A.J., Lanzerotti L.J., Soto-Chavez A.R., Kim H., Kuzichev I.V., and Goodwin L.V. Mirror instabilities in the inner magnetosphere and their potential for localized ULF wave generation. J. Geophys. Res.: Space Phys. 2021, vol. 126(2), p. e2020JA028773. DOI: 10.1029/2020JA028773.

32.

Crabtree C., Chen L. Finite gyroradius theory of drift compressional modes. Geophys. Res. Lett. 2004, vol. 31, pp. L17804. DOI: 10.1029/2004GL020660.

33.

Crabtree C., Horton W., Wong H.V., van Dam J.W. Bounce-averaged stability of compressional modes in geotail flux tubes. J. Geophys. Res. 2003, vol. 108, pp. 1084. DOI: 10.1029/2002JA009555.

34.

Cummings W.D., O’Sullivan R.J., Coleman P.J. Standing Alfvén waves in the magnetosphere. J. Geophys. Res. 1969, vol. 74, pp. 778-793. DOI: 10.1029/JA074i003p00778.

35.

Da Silva L.A., Shi J., Alves L.R., Sibeck D., Marchezi J.P., Medeiros C., et al. High-energy electron flux enhancement pattern in the outer radiation belt in response to the Alfvénic fluctuations within high-speed solar wind stream: A statistical analysis. J. Geophys. Res.: Space Phys. 2021, vol. 126, no. 8. DOI: 10.1029/2021JA029363.

36.

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: 10.1002/grl.50800.

37.

Degeling A.W., Rankin R., Kabin K., Marchand R., Mann I.R. The effect of ULF compressional modes and field line resonances on relativistic electron dynamics. Planet. Space Sci. 2007, vol. 55(6), pp. 731-742. DOI: 10.1016/j.pss.2006.04.039.

38.

Degeling A.W., Ozeke L.G., Rankin R., Mann I.R., and Kabin K. Drift resonant generation of peaked relativistic electron distributions by Pc 5 ULF waves. J. Geophys. Res.: Space Phys. 2008, vol. 113 (A2), pp. A02208. DOI: 10.1029/2007JA012411.

39.

Degeling A.W., Rankin R., Wang Y., Shi Q.Q., Zong Q.G. Alteration of particle drift resonance dynamics near poloidal mode field line resonance structures. J. Geophys. Res.: Space Phys. 2019, vol. 124 (9), pp. 7385-7401. DOI: 10.1029/2019JA026946.

40.

Degtyarev V.I., Kharchenko I.P., Potapov A.S., Tsegmed B., Chudnenko S.E. Qualitative estimation of magnetic storm efficiency in producing relativistic electron flux in the Earth’s outer radiation belt using geomagnetic pulsations data. Adv. Space Res. 2009, vol. 43, pp. 829-836. DOI: 10.1016/j.asr.2008.07.004.

41.

Demekhov A.G. Recent progress in understanding Pc1 pearl formation. J. Atmos. Solar-Terr. Phys. 2007, vol. 69, pp. 1599-1774. DOI: 10.1016/j.jastp.2007.01.014.

42.

Demekhov A.G., Trakhtengerz V.Yu., Rycroft M., Nann D. Electron acceleration in the magnetosphere by whistler-mode waves of varying frequency. Geomagnetism and Aeronomy. 2006, vol. 46, iss. 6, pp.711-716. DOI: 10.1134/S0016793206060053.

43.

Drozdov A.Y., Allison H.J., Shprits Y.Y., Elkington S.R., Aseev N.A. A comparison of radial diffusion coefficients in 1D and 3D long-term radiation belt simulations. J. Geophys. Res.: Space Phys. 2021. Vol. 126, no. 8, article id. e28707. DOI: 10.1029/2020JA028707.

44.

Dungey J.W. Electrodynamics of the Outer Atmospheres. Pennsylvania State University, Ionosphere Research Laboratory, 1954. 52 p.

45.

Dungey J.W. Effects of electromagnetic perturbations on particles trapped in the radiation belts. Space Sci. Rev. 1964, vol. 4, pp. 199-222. DOI: 10.1007/BF00173882.

46.

Elkington S.R. A Review of ULF Interactions with Radiation Belt Electrons. Magnetospheric ULF Waves: Synthesis and New Directions. Geophys. Monograph Ser. 2006, vol. 169, pp. 177-194, Washington: American Geophysical Union Publ., DC, USA, 2006. DOI: 10.1029/169GM12.

47.

Elkington S.R., Sarris T.E. The role of Pc-5 ULF waves in the radiation belts: Current understanding and open questions. Waves, Particles, and Storms in Geospace. 2016, pp. 80-101. Oxford University Press, 2016. DOI: 10.1093/acprof:oso/9780198705246.003.0005.

48.

Elkington S.R., Hudson M.K., Chan A.A. Acceleration of relativistic electrons via drift-resonant interaction with toroidal-mode Pc-5 ULF oscillations. Geophys. Res. Lett. 1999, vol. 26 (21), pp. 3273-3276. DOI: 10.1029/1999GL003659.

49.

Elkington S.R., Hudson M.K., Chan A.A. Resonant acceleration and diffusion of outer zone electrons in an asymmetric geomagnetic field. J. Geophys. Res. 2003, vol. 108 (A3), pp. 1116. DOI: 10.1029/2001JA009202.

50.

Fälthammar C.-G. Effects of time-dependent electric fields on geomagnetically trapped radiation. J. Geophys. Res. 1965, vol. 70 (11), pp. 2503-2516. DOI: 10.1029/JZ070i011p02503.

51.

Fälthammar C.-G. Radial diffusion by violation of the third adiabatic invariant. Earth’s Particles and Fields. 1968, pp. 157-169.

52.

Fei Y., Chan A.A., Elkington S.R., Wiltberger M.J. Radial diffusion and mhd particle simulations of relativistic electron transport by ULF waves in the September 1998 storm. J. Geophys. Res.: Space Phys. 2006, vol. 111 (A12), pp. A12209. DOI: 10.1029/2005JA011211.

53.

Feygin F. Z., Khabazin Yu. G. Slow drift mirror kinetic instability at a finite electron temperature in a nonmaxwellian space plasma. Geomagnetism and Aeronomy. 2014, vol. 54 (6), pp. 727-734. DOI: 10.1134/S0016793214060103.

54.

Foster J.C., Wygant J.R., Hudson M.K., Boyd A.J., Baker D.N., Erickson P.J., and Spence H.E. Shock induced prompt relativistic electron acceleration in the inner magnetosphere. J. Geophys. Res.: Space Phys. 2015, vol. 120 (3), pp. 1661-1674. DOI: 10.1002/2014JA020642.

55.

