Иркутск, Россия
Иркутск, Россия
We have carried out a numerical analysis of the spatial structure of Alfvén waves in a finite pressure inhomogeneous plasma in a dipole model of the magnetosphere. We have considered three magnetosphere models differing in maximum plasma pressure and pressure gradient. The problem of wave eigenfrequencies was addressed. We have established that the poloidal frequency can be either greater or less than the toroidal frequency, depending on plasma pressure and its gradient. The problem of radial wave vector component eigenvalues was considered. We have found points of Alfvén wave reflection in various magnetosphere models. The wave propagation region in the cold plasma model is shown to be significantly narrower than that in models with finite plasma pressure. We have investigated the structure of the main Alfvén wave harmonic when its polarization changes in three magnetosphere models. A numerical study into the effect of plasma pressure on the structure of behavior of all Alfvén wave electric and magnetic field components has been carried out. We have established that for certain parameters of the magnetosphere model the magnetic field can have three nodes, whereas in the cold plasma model there is only one. Moreover, the longitudinal magnetic field component changes sign twice along the magnetic field line.
MHD waves, dipole model of the magnetosphere, MHD resonances
1. Agapitov A.V., Cheremnykh O.K., Parnowski A.S. Ballooning perturbations in the inner magnetosphere of the Earth: Spectrum, stability and eigenmode analysis. Adv. Space Res. 2008. Vol. 41, no. 10, pp. 1682-1687. DOI:https://doi.org/10.1016/j.asr.2006.12.040.
2. Agapitov O., Glassmeier K.H., Plaschke F., Auster H.U., Constantinescu D., Angelopoulos V., Magnes W., Nakamura R., Carlson C.W., Frey S., McFadden J.P. Surface waves and field line resonances: A THEMIS case study. J. Geophys. Res. 2009, vol. 114, p. A00C27. DOI:https://doi.org/10.1029/2008JA013553.
3. 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:https://doi.org/10.1029/90JA02346.
4. Cheremnykh O.K., Parnowski A.S. Flute and ballooning modes in the inner magnetosphere of the Earth: Stability and influence of the ionospheric conductivity. Space Sci.: New Res. New York, Nova Science Publ., 2006, pp. 71-108.
5. Clausen L.B., Yeoman T.K. Comprehensive survey of Pc4 and Pc5 band spectral content in Cluster magnetic field data. Ann. Geophys. 2009, vol. 27, no. 8, pp. 3237-3248. DOI: 10.5194angeo-27-3237-2009.
6. Cummings W.D., O’Sullivan R.L., Coleman P.J. Standing Alfvén waves in the magnetosphere. J. Geophys. Res. 1969, vol. 74, no. 3, pp. 778-793.
7. 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, no. 16, pp. 4127-4132.
8. Elsden T., Wright A. N. Polarization properties of 3-D field line resonances. J. Geophys. Res.: Space Phys. 2022, vol. 127, no. 2, pp. e2021JA030080. DOI:https://doi.org/10.1029/2021JA03 0080.
9. Fedorov E., Pilipenko V., Engebretson M.J. ULF wave damping in the auroral acceleration region. J. Geophys. Res. 2001, vol. 106, no. A4, pp. 6203-6212. DOI:https://doi.org/10.1029/2000JA000022.
10. Glassmeier K.H., Othmer C., Cramm R., Stellmacher M., Engebretson M. Magnetospheric field line resonance: a comparative planetology approach. Surveys in Geophys. 1999, vol. 20, pp. 61-109. DOI:https://doi.org/10.1016/0273-1177(88)90154-8.
11. Guglielmi A.V. Polarization splitting of Alfvén spectrum of the magnetosphere. Geomagnetizm i aeronomiya [Geomagnetism and Aeronomy]. 1970, vol. 10, pp. 524-530 (In Russian).
12. Guglielmi A.V., Potapov A.S. Concerning one peculiarity of the MHD-wave field in an inhomogeneous plasma. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa [Res. on Geomagnetism, Aeronomy and Solar Phys.]. 1984, vol. 70, pp. 149-157. (In Russian).
13. Guglielmi A.V., Zolotukhina N.A. The excitation of magnetospheric Alfvén oscillations by an asymmetric ring current. Issledovaniya po geomagnetizmu, aeronomii i fizike Solntsa [Res. on Geomagnetism, Aeronomy and Solar Phys.]. 1980, iss. 50, pp.129-137. (In Russian).
14. Hameiri E., Laurence P., Mond M. The ballooning instability in space plasmas. J. Geophys. Res. 1991, vol. 96, no. A2, pp. 1513-1526. DOI:https://doi.org/10.1029/90JA02100.
