Abstract and keywords
Abstract (English):
We have studied propagation of hydromagnetic (MHD) waves in one-dimensionally inhomogeneous finite pressure plasma with curved field lines. Magnetic surfaces are considered to be concentric cylinders, where the cylinder’s radius models the radial coordinate in Earth’s magnetosphere. The waves are supposed to be azimuthally small-scale. In this approximation there are only two MHD modes — Alfvén and slow magnetosonic (SMS). We have derived an ordinary differential equation for the spatial structure of the wave field in this model. We have examined the character of the singularity on the surface of Alfvén and SMS resonances and the influence of field line curvature on them. We have determined wave transparent regions. The SMS transparent region was found to essentially broaden as compared to the straight field line case. The very existence of the Alfvén transparent region is caused by the field line curvature and finite plasma pressure; otherwise, the wave structure is represented by a localized resonance.

MHD waves, cylinder model of the magnetosphere, MHD resonances
Publication text (PDF): Read Download

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:

2. Agapitov A.V., Parnowski A.S., Cheremnykh O.K. Spectrum of transversally small-scale perturbations in the inner Earth’s magnetosphere. Kinematika i Fizika Nebesnykh Tel. [Kinematics and Physics of Celestial Bodies]. 2006. vol. 22, no. 6, pp. 387-401. (In Russian).

3. Berngardt O., Space weather impact on radio device operation. Solar-Terr. Phys. 2017, vol. 3, no. 3, pp. 37-53. DOI:

4. Bhattacharjee A., Ma Z., Wang X. Dynamics of thin current sheets and their disruption by ballooning instabilities: A mechanism for magnetospheric substorms. Physics of Plasmas. 1998, vol. 5, pp. 2001-2009. DOI:

5. Burdo O.S., Cheremnykh O.K., Verkhoglyadova O.P. Study of ballooning modes in the inner magnetosphere of the Earth. Izvestiya Akademii nauk. Fizika [Bulletin of the Russian Academy of Sciences: Physics]. 2000, vol. 64, pp. 1896-1900. (In Russian).

6. Chen L., Hasegawa A. A theory of long period magnetic pulsations. 1. Steady state excitation of field line resonance. J. Geophys. Res. 1974, vol. 79, iss. 7, pp. 1024-1032. DOI: 10.1029/ JA079i007p01024.

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

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

9. Chelpanov M.A., Mager O.V., 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. V. 121. P. 1315-1326. DOI:

10. Cheremnykh O.K., Klimushkin D., Kostarev D.V. On the structure of azimuthally small-scale ULF oscillations of hot space plasma in a curved magnetic field. Modes with continuous spectrum. Kinematics and Physics of Celestrial Bodies. 2014, vol. 30, no. 5, pp. 209-222.

11. Cheremnykh O.K., Klimushkin D.Yu., Mager P.N. On the Structure of Azimuthally Small-Scale ULF Oscillations of a Hot Space Plasma in a Curved Magnetic Field: Modes with Discrete Spectra. Kinematics and Physics of Celestial Bodies. 2016, vol. 32, no. 3, pp. 120-128.

12. Cheremnykh O.K., Kryshtal A.N., Tkachenko A.A. Kink mode m = 1 in magnetic tube with discontinuous magnetic field. Adv. Space Res. 2018, vol. 61, pp. 603-610. DOI:

13. 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.

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

15. Guglielmi A.V., Potapov A.S. Concerning one peculiarity of the MHD-wave field in an inhomogeneous plasma. Issledobaniya po geomagnetizmu, aeronomii i fizike Solntsa [Res. on Geomagnetism, Aeronomy and Solar Physics]. 1984, vol. 70, pp. 149-157. (In Russian).

16. Golovchanskaya I.V., Kullen A., Maltsev Y.P., Biernat H. Ballooning instability at the plasma sheet-lobe interface and its implications for polar arc formation. J. Geophys. Res. 2006, vol. 111, no. A11216. DOI:

17. Hasegawa A. Drift mirror instability of the magnetosphere. Physics of Fluids. 1969, vol. 12, pp. 2642-2650. DOI:

18. Kaneko T., Goossens M., Soler R., Terradas J., Van Doorsselaere T., Yokoyama T., Wright A.N. Apparent cross-field superslow propagation of magnetohydrodynamic waves in solar plasmas. The Astrophysical J. 2015, vol. 812, no. 2, pp. 2369-2375. DOI:

19. Klimushkin D.Yu. Spatial structure of small-scale azimuthal hydromagnetic waves in an axisymmetric magnetospheric plasma with finite pressure. Plasma Phys. Rep. 1997, vol. 23, pp. 858-871.