Glassmeier K.-H. Reply to the comment by I.R. Mann and G. Chisham. Ann. Geophys. 2000, vol. 18, pp. 167-169. DOI: 10.1007/s00585-000-0167-y.

56.

Glassmeier K.-H., Buchert S., Motschmann U., Korth A., Pedersen A. Concerning the generation of geomagnetic giant pulsations by drift-bounce resonance ring current instabilities. Ann. Geophys. 1999, vol. 17, pp. 338-350. DOI: 10.1007/s00585-999-0338-4.

57.

Gubar’ Yu. I. Drift resonance of relativistic electrons with ULF waves as a nonlinear resonance. Cosmic Res. 2010, vol. 48 (4), pp. 300-307. DOI: 10.1134/S0010952510040039.

58.

Guglielmi A. and Potapov A. Frequency-modulated ULF waves in near-Earth space. Phys. Usp. 2021, vol. 64(5), pp. 87-92. DOI: 10.3367/UFNe.2020.06.038777.

59.

Guglielmi A.V., Zolotukhina N.A. Excitation of Alfvén oscillations of the magnetosphere by the asymmetric ring current. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa [Research on Geomagnetism, Aeronomy and Solar Physics]. Nauka Publ., 1980, iss. 50, pp. 129-137. (In Russian).

60.

Hamlin D.A., Karplus R., Vik R.C., Watson K.M. Mirror and azimuthal drift frequencies for geomagnetically trapped particles. J. Geophys. Res. 1961, vol. 66 (1), pp. 1-4. DOI: 10.1029/JZ066i001p00001.

61.

Hao Y.X., Zong Q.-G., Wang Y.F., Zhou X.-Z., Zhang H., Fu S.Y., et al. Interactions of energetic electrons with ULF waves triggered by interplanetary shock: Van Allen Probes observations in the magnetotail. J. Geophys. Res.: Space Phys. 2014, vol. 119, pp. 8262-8273. DOI: 10.1002/2014JA020023.

62.

Hao Y.X., Zong Q.-G., Zhou X.-Z., Rankin R., Chen X.R., Liu Y., et al. Global-scale ULF waves associated with SSC accelerate magnetospheric ultrarelativistic electrons. J. Geophys. Res.: Space Phys. 2019, vol. 124 (3), pp. 1525-1538. DOI: 10.1029/2018JA026134.

63.

Hasegawa A. Drift mirror instability of the magnetosphere. Phys. Fluids. 1969, vol. 12, pp. 2642-2650. DOI: 10.1063/1.1692407.

64.

Higuchi T., Kokubun S. Waveform and polarization of compressional Pc-5 waves at geosynchronous orbit. J. Geophys. Res. 1988, vol. 93, pp. 14433-14443. DOI: 10.1029/JA093iA12p14433.

65.

Huba J.D., Drake J.F. Physical mechanism of wave-particle resonances in an inhomogeneous magnetic field. I - Linear theory. Phys. Fluids. 1981, vol. 24, pp.1650-1654. DOI: 10.1063/1.863588.

66.

Huba J.D., Drake J.F. Physical mechanism of wave-particle resonances in a curved magnetic field. Phys. Fluids. 1982, vol. 25, pp. 1207-1210. DOI: 10.1063/1.863891.

67.

Hudson M.K., Elkington S.R., Lyon J.G., Goodrich C.C., Rosenberg T.J. Simulation of Radiation Belt Dynamics Driven by Solar Wind Variations. Sun-Earth Plasma Connections. Geophys. Monograph Ser. 1999, vol. 109, pp. 171-182. Washington: American Geophysical Union Publ., DC, USA, 1999. DOI: 10.1029/GM109p0171.

68.

Hughes W.J., Southwood D.J., Mauk B., McPherron R.L., Barfield J.N. Alfvén waves generated by an inverted plasma energy distribution. Nature. 1978, vol. 275, pp. 43-45. DOI: 10.1038/275043a0.

69.

Hughes W.J., McPherron R.L., Barfield J.N., Mauk B.H. A compressional Pc4 pulsation observed by three satellites in geostationary orbit near local midnight. Planet. Space Sci. 1979, vol. 27, pp. 821-840. DOI: 10.1016/0032-0633(79)90010-2.

70.

James M.K., Yeoman T.K., Mager P.N., Klimushkin D.Yu. The spatio-temporal characteristics of ULF waves driven by substorm injected particles. J. Geophys. Res.: Space Phys. 2013, vol. 118, pp. 1737-1749. DOI: 10.1002/jgra.50131.

71.

Karpman V.I., Meerson B.I., Mikhailovsky A.B., Pokhotelov O.A. The effects of bounce resonances on wave growth rates in the magnetosphere. Planet. Space Sci. 1977, vol. 25, pp. 573-585. DOI: 10.1016/0032-0633(77)90064-2.

72.

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.

73.

Klimushkin D.Yu. Resonators for hydromagnetic waves in the magnetosphere. J. Geophys. Res. 1998, vol. 103, pp. 2369-2375. DOI: 10.1029/97JA02193.

74.

Klimushkin D.Yu. The propagation of high-𝑚 Alfvén waves in the Earth’s magnetosphere and their interaction with high-energy particles. J. Geophys. Res. 2000, vol. 105, pp. 23,303-23,310. DOI: 10.1029/1999JA000396.

75.

Klimushkin D.Yu., Chen L. Eigenmode stability analysis of drift-mirror modes in nonuniform plasmas. Ann. Geophys. 2006, vol. 24 (10), pp. 2435-2439. DOI: 10.5194/angeo-24-2435-2006.

76.

Klimushkin D.Yu., Kostarev D.V. Two kinds of mirror modes in a nonzero electron-temperature plasma. Plasma Physics and Controlled Fusion. 2012, vol. 54 (9), pp. 092001. DOI: 10.1088/0741-3335/54/9/092001.

77.

Klimushkin D.Yu., Mager P.N. The spatio-temporal structure of impulse-generated azimuthal small-scale Alfvén waves interacting with high-energy charged particles in the magnetosphere. Ann. Geophys. 2004, vol. 22, pp. 1053-1060. DOI: 10.5194/angeo-22-1053-2004.

78.

Klimushkin D.Yu., Mager P.N. Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment. Planet. Space Sci. 2011, vol. 59, pp. 1613-1620. DOI: 10.1016/j.pss.2011.07.010.

79.

Klimushkin D.Yu., Mager P.N. Coupled Alfvén and drift-mirror modes in non-uniform space plasmas: a gyrokinetic treatment. Plasma Physics and Controlled Fusion. 2012, vol. 54 (1), pp. 015006. DOI: 10.1088/0741-3335/54/1/015006.

80.