15. Karpman V.I., Meerson B.I., Mikhailovsky A.B., Pokhotelov O.A. The effects of bounce resonances on wave growth rates in the magnetosphere. Planetary and Space Sci. 1977, vol. 25, no. 6, pp. 573-585. DOI:https://doi.org/10.1016/0032-0633(77)90064-2.
16. Keiling A. The dynamics of the Alfvénic oval. J. Atmos. Solar-Terr. Phys. 2021, vol. 219, p. 105616. DOI:https://doi.org/10.1016/j.jastp.2021.105616.
17. 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.
18. Klimushkin D.Yu., Leonovich A.S., 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, no. A6, pp. 9527-9534. DOI:https://doi.org/10.1029/94JA03233.
19. 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, no. 1, pp. 267-288. DOI:https://doi.org/10.5194/angeo22-267-2004.
20. 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.
21. Kostarev D.V., Mager P.N., Klimushkin D.Yu. Alfvén’s wave parallel electric field in the dipole model of the magnetosphere: gyrokinetic treatment. J. Geophys. Res.: Space Phys. 2021, vol. 126, no. 2, p. e2020JA028611. DOI:https://doi.org/10.1029/2020JA028611.
22. Krylov A.L., Lifshitz A.E. Quasi-Alfvén oscillations of magnetic surfaces. Planetary and Space Sci. 1984, vol. 32, no. 4, pp. 481-492. DOI:https://doi.org/10.1016/0032-0633(84)90127-2.
23. Leonovich A.S., Kozlov D.A. On ballooning instability in current sheets. Plasma Phys. Controlled Fusion. 2013, vol. 55, no. 8, pp. 17. DOI:https://doi.org/10.1088/0741-3335/55/8/085013.
24. Leonovich A.S., Mazur V.A. The spatial structure of poloidal Alfvén oscillations of an axisymmetric magnetosphere. Planetary and Space Sci. 1990, vol. 38, no. 10, pp. 1231-1241. DOI:https://doi.org/10.1016/0032-0633(90)90128-D.
25. Leonovich A.S., Mazur V.A. A theory of transverse small-scale standing Alfvén waves in an axially symmetric magnetosphere. Planetary and Space Sci. 1993, vol. 41, no. 9, pp. 697-717. DOI:https://doi.org/10.1016/0032-0633(93)90055-7.
26. 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.
27. 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).
28. 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/10.1007/s00585-998-0914-z.
29. Leonovich A.S., Zong Q.G., Kozlov D.A., Kotovschikov I.P. The field of shock-generated Alfvén oscillations near the plasmapause. J. Geophys. Res.: Space Phys. 2021, vol. 126, no. 8, p. e2021JA029488. DOI:https://doi.org/10.1029/2021JA029488.
30. Lysak R.L., Song Y. Magnetosphere-ionosphere coupling by Alfvén waves: Beyond current continuity. Adv. Space Res. 2006, vol. 38, no. 8, pp. 1713-1719. DOI:https://doi.org/10.1016/j.asr.2005.08.038.
31. Mager O.V. Alfvén waves generated through the driftbounce resonant instability in the ring current: A THEMIS multi-spacecraft case study. J. Geophys. Res.: Space Phys. 2021, vol. 126, no. 11, p. e2021JA029241. DOI:https://doi.org/10.1029/2021JA029241.
32. Mager P.N., Klimushkin D.Yu. Generation of Alfvén waves by a plasma inhomogeneity moving in the Earth's magnetosphere. Plasma Physics Rep. 2007, vol. 33, no. 5, pp. 391-398. DOI:https://doi.org/10.1134/S1063780X07050042.
33. 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, no. 1, p. e2020JA028455. DOI:https://doi.org/10.1029/2020JA028455.
34. Mager P.N., Klimushkin D.Yu., Pilipenko V.A., Schafer S. Field-aligned structure of poloidal Alfvén waves in a finite pressure plasma. Ann. Geophys. 2009, vol. 27, no. 10, pp. 3875-3882. DOI: ann-geophys.net/27/3875/2009.
35. 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.
36. Mann I.R., Wright A.N. Finite lifetime of ideal poloidal Alfvén waves J. Geophys. Res. 1995, vol. 100, no. A12, pp. 23677-23686. DOI:https://doi.org/10.1029/95JA02689.
37. 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., 2012. DOI:https://doi.org/10.1029/2012GM001349.
38. Mazur V.A., Chuiko D.A. Excitation of a magnetospheric MHD cavity by Kelvin-Helmholtz instability. Plasma Phys. Rep. 2011, vol. 37, no. 11, pp. 913-934. DOI:https://doi.org/10.1134/S1063780X11090121.