20. Klimushkin D.Yu. Theory of azimuthally small-scale hydromagnetic waves in the axisymmetric magnetosphere with finite plasma pressure. Ann. Geophys. 1998, vol. 16, pp. 303-321.

21. 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:

22. 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:

23. 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, iss. 3, pp. 18-27. DOI:

24. 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:

25. 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:

26. Liu W.W. Physics of the explosive growth phase: Ballooning instability revisited. J. Geophys. Res. 1997, vol. 102, no. A3, iss. 2156-2202, pp. 4927-4931. DOI:

27. 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:

28. Mager P.N., Mikhailova O.S., Mager O.V., D.Yu. Klimushkin. 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:

29. Mager P.N., Klimushkin D.Yu. Non-resonant instability of coupled Alfvén and drift compressional modes in magnetospheric plasma. Plasma Physics and Controlled Fusion. 2017, vol. 59, no. 9, p. 095005 DOI:

30. 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, pp. 603-612.

31. Mazur V.A., Chuiko D.A. Kelvin-Helmholtz instability on the magnetopause, magnetohydrodynamic waveguide in the outer magnetosphere, and Alfvén resonance deep in the magnetosphere. Plasma Phys. Rep. 2013, vol. 39, no. 6, pp. 488-503.

32. McPherron R.L. Magnetic pulsations: Their sources and relation to solar wind and geomagnetic activity // Surveys in Geophysics. 2005. V. 26. P. 545-592. DOI:

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

34. Moiseev A.V., Baishev D.G., Mullayarov V.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:

35. Moore T.E., Gallagher D.L. MHD wave breaking in the outer plasmasphere. Geophys Res. Lett. 1987, vol. 14, no. 10, pp. 1007-1010.

36. 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:

37. Rae I.J., Murphy K.R., Watt C.E.J., Rostoker G., Rankin R., Mann I.R. Field line resonances as a trigger and a tracer for substorm onset. J. Geophys. Res.: Space Phys. 2014, vol. 119, no. 1, pp. 5343-5363. DOI:

38. Rosenbluth M.N. Magnetic trapped-particle modes. Phys. Rev. Lett. 1981, vol. 46, pp. 1525-1528. DOI: 10.1103/ PhysRevLett.46.1525.

39. 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. 2018a, vol. 123, no. 11, pp. 9406-9419. DOI:

40. Rubtsov A.V., Mager P.N., Klimushkin D.Yu. Ballooning instability of azimuthally small scale coupled Alfvén and slow magnetoacoustic modes in two-dimensionally inhomogeneous magnetospheric plasma. Physics of Plasmas. 2018b, vol. 25, no. 10, 102903 p. DOI:

41. Southwood L. Some features of field line resonances in the magnetosphere. Planet. Space Sci. 1974, vol. 22, pp. 483-491. DOI:

42. Southwood D.J., Saunders M.A. Curvature coupling of slow and Alfvén MHD waves in a magnetotail field configuration. Planet. Space Sci. 1985, vol. 33, pp. 127-134. DOI:

43. Takahashi K., Denton R.E., Motoba T., et al. Impulsively Excited Nightside Ultralow Frequency Waves Simultaneously Observed on and off the Magnetic Equator. J. Geophys. Res.: Space Phys. 2018, vol. 45, no. 16, pp. 7918-7926. DOI:

44. 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:

45. Walker A.D.M. Theory of magnetospheric standing hydromagnetic waves with large azimuthal wave number, 1, Coupled magnetosonic and Alfvén waves. J. Geophys. Res. 1996, vol. 101, pp. 27133-27148. DOI:

46. Woch J., Kremser G., Korth A., Pokhotelov O.A., Pilipenko V.A., Nezlina Yu.M., Amata E. Curvature-driven drift mirror instability in the magnetosphere. 1988, vol. 36, pp. 383-393. DOI:

47. Yumoto K. Characteristics of localized resonance coupling oscillations of the slow magnetosonic wave in a non-uniform plasma. Planet. Space Sci. 1985, vol. 33, pp. 1029-1036. DOI:

48. Zolotukhina N.A. Excitation of Alfvén waves in the magnetosphere by a moving source. Issledobaniya po geomagnetizmu, aeronomii i fizike Solntsa [Res. on Geomagnetism, Aeronomy and Solar Physics]. 1974, vol. 34, pp. 20-23. (In Russian).

Login or Create
* Forgot password?