Klimushkin D.Yu., Leonovich A.S., and Mazur V.A. On the propagation of transversally small-scale standing Alfvén waves in a three-dimensionally inhomogeneous magnetosphere. J. Geophys. Res. 1995, vol. 100, pp. 9527-9534. DOI: 10.1029/94JA03233.

81.

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. 267-288. DOI: 10.5194/angeo-22-267-2004.

82.

Klimushkin D.Yu., Mager P.N., Pilipenko V.A. On the ballooning instability of the coupled Alfvén and drift compressional modes. Earth, Planets and Space. 2012, vol. 64, pp. 777-781. DOI: 10.5047/eps.2012.04.002.

83.

Korablev L.V., Rudakov L.I. Instability of a plasma with an isotropic distribution function. Sov. Phys. JETP, Engl. Transl. 1968, vol. 27, pp. 439-440.

84.

Kostarev D.V., Mager P.N. Drift-compression waves propagating in the direction of energetic electron drift in the magnetosphere. Solar-Terr. Phys. 2017, vol. 3, pp. 18-27. DOI: 10.12737/stp-33201703.

85.

Kostarev D.V., Mager P.N., Klimushkin D.Yu. Alfvén wave parallel electric field in the dipole model of the magnetosphere: gyrokinetic treatment. J. Geophys. Res.: Space Phys. 2021, vol. 126 (2), pp. e2020JA028611. DOI: 10.1029/2020JA028611.

86.

Kozyreva O., Pilipenko V., Engebretson M.J., Yumoto K., Watermann J., Romanova N. In search of a new ULF wave index: Comparison of Pc5 power with dynamics of geostationary relativistic electrons. Planet. Space Sci. 2007, vol. 55 (6), pp. 755-769. DOI: 10.1016/j.pss.2006.03.013.

87.

Kozyreva O.V., Pilipenko V.A., Engebretson M.J. Klimushkin D.Yu., Mager P.N Solar-Terr. Phys. 2016, vol. 2, pp. 35-45. DOI: 10.12737/20999.

Kozyreva O.V., Pilipenko V.A., Engebretson M.J. Klimushkin D.Yu., Mager P.N Solar-Terr. Phys. 2016, vol. 2, pp. 35-45. DOI: 10.12737/20999

88.

Lanzerotti L.J., Hasegawa A., Maclennan C.G. Drift mirror instability in the magnetosphere: Particle and field oscillations and electron heating. J. Geophys. Res. 1969, vol. 74 (24) , pp. 5565-5578. DOI: 10.1029/JA074i024p05565.

89.

Le G., Chi P.J., Strangeway R.J., Russell C.T., Slavin J.A., Takahashi K., Singer H.J., et al. Global observations of magnetospheric high-𝑚 poloidal waves during the 22 June 2015 magnetic storm. Geophys. Res. Lett. 2017, vol. 44, pp. 3456-3464. DOI: 10.1002/2017GL073048.

90.

Lejosne S. Analytic expressions for radial diffusion. J. Geophys. Res.: Space Phys. 2019, vol. 124(6), pp. 4278-4294. DOI: 10.1029/2019JA026786.

91.

Lejosne S., Kollmann P. Radiation belt radial diffusion at Earth and beyond. Space Sci. Rev. 2020, vol. 216 (1), p. 19. DOI: 10.1007/s11214-020-0642-6.

92.

Leonovich A.S., Mazur V.A. A theory of transverse small-scale standing Alfvén waves in an axially symmetric magnetosphere. Planet. Space Sci. 1993, 41, pp. 697-717. DOI: 10.1016/0032-0633(93)90055-7.

93.

Leonovich A.S., Mazur V.A. Magnetospheric resonator for transverse-small-scale standing Alfvén waves. Planet. Space Sci. 1995, vol. 43, pp. 881-883, DOI: 10.1016/0032-0633(94)00206-7.

94.

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. DOI: 10.1007/s00585-996-0545-1.

95.

Leonovich A.S., Mazur V.A. Standing Alfvén waves in an axisymmetric magnetosphere excited by a non-stationary source. Ann. Geophys. 1998, vol. 16, pp. 914-920. DOI: 10.1007/s00585-998-0914-z.

96.

Leonovich A.S., Mazur V.A. Lineynaya teoriya MGD kolebanii v magnitosfere [Linear theory of MHD oscillations in the magnetosphere]. Moscow, Fizmatlit, 2016. 480 p. (In Russian).

97.

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: 10.1002/2015JA021044.

98.

Li L., Cao J., and Zhou G. Combined acceleration of electrons by whistler-mode and compressional ULF turbulences near the geosynchronous orbit. J. Geophys. Res.: Space Phys. 2005, vol. 110 (A3), pp. A03203. DOI: 10.1029/2004JA010628.

99.

Lifshits A.E., Fedorov E.N. Hydromagnetic oscillations of the magnetospheric-ionospheric resonator. Doklady AN SSSR [Reports of AS USSR]. 1986, vol. 287, pp. 90-94. (In Russian).

100.

Lin C.S., Parks G.K. The coupling of Alfvén and compressional waves. J. Geophys. Res. 1978, vol. 83 (A6), pp. 2628-2636. DOI: 10.1029/JA083iA06p02628.

101.

Lin N., McPherron R.L., Kivelson M.G., Williams D.J. An unambiguous determination of the propagation of a compressional Pc-5 wave. J. Geophys. Res. 1988, vol. 93 (A6), pp. 5601-5612. DOI: 10.1029/JA093iA06p05601.

102.

Liu W.W., Rostoker G., Baker D. N. Internal acceleration of relativistic electrons by large amplitude ULF pulsations. J. Geophys. Res.: Space Phys. 1999, vol. 104 (A8), pp. 17391-17407. DOI: 10.1029/1999JA900168.

103.

Liu W., Cao J.B., Li X., Sarris T.E., Zong Q.-G., Hartinger M., et al. Poloidal ULF wave observed in the plasmasphere boundary layer. J. Geophys. Res.: Space Phys. 2013, vol. 118 (7), pp. 4298-4307. DOI: 10.1002/jgra.50427.

104.

Longmire C. L. Elementary Plasma Physics. Interscience Publ. New York, London, 1963. 296 p.

105.

Loto’aniu T.M., Mann I.R., Ozeke L.G., Chan A.A., Dent Z.C., Milling D.K. Radial diffusion of relativistic electrons into the radiation belt slot region during the 2003 Halloween geomagnetic storms. J. Geophys. Res.: Space Phys. 2006, vol. 111 (A4), pp. A04218. DOI: 10.1029/2005JA011355.

106.