39. Mazur N.G., Fedorov E.N., Pilipenko V.A. Dispersion relation for ballooning modes and condition of their stability in the near-Earth plasma. Geomagnetism and Aeronomy. 2012, vol. 52, no. 5, pp. 603-612. DOI:https://doi.org/10.1134/S0016793212050118.
40. Mazur N.G., Fedorov E.N., Pilipenko V.A. Longitudinal structure of ballooning MHD disturbances in a model magnetosphere. Cosmic Res. 2014, vol. 52, no. 3, pp. 175-184. DOI:https://doi.org/10.1134/S0010952514030071.
41. Mishin V.V., Klibanova Yu.Yu., Tsegmed B. Solar wind inhomogeneity front inclination effect on properties of front-caused long-period geomagnetic pulsations. Cosmic Res. 2013, vol. 51, no. 2, pp. 96-107. DOI:https://doi.org/10.1134/S0010952513020020.
42. Pilipenko V., Fedorov E., Engebretson M.J., Yumoto K. Energy budget of Alfvén wave interactions with the auroral acceleration region. J. Geophys. Res. 2004, vol. 109, no. A10, p. A10204. DOI:https://doi.org/10.1029/2004JA010440.
43. Pilipenko, V., Kozyreva O., Fedorov E., Uspensky M., Kauristie K. Latitudinal amplitude-phase structure of MHD waves: STARE radar and IMAGE magnetometer observations and modeling. Solar-Terr. Phys. 2016, vol. 2, iss. 3, pp. 41-51. DOI:https://doi.org/10.12737/19418.
44. 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, no. 2, pp. 124-140. DOI:https://doi.org/10.1134/S0010952512020086.
45. Radoski H.R. Highly asymmetric MHD resonances. The guided poloidal mode. J. Geophys. Res. 1967, vol. 72, no. 15, pp. 4026-4033. DOI:https://doi.org/10.1029/JZ072i015p04026.
46. Rubtsov A.V., Mager P.N., Klimushkin D.Yu. Ballooning instability in the magnetospheric plasma: Two-dimensional eigenmode analysis. J. Geophys. Res.: Space Phys. 2020, vol. 125, no. 1, pp. e2019JA027024. DOI:https://doi.org/10.1029/2019JA027024.
47. Safargaleev V.V., Maltsev, Yu.P. Internal gravity waves in the plasma sheet. Geomagnetism and Aeronomy. 1986, vol. 26, no. 2, pp. 220-223.
48. Samson J.C. ULF wave studies using ground-based arrays. Adv. Space Res. 1988, vol. 8, pp. 399-411. DOI:https://doi.org/10.1016/0273-1177(88)90154-8.
49. Southwood D.J. Wave generation in the terrestrial magnetosphere. Space Sci. Rev. 1983, vol. 34, no. 3, pp. 259-270. DOI:https://doi.org/10.1007/BF00175282.
50. Southwood D.J., Saunders M.A. Curvature coupling of slow and Alfvén MHD waves in a magnetotail field configuration. Planetary and Space Sci. 1985, vol. 33, no. 1, pp. 127-134. DOI:https://doi.org/10.1016/0032-0633(85)90149-7.
51. 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:https://doi.org/10.1029/2017JA025139.
52. 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:https://doi.org/10.1002/2017JA024869.
53. Tamao T. Magnetosphere-ionosphere interaction through hydromagnetic waves. Achievements of the International Magnetospheric Study (IMS). ESA Special Publ. 1984b, vol. 217, no. 1, pp. 427-435.
54. Walker A.D.M. Theory of magnetospheric standing hydromagnetic waves with large azimuthal wave number. 1. Coupled magnetosonic and Alfvén waves. J. Geophys. Res. 1987, vol. 92, no. A9, pp. 10039-10045. DOI:https://doi.org/10.1029/JA092iA09p10039.
55. Wright A., Degeling A.W., Elsden T. Resonance Maps for 3D Alfvén waves in a compressed dipole field. J. Geophys. Res.: Space Phys. 2022, vol. 127, no. 4. p. e2022JA030294. DOI:https://doi.org/10.1029/2022JA030294.
56. 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, no. A11, pp. 10369-10381. DOI:https://doi.org/10.1002/2017JA024376.
57. Xing X., Wolf R.A. Criterion for interchange instability in a plasma connected to a conducting ionosphere. J. Geophys. Res. 2007, vol. 112, no. A12, p. A12209. DOI:https://doi.org/10.1029/2007JA012535.
58. 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, no. 1. p. 10. DOI: 10.1007s41614-017-0011-4.