Mager O.V. Alfvén waves generated through the drift-bounce resonant instability in the ring current: A THEMIS multi-spacecraft case study. J. Geophys. Res.: Space Phys. 2021, vol. 126, iss. 11. e2021JA029241. DOI: 10.1029/2021 JA029241.

107.

Mager O.V., Chelpanov M.A., Mager P.N., Klimushkin D.Yu., Berngardt O.I. Conjugate ionosphere-magnetosphere observations of a sub-Alfvénic compressional intermediate-𝑚 wave: A case study using EKB Radar and Van Allen Probes. J. Geophys. Res.: Space Phys. 2019, vol. 124 (5), pp. 3276-3290. DOI: 10.1029/2019JA026541.

108.

Mager P.N., Klimushkin D.Yu. Spatial localization and azimuthal wave numbers of Alfvén waves generated by drift-bounce resonance in the magnetosphere. Ann. Geophys. 2005, vol. 23, pp. 3775-3784. DOI: 10.5194/angeo-23-3775-2005.

109.

Mager P.N., Klimushkin D.Yu. Generation of Alfvén waves by a plasma inhomogeneity moving in the Earth’s magnetosphere. Plasma Phys. Rep. 2007, vol. 33, pp. 391-398. DOI: 10.1134/S1063780X07050042.

110.

Mager P. N., Klimushkin D. Yu. Alfvén ship waves: high-m ULF pulsations in the magnetosphere, generated by a moving plasma inhomogeneity. Ann. Geophys. 2008, vol. 26, pp. 1653-1663. DOI: 10.5194/angeo-26-1653-2008.

111.

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.

112.

Mager P.N., Klimushkin D.Yu. Non-resonant instability of coupled Alfvén and drift compressional modes in magnetospheric plasma. Plasma Physics and Controlled Fusion, vol. 59 (9) , pp. 095005, 2017. DOI: 10.1088/1361-6587/aa790c.

113.

Mager P.N., Klimushkin D.Yu. The field line resonance in the three-dimensionally inhomogeneous magnetosphere: principal features. J. Geophys. Res.: Space Phys. 2021, vol. 126 (1), p. e2020JA028455. DOI: 10.1029/2020JA028455.

114.

Mager P.N., Klimushkin D.Yu., Kostarev D.V. Drift-compressional modes generated by inverted plasma distributions in the magnetosphere. J. Geophys. Res.: Space Phys. 2013, vol. 118, pp. 4915-4923. DOI: 10.1002/jgra.50471.

115.

Mager P.N., Berngardt O.I., Klimushkin D.Yu., Zolotukhina N.A., Mager O.V. First results of the high resolution multibeam ULF wave experiment at the Ekaterinburg SuperDARN Radar: Ionospheric signatures of coupled poloidal Alfvén and drift-compressional modes. J. Atmos. Solar-Terr. Phys. 2015, vol. 130-131, pp. 112-126. DOI: 10.1016/j.jastp.2015.05.017.

116.

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: 10.1029/2018GL079596.

117.

Mann I.R., Chisham G. Comment on “Concerning the generation of geomagnetic giant pulsations by drift-bounce resonance ring current instabilities” by K.-H. Glassmeier et al. Ann. Geophysicae, vol. 17, 338-350, (1999). Ann. Geophys. 2000, vol. 18, pp. 161-166. DOI: 10.1007/s00585-000-0161-4.

118.

Mann I.R., Wright A.N. Finite lifetimes of ideal poloidal Alfvén waves. J. Geophys. Res. 1995, vol. 100, pp. 23677-23686. DOI: 10.1029/95JA02689.

119.

Mann I.R., Murphy K.R., Ozeke L.G., Rae I.J., Milling D.K., Kale A.A., Honary F.F. The Role of Ultralow Frequency Waves in Radiation Belt Dynamics. Geophys. Monograph Ser. 2012, vol. 199, pp. 69-92. Washington: American Geophysical Union Publ., DC, USA, 2012. DOI: 10.1029/2012GM001349.

120.

Mann I.R., Lee E.A., Claudepierre S.G., Fennell J.F., Degeling A., Rae I.J., et al. Discovery of the action of a geophysical synchrotron in the Earth’s Van Allen radiation belts. Nature Communications. 2013, vol. 4, pp. 2795. DOI: 10.1038/ncomms3795.

121.

Mathie R.A., Mann I.R.A correlation between extended intervals of ULF wave power and storm-time geosynchronous relativistic electron flux enhancements. Geophys. Res. Lett. 2000, vol. 27 (20), pp. 3261-3264. DOI: 10.1029/2000GL003822.

122.

Mathie R.A., Mann I.R. On the solar wind control of Pc5 ULF pulsation power at mid-latitudes: Implications for MeV electron acceleration in the outer radiation belt. J. Geophys. Res.: Space Phys. 2001, vol. 106 (A12), pp. 29783-29796. DOI: 10.1029/2001JA000002.

123.

Migliuolo S. High-𝛽 theory of low-frequency magnetic pulsations. J. Geophys. Res. 1983, vol. 88 (A3), pp. 2065-2074. DOI: 10.1029/JA088iA03p02065.

124.

Mikhailovskii A.B., Pokhotelov O.A. New mechanism for generation of geomagnetic pulsations by fast particles. Soviet J. Plasma Phys. 1975, vol. 1, pp. 786-792.

125.

Mikhailovskii A.B., Pokhotelov O.A. Electromagnetic trapped-electron instability in the magnetosphere. Soviet J. Plasma Phys. 1976, vol. 2, pp. 928-935.

126.

Mikhaǐlovskiǐ A.B., Fridman A.M. Drift waves in a finite-pressure plasma. Soviet J. Experimental and Theoretical Phys. 1967, vol. 24, pp. 965-974.

127.

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 (3), pp. 3013-3039. DOI: 10.1002/2016JA023770.

128.

Moiseev A.V., Baishev D.G., Mullayarov V.A., Samsonov S.N., Uozumi T., Yoshikava A., et al. The development of compression long-period pulsations on the recovery phase of the magnetic storm on May 23, 2007. Cosmic Res. 2016, vol. 54, pp. 31-39. DOI: 10.1134/S0010952516010123.

129.

Moiseev A.V., Starodubtsev S.A., Mishin V.V. Features of excitation and azimuthal and meridional propagation of long-period Pi3 oscillations of the geomagnetic field on December 8, 2017. Solar-Terr. Phys. 2020, vol. 6, pp. 46-59. DOI: 10.12737/stp-63202007.

130.

Motoba T., Takahashi K., Ukhorskiy A., Gkioulidou M., Mitchell D.G., Lanzerotti L.J., et al. Link between premidnight second harmonic poloidal waves and auroral undulations: Conjugate observations with a Van Allen Probe spacecraft and a THEMIS all-sky imager. J. Geophys. Res. 2015, vol. 120, pp. 1814-1831. DOI: 10.1002/2014JA020863.

131.

Ng P.H., Patel V.L. The coupling of shear Alfvén and compressional waves in high-m magnetospheric plasma. J. Geophys. Res. 1983, vol. 88 (A12) , pp. 10035-10040. DOI: 10.1029/JA088iA12p10035.

132.

Ng P.H., Patel V.L., Chen S. Drift compressional instability in the magnetosphere. J. Geophys. Res. 1984, vol. 89, pp. 10763-10769. DOI: 10.1029/JA089iA12p10763.

133.

Northrop T.G. The Adiabatic Motion of Charged Particles. Interscience, New York, 1963.

134.

O’Brien T.P., Lorentzen K.R., Mann I.R., Meredith N.P., Blake J.B., Fennell J.F., et al. Energization of relativistic electrons in the presence of ULF power and MeV microbursts: Evidence for dual ULF and VLF acceleration. J. Geophys. Res.: Space Phys. 2003, vol. 108 (A8), pp. 1329. DOI: 10.1029/2002JA009784.

135.

Oimatsu S., Nose M., Takahashi K., Yamamoto K., Keika K., Kletzing C. A., et al. Van Allen probes observations of drift-bounce resonance and energy transfer between energetic ring current protons and poloidal Pc4 wave. J. Geophys. Res.: Space Phys. 2018, vol. 123 (5), pp. 3421-3435. DOI: 10.1029/2017JA025087.

136.

Ozeke L.G., Mann I.R., Murphy K.R., Rae I.J., Milling D.K., Elkington S. R., et al. ULF wave derived radiation belt radial diffusion coefficients. J. Geophys. Res. 2012, vol. 117, p. A04222. DOI: 10.1029/2011JA017463.

137.

Ozeke L.G., Mann I.R., Murphy K.R., Rae J.I., and Milling D.K. Analytic expressions for ULF wave radiation belt radial diffusion coefficients. J. Geophys. Res.: Space Phys. 2014, vol. 119, pp. 1587-1605. DOI: 10.1002/ 2013JA019204.

138.

Ozeke L.G., Mann I.R., Murphy K.R., Degeling A.W., Claudepierre S.G., Spence H.E. Explaining the apparent impenetrable barrier to ultra-relativistic electrons in the outer Van Allen belt. Nature Communications. 2018, vol. 9, p. 1844. DOI: 10.1038/s41467-018-04162-3.

139.

Pilipenko V., Kleimenova N., Kozyreva O., Engebretson M., Rasmussen O. Long-period magnetic activity during the may 15, 1997 storm. J. Atmos. Terr. Phys. 2001, vol. 63, pp. 489-501. DOI: 10.1016/S1364-6826(00)00189-9.

140.

Pilipenko V.A., Pokhotelov O.A. Drift-mirror instability in a curved magnetic field. Geomagnetism and Aeronomy. 1977, vol. 17, pp. 161-163.

141.

Pilipenko V.A., Pokhotelov O.A., Feigin F.Z. Influence of bounce resonances on excitation of Alfvén waves beyond the plasmasphere. Geomagnetism and Aeronomy. 1977, vol. 17, pp. 894-899.

142.

Pilipenko V.A., Klimushkin D.Yu., Mager P.N., Engebretson M.J., Kozyreva O.V. Generation of resonant Alfvén waves in the auroral oval. Ann. Geophys. 2016, vol. 34 (2), pp. 241-248. DOI: 10.5194/angeo-34-241-2016.

143.

Pilipenko V.A., Belakhovsky V.B., Samsonov S.N. On a possible acceleration mechanisms of electrons up to the relativistic energies in the Earth magnetosphere. Transactions Kola science centre RAS. 2017, vol. 8, pp. 24-30. (In Russian).

144.

Pokhotelov O.A., Pilipenko V.A. Contribution to the theory of the drift-mirror instability of the magnetospheric plasma. Geomagnetism and Aeronomy. 1976, vol. 16, pp. 296-299.

145.

Pokhotelov O.A., Pilipenko V.A., Amata E. Drift anisotropy instability of a finite-beta magnetospheric plasma. Planet. Space Sci. 1985, vol. 33, pp. 1229-1241. DOI: 10.1016/0032-0633(85)90001-7.

146.

Pokhotelov O.A., Balikhin M.A., Alleyne H.S.-C.K., Onishchenko O.G. Mirror instability with finite electron temperature effects. J. Geophys. Res. 2000, vol. 105, pp. 2393-2402. DOI: 10.1029/1999JA900351.

147.

Pokhotelov O.A., Khabazin Y.G., Mann I.R., Milling D.K., Shukla R.K., and Stenflo L. Giant pulsations: A nonlinear phenomenon. J. Geophys. Res.: Space Phys. 2000, vol. 105 (A5), pp. 10691-10702. DOI: 10.1029/1999JA900506.

148.

Pokhotelov O.A., Balikhin M.A., Sagdeev R.Z., and Treumann R.A. Halo and mirror instabilities in the presence of finite larmor radius effects. J. Geophys. Res.: Space Phys. 2005, vol. 110 (A10), pp. A10206. DOI: 10.1029/2004JA010933.

149.

Potapov A.S. ULF wave activity in high-speed streams of the solar wind: Impact on the magnetosphere. J. Geophys. Res.: Space Phys. 2013, vol. 118, pp. 6465-6477. DOI: 10.1002/2013JA019119.

150.

Potapov A. Relativistic electrons of the outer radiation belt and methods of their forecast (Review). Solar-Terr. Phys. 2017, vol. 3 (1), pp. 57-72. DOI: 0.12737/article_58f9703837c248.84596315.

151.

Potapov A., Guglielmi A., Tsegmed B., Kultima J. Global Pc5 event during 29-31 October 2003 magnetic storm. Adv. Space Res. 2006, vol. 38 (8), pp. 1582-1586. DOI: 10.1016/j.asr.2006.05.010.

152.

Potapov A.S., Amata E., Polyushkina T.N., Coco I., Ryzhakova L.V. A case study of global ULF pulsations using data from space borne and ground-based magnetometers and a SuperDARN radar. Kosmichna Nauka i Tekhnologia. 2011, vol. 17(6), pp. 54-67. DOI: 10.15407/knit2011.06.054.

153.

Potapov A.S., Tsegmed B., Ryzhakova L.V. Relationship between the fluxes of relativistic electrons at geosynchronous orbit and the level of ULF activity on the Earth’s surface and in the solar wind during the 23rd solar activity cycle. Cosmic Res. 2012, vol. 50 (2), pp. 124-140. DOI: 10.1134/S0010952512020086.

154.

Potapov A.S., Polyushkina T.N., Pulyaev V.A. Observations of ULF waves in the solar corona and in the solar wind at the Earth’s orbit. J. Atmos. Solar-Terr. Phys. 2013, vol. 102, pp. 235-242. DOI: 10.1016/j.jastp.2013.06.001.

155.

Radoski H.R. Highly asymmetric MHD resonances. The guided poloidal mode. J. Geophys. Res. 1967, vol. 72, pp. 4026-4033. DOI: 10.1029/JZ072i015p04026.

156.

Radoski H.R. A theory of latitude dependent geomagnetic micproulsations: the asymptotic fields. J. Geophys. Res. 1974, vol. 79, pp. 595-613. DOI: 10.1029/JA079i004p00595.

157.

Rae I.J., Mann I.R., Watt C.E.J., Kistler L.M., Baumjohann W. Equator-S observations of drift mirror mode waves in the dawnside magnetosphere. J. Geophys. Res. 2007, vol. 112 (A11), pp. A11203. DOI: 10.1029/2006JA012064.

158.

Rankin R., Wang C.R., Wang Y.F., Zong Q.G., Zhou X.Z., Degeling A.W., et al. Ultra-Low-Frequency Wave-Particle Interactions in Earth’s Outer Radiation Belt. Geophys. Monograph Ser. 2020, vol. 248, pp. 189-205. Washington: American Geophysical Union Publ., DC, USA, 2020. DOI: 10.1002/9781119509592.ch11.

159.

Ren J., Zong Q.G., Zhou X.Z., Rankin R., Wang Y.F. Interaction of ULF waves with different ion species: Pitch angle and phase space density implications. J. Geophys. Res.: Space Phys. 2016, vol. 121 (10), pp. 9459-9472. DOI: 10.1002/2016JA022995.2016JA022995.

160.

Ren J., Zong Q.G., Zhou X.Z., Rankin R., Wang Y.F., Gu S.J., and Zhu Y.F. Phase relationship between ULF waves and drift-bounce resonant ions: A statistical study. J. Geophys. Res.: Space Phys. 2017, vol. 122, pp. 7087-7096. DOI: 10.1002/2016JA023848.2016JA023848.

161.

Ren J., Zong Q.G., Zhou X.Z., Spence H.E., Funsten H.O., Wygant J.R., Rankin R. Cold plasmaspheric electrons affected by ULF waves in the inner magnetosphere: A Van Allen Probes statistical study. J. Geophys. Res.: Space Phys. 2019, vol. 124, pp. 7954-7965. DOI: 10.1029/2019JA027009.

162.

Romanova N., Pilipenko V. ULF wave indices to characterize the solar wind-magnetosphere interaction and relativistic electron dynamics. Acta Geophysica. 2009, vol. 57 (1), pp. 158-170. DOI: 10.2478/s11600-008-0064-4.

163.

Romanova N., Pilipenko V., Yagova N.V., Belov A.V. Statistical correlation of the rate of failures on geosynchronous satellites with fluxes of energetic electrons and protons. Cosmic Res. 2005, vol. 43 (3), pp. 179-185. DOI: 10.1007/s10604-005-0032-6.

164.

Rostoker G., Skone S., Baker D.N. On the origin of relativistic electrons in the magnetosphere associated with some geomagnetic storms. Geophys. Res. Lett. 1998, vol. 25 (19), pp. 3701-3704. DOI: 10.1029/98GL02801.

165.

Rubtsov A.V., Agapitov O.V., Mager P.N., Klimushkin D.Yu., Mager O.V., Mozer F.S., Angelopoulos V. Drift resonance of compressional ULF waves and substorm-injected protons from multipoint THEMIS measurements. J. Geophys. Res.: Space Phys. 2018, vol. 123 (11), pp. 9406-9419. DOI: 10.1029/2018JA025985.

166.

Rubtsov A.V., Mikhailova O.S., Mager P.N., et al. Multispacecraft observation of the presubstorm long-lasting poloidal ULF wave. Geophys. Res. Lett. 2021, vol. 48, iss. 23. e2021GL096182. DOI: 10.1029/2021GL096182.

167.

Saka O., Iijima T., Yamagishi H., Sato N., Baker D.N. Excitation of Pc-5 pulsations in the morning sector by a local injection of particles in the magnetosphere. J. Geophys. Res. 1992, vol. 97, pp. 10,693-10,701. DOI: 10.1029/92JA00441.

168.

Saka O., Watanabe O., Baker D.N. A possible driving source for transient field line oscillations in the postmidnight sector at geosynchronous altitudes. J. Geophys. Res. 1996, vol. 101, pp. 24,719-24,726. DOI: 10.1029/96JA02039.

169.

Sandhu J.K., Rae I.J., Wygant J.R., Breneman A.W., Tian S., Watt C.E.J., et al. ULF wave driven radial diffusion during geomagnetic storms: A statistical analysis of Van Allen Probes observations. J. Geophys. Res.: Space Phys. 2021, vol. 126 (4), p. e2020JA029024. DOI: 10.1029/2020JA029024.

170.

Sarris T.E., Wright A.N., Li X. Observations and analysis of Alfvén wave phase mixing in the Earth’s magnetosphere. J. Geophys. Res.: Space Phys. 2009, vol. 114, p. A03218. DOI: 10.1029/2008JA013606.

171.

Schulz M., Lanzerotti L.J. Particle diffusion in the radiation belts. Springer-Verlag, Berlin, Heidelberg, New York, 1974. 218 p.

172.

Shprits Y.Y., Elkington S.R., Meredith N.P., Subbotin D.A. Review of modeling of losses and sources of relativistic electrons in the outer radiation belt. I: Radial transport. J. Atmos. Solar-Terr. Phys. 2008, vol. 70 (14), pp. 1679-1693. DOI: 10.1016/j.jastp.2008.06.008.

173.

Simms L.E., Engebretson M.J., Rodger C.J., Dimitrakoudis S., Mann I.R., Chi P.J. The combined influence of lower band chorus and ULF waves on radiation belt electron fluxes at individual l-shells. J. Geophys. Res.: Space Phys. 2021, vol. 126 (5), p. e2020JA028755. DOI: 10.1029/2020JA028755.

174.

Southwood D.J. Preservation of the second adiabatic invariant during cross- L diffusion. J. Geophys. Res. 1972, vol. 77 (7) , pp. 1123-1127. DOI: 10.1029/JA077i007p01123.

175.

Southwood D.J. The behaviour of ULF waves and particles in the magnetosphere. Planet. Space Sci. 1973, vol. 21, pp. 53-65. DOI: 10.1016/0032-0633(73)90019-6.

176.

Southwood D.J. Some features of field line resonances in the magnetosphere. Planet. Space Sci. 1974, vol. 22, pp. 483-491. DOI: 10.1016/0032-0633(74)90078-6.

177.

Southwood D.J. A general approach to low-frequency instability in the ring current plasma. J. Geophys. Res.: Space Phys. 1976, vol. 81, pp. 3340-3348. DOI: 10.1029/JA081i019p03340.

178.

Southwood D.J. Low frequency pulsation generation by energetic particles. J. Geomagn. Geoelectricity. 1980, Suppl. II, vol. 32, pp. 75-88.

179.

Southwood D.J., Kivelson M.G. Charged particle behavior in low-frequency geomagnetic pulsations. 1. Transverse waves. J. Geophys. Res. 1981, vol. 86 (A7), pp. 5643-5655. DOI: 10.1029/JA086iA07p05643.

180.

Southwood D.J., Kivelson.M.G. Charged particle behavior in low-frequency geomagnetic pulsations. 2. Graphical approach. J. Geophys. Res. 1982, vol. 87, pp. 1707-1710. DOI: 10.1029/JA087iA03p01707.

181.

Southwood D. J., Dungey J. W., Etherington R. J. Bounce resonant interactions between pulsations and trapped particles. Planet. Space Sci. 1969, vol. 17, pp. 349-361. DOI: 10.1016/0032-0633(69)90068-3.

182.

Su S.Y., Konradi A., Fritz T.A. On propagation direction of ring current proton ULF waves observed by ATS 6 at 6.6RE. J. Geophys. Res. 1977, vol. 82(13), pp. 1859-1868. DOI: 10.1029/JA082i013p01859.

183.

Su Z., Zhu H., Xiao F., Zong Q. G., Zhou X. Z., Zheng H., et al. Ultra-low-frequency wave-driven diffusion of radiation belt relativistic electrons. Nature Communications. 2015, vol. 6, p. 10096. DOI: 10.1038/ncomms10096.

184.

Tajiri M. Propagation of hydromagnetic waves in collisionless plasma. II. Kinetic approach. J. Physical Society of Japan. 1967, vol. 22 (6), pp. 1482-1494. DOI: 10.1143/JPSJ.22.1482.

185.

Takahashi K. New observations, new theoretical results and controversies regarding Pc3-5 waves. Adv. Space Res. 1996, vol. 17 (10), pp. 63-71. DOI: 10.1016/0273-1177(95)00696-C.

186.

Takahashi K., Fennell J.F., Amata E., and Higbie P.R. Field-aligned structure of the storm time Pc5 wave of November 14-15, 1979. J. Geophys. Res.: Space Phys. 1987, vol. 92 (A6), pp. 5857-5864. DOI: 10.1029/JA092iA06p05857.

187.

Takahashi K., McEntire R.W., Lui A.T.Y., Potemra T.A. Ion flux oscillations associated with a radially polarized transverse Pc5 magnetic pulsation. J. Geophys. Res. 1990, vol. 95, pp. 3717-3731. DOI: 10.1029/JA095iA04p03717.

188.

Takahashi K., Claudepierre S.G., Rankin R., Mann I., Smith C.W. Van Allen Probes Observation of a Fundamental Poloidal Standing Alfvén wave event related to giant pulsations. J. Geophys. Res.: Space Phys. 2018a, vol. 123, pp. 4574-4593. DOI: 10.1029/2017JA025139.

189.

Takahashi K., Oimatsu S., Nose 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. 2018b, vol. 123, pp. 611-637. DOI: 10.1002/2017JA024869.

190.

Tamao T. Interaction of energetic particles with HM-waves in the magnetosphere. Planet. Space Sci. 1984a, vol. 32, pp. 1371-1386. DOI: 10.1016/0032-0633(84)90080-1.

191.

Tamao T. Magnetosphere - ionosphere interaction through hydromagnetic waves. Achievements of the International Magnetospheric Study (IMS). ESA Special Publ. 1984b, vol. 217, pp. 427-435.

192.

Tian A., Xiao K., Degeling A.W., Shi Q., Park J.-S., Nowada M., Pitkänen T. Reconstruction of plasma structure with anisotropic pressure: Application to Pc5 compressional wave. Astrophys. J. 2020, vol. 889 (1), pp. 35. DOI: 10.3847/1538-4357/ab6296.

193.

Trakhtengerts V.Y., Rycroft M.J. Whistler and Alfvén Mode Cyclotron Masers in Space. Cambridge University Press, 2008. 354 p.

194.

Tsurutani B.T., Lakhina G.S. Some basic concepts of wave-particle interactions in collisionless plasmas. Rev. Geophys. 1997, vol. 35 (4), pp. 491-501. DOI: 10.1029/ 97RG02200.

195.

Ukhorskiy A., Sitnov M.I. Radial transport in the outer radiation belt due to global magnetospheric compressions. J. Atmos. Solar-Terr. Phys. 2008, vol. 70 (14), pp. 1714-1726. DOI: 10.1016/j.jastp.2008.07.018.

196.

Ukhorskiy A.Y., Anderson B.J., Takahashi K., Tsyganenko N.A. Impact of ULF oscillations in solar wind dynamic pressure on the outer radiation belt electrons. Geophys. Res. Lett. 2006, vol. 33 (6), pp. L06111. DOI: 10.1029/2005GL024380.

197.

Ukhorskiy A.Y., Sitnov M.I., Takahashi K., Anderson B.J. Radial transport of radiation belt electrons due to stormtime Pc5 waves. Ann. Geophys. 2009, vol. 27, pp. 2173-2181. DOI: 10.5194/angeo-27-2173-2009.

198.

Vaivads A., Baumjohann W., Georgescu E., Haerendel G., Nakamura R., Lessard M. R., et al. Correlation studies of compressional Pc5 pulsations in space and Ps6 pulsations on the ground. J. Geophys. Res.: Space Phys. 2001, vol. 106 (A12), pp. 29797-29806. DOI: 10.1029/2001JA900042.

199.

Vetoulis G., Chen L. Global structures of Alfvén-ballooning modes in magnetospheric plasmas. Geophys. Res. Lett. 1994, vol. 21, pp. 2091-2094. DOI: 10.1029/94GL01703.

200.

Walker A. D. M., Greenwald R. A., Korth A., Kremser G. STARE and GEOS-2 observations of a storm time Pc5 ULF pulsation. J. Geophys. Res. 1982, vol. 87, pp. 9135-9146. DOI: 10.1029/JA087iA11p09135.

201.

Wang B., Zhang H., Liu Z., Liu T., Li X., Angelopoulos V. Energy modulations of magnetospheric ions induced by foreshock transient-driven ultralow-frequency waves. Geophys. Res. Lett. 2021, vol. 48 (10), e2021GL093913. DOI: 10.1029/2021GL093913.

202.

Wang C., Rankin R., Zong Q. Fast damping of ultralow frequency waves excited by interplanetary shocks in the magnetosphere. J. Geophys. Res.: Space Phys. 2015, vol. 120, pp. 2438-2451. DOI: 10.1002/2014JA020761.

203.

Watson C., Jayachandran P.T., Singer H.J., Redmon R.J., Danskin D. GPS TEC response to Pc4 “giant pulsations”. J. Geophys. Res.: Space Phys. 2016, vol. 121 (2), pp. 1722-1735. DOI: 10.1002/2015JA022253.

204.

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 Planetary Phys. 2019, vol. 3 (3), pp. 190-203. DOI: 10.26464/epp2019021.

205.

Woch J., Kremser G., Korth A., Pokhotelov O.A., Pilipenko V.A. Curvature-driven drift mirror instability in the magnetosphere. Planet. Space Sci. 1988, vol. 36, pp. 383-393. DOI: 10.1016/0032-0633(88)90126-2.

206.

Woch J., Kremser G., Korth A. A comprehensive investigation of compressional ULF waves observed in the ring current. J. Geophys. Res. 1990, vol. 95, pp. 15113-15132. DOI: 10.1029/JA095iA09p15113.

207.

Wright D.M., Yeoman T.K., Rae I.J., Storey J., Stockton-Chalk A.B., Roeder J.L., Trattner K.J. Ground-based and Polar spacecraft observations of a giant (Pg) pulsation and its associated source mechanism. J. Geophys. Res. 2001, vol. 106, pp. 10837-10852. DOI: 10.1029/2001JA900022.

208.

Xia Z., Chen L., Zheng L., Chan A.A. Eigenmode analysis of compressional poloidal modes in a selfconsistent magnetic field. J. Geophys. Res.: Space Phys. 2017, vol. 122 (A11), pp. 10369-10381. DOI: 10.1002/2017JA024376.

209.

Yagova N.V., Pilipenko V.A., Sakharov Y.A., Selivanov V.N. Spatial scale of geomagnetic Pc5/Pi3 pulsations as a factor of their efficiency in generation of geomagnetically induced currents. Earth, Planets and Space. 2021, vol. 73 (1), pp. 88. DOI: 10.1186/s40623-021-01407-2.

210.

Yamakawa T., Seki K., Amano T., Takahashi N., Miyoshi Y. Excitation of internally driven ULF waves by the drift-bounce resonance with ring current ions based on the drift-kinetic simulation. J. Geophys. Res.: Space Phys. 2020, vol. 125 (11), p. e28231. DOI: 10.1029/2020JA028231.

211.

Yamamoto K., Nose M., Keika K., Hartley D.P., Smith C.W., MacDowall R.J., et al. Eastward propagating second harmonic poloidal waves triggered by temporary outward gradient of proton phase space density: Van Allen Probe A observation. J. Geophys. Res.: Space Phys. 2019, vol. 124 (12), pp. 9904-9923. DOI: 10.1029/2019JA027158.

212.

Yang B., Zong Q.-G., Fu S.Y., Li X., Korth A., Fu H.S., et al. The role of ULF waves interacting with oxygen ions at the outer ring current during storm times. J. Geophys. Res.: Space Phys. 2011, vol. 116 (A1), p. A01203. DOI: 10.1029/2010JA015683.

213.

Yeoman T. K., Wright D. M., Chapman P.J., Stockton-Chalk A.B. High-latitude observations of ULF waves with large azimuthal wave numbers. J. Geophys. Res. 2000, vol. 105, pp. 5453-5462. DOI: 10.1029/1999JA005081.

214.

Yeoman T.K., Klimushkin D.Yu., Mager P.N. Intermediate-m ULF waves generated by substorm injection: a case study. Ann. Geophys. 2010, vol. 28, pp. 1499-1509. DOI: 10.5194/angeo-28-1499-2010.

215.

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.

216.

Zelenyi L.M., Veselovsky I.S. Plasma heliogeophysics. Vol. 2. Moscow, Fizmatlit, 2010. (In Russian). 560 p.

217.

Zhai C., Shi X., Wang W., Hartinger M.D., Yao Y., Peng W., et al. Characterization of high-m ULF wave signatures in GPS TEC data. Geophys. Res. Lett. 2021, vol. 48 (14), p. e2021GL094282. DOI: 10.1029/2021GL094282.

218.

Zhou X.-Z., Wang Z.-H., Zong Q.-G., Rankin R., Kivelson M.G., Chen X.-R., et al. Charged particle behavior in the growth and damping stages of ultralow frequency waves: Theory and Van Allen Probes observations. J. Geophys. Res.: Space Phys. 2016, vol. 121 (4), pp. 3254-3263. DOI: 10.1002/2016JA022447.

219.

Zolotukhina N.A. On excitation of Alfvén waves in the magnetosphere by a moving source. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa [Research on Geomagnetism, Aeronomy and Solar Physics]. Nauka Publ., 1974, iss. 34, pp. 20-23. (In Russian).

220.

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: 10.5194/angeo-26-2053-2008.

221.

Zong Q.-G., Zhou X.-Z., Wang Y. F., Li X., Song P., Baker D. N., et al. Energetic electron response to ULF waves induced by interplanetary shocks in the outer radiation belt. J. Geophys. Res. 2009, vol. 114 (A10), pp. A10204. DOI: 10.1029/2009JA014393.

222.

Zong Q.-G., Yuan C. J., Yang B., Wang C.R., Zhang X.Y. Fast acceleration of “killer” electrons and energetic ions by interplanetary shock stimulated ULF waves in the inner magnetosphere. Chinese Sci. Bull. 2011, vol. 56 (12), p. 1188. DOI: 10.1007/s11434-010-4308-8.

223.

Zong Q.-G., Wang Y. F., Zhang H., Fu S. Y., Zhang H., Wang C. R., et al. Fast acceleration of inner magnetospheric hydrogen and oxygen ions by shock induced ULF waves. J. Geophys. Res. 2012, vol. 117 (A11), p. A11206. DOI: 10.1029/2012JA018024.

224.

Zong Q.-G., Rankin R., Zhou X. The interaction of ultra-low-frequency Pc3-5 waves with charged particles in Earth’s magnetosphere. Rev. Modern Plasma Phys. 2017, vol. 1 (1), p. 10. DOI: 10.1007/s41614-017-0011-4.

225.

Zong Q.-G., Leonovich A. S., Kozlov D. A. Resonant Alfvén waves excited by plasma tube/shock front interaction. Physics of Plasmas. 2018, vol. 25 (12), p. 122904. DOI: 10.1063/1.5063508.