Discrete ULF modes in the Earth’s magnetosphere near the Alfven frequency minimum

1Cheremnykh, SO, 1Zhuk, IT
1Space Research Institute under NAS and National Space Agency of Ukraine, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2017, 33(1):38-54
Start Page: Space Physics
Language: Russian

The equation of small oscillations of ULF waves in the magnetosphere of the Earth was received taking into account the fast magnetosonic waves. The spectrum of discrete Alfven modes near the minimum Alfven frequency was investigated with the help of this equation.

Keywords: Alfven modes, discrete spectrum, magnetic field, magnetosphere of the Earth

1.G. Bateman and A. Erdélyi, Higher Transcendental Functions (McGraw-Hill, New York, 1953; Nauka, Moscow, 1974), Vol.2.zbMATH

2.M. Goossens, “MHD waves and wave heating in nonuniform plasmas,” in Advances in Solar System Magnetohydrodynamics, Ed. by E. R. Priest and A. W. Hood (Cambridge Univ. Press, Cambridge, 1991; Mir, Moscow, 1995), p.135.

3.D. Yu. Klimushkin, “Spatial structure of small-scale azimuthal hydrodynamic waves in an axisymmetric magnetospheric plasma with finite pressure,” Plasma Phys. Rep. 23, 858–871 (1997).

4.Yu. P. Ladikov-Roev and S. O. Cheremnykh, “On the plasma pressure distribution in the equatorial region of the Earth’s magnetosphere,” Kosm. Nauka Tekhnol. 16 (1), 86–89 (2010).

5.N. G. Mazur, E. N. Fedorov, and V. A. Pilipenko, “Dispersion relation for ballooning modes and condition of their stability in the near-earth plasma,” Geomagn. Aeron. (Engl. Transl.) 52, 603–612 (2012).

6.A. Nishida, Geomagnetic Diagnosis of the Magnetosphere (Springer-Verlag, New York, 1978; Mir, Moscow, 1980).

7.A. S. Parnowski and O. K. Cheremnykh, “Spectrum of ballooning perturbations with arbitrary polarization in the inner magnetosphere of the Earth,” Kosm. Nauka Tekhnol. 12 (1), 49–56 (2006).

8.E. R. Priest, Solar Magnetohydrodynamics (Reidel, Dordrecht, 1982; Mir, Moscow, 1985). https://doi.org/10.1007/978-94-009-7958-1

9.V. D. Pustovitov and V. D. Shafranov, “Equilibrium and stability of plasma in stellarators,” Vopr. Teor. Plazmy, No. 15, 146–293 (1987).

10.B. Roberte, “MHD waves in the Sun,” in Advances in Solar System Magnetohydrodynamics, Ed. by E. R. Priest and A. W. Hood (Cambridge University Press, Cambridge, 1991; Mir, Moscow, 1995), p.105.

11.O. K. Cheremnykh, D. Yu. Klimushkin, and D. V. Kostarev, “On the structure of azimuthally small-scale ULF oscillations of hot space plasma in a curved magnetic field. Modes with continuous spectrum,” Kinematics Phys. Celestial Bodies 30, 209–222 (2014).

12.O. K. Cheremnykh, D. Yu. Klimushkin, and P. N. Mager, “On the structure of azimuthally small-scale ULF oscillations of a hot space plasma in a curved magnetic field: Modes with discrete spectra,” Kinematics Phys. Celestial Bodies 32, 120–128 (2016).

13.S. O. Cheremnykh, “On the polarization of transversally small-scale MHD modes in the Earth’s magnetosphere,” Kosm. Nauka Tekhnol. 19, 57–64 (2013).

14.O. Agapitov and O. Cheremnykh, “Magnetospheric ULF waves driven by external sources” (2015).

15.O. Agapitov and O. Cheremnykh, “Natural oscillations of the Earth magnetosphere associated with solar wind sudden impulses,” Ukr. J. Phys. 53, 508–512 (2008).

16.Zh. N. Andrushchenko, O. K. Cheremnykh, and J. W. Edenstrasser, “Global Alfvén eigenmodes in a stellarator with trapped energetic particles,” Phys. Plasmas 6, 2462–2471 (1999).

17.O. S. Burdo, O. K. Cheremnykh, and O. P. Verkhoglyadova, “Study of ballooning modes in the inner magnetosphere of the Earth,” Izv. Ross. Akad. Nauk, Ser. Fiz. 64, 1896–1900 (2000).

18.C. Z. Cheng, “Magnetospheric equilibrium with anisotropic pressure,” J. Geophys. Res.: Space Phys. 97, 1497–1510 (1992).

19.O. K. Cheremnykh and S. M. Revenchuk, “Dispersion relations for the Suydam problem,” Plasma Phys. Controlled Fusion 34, 55–75 (1992).

20.O. K. Cheremnykh and A. S. Parnowski, “Flute and ballooning modes in the inner magnetosphere of the Earth: Stability and influence of the ionospheric conductivity,” in Space Science: New Research, Ed. by N. S. Maravell (Nova Sci., New York, 2006), pp. 97–139.

21.O. K. Cheremnykh, “Transversally small-scale perturbations in arbitrary plasma configurations with magnetic surfaces,” Plasma Phys. Controlled Fusion 52, 095006 (2010).

22.O. K. Cheremnykh and V. V. Danilova, “Transversal small-scale MHD perturbations in space plasma with magnetic surfaces,” Kinematics Phys. Celestial Bodies 27, 98–108 (2011).

23.S. O. Cheremnykh and O. V. Agapitov, “MHD waves in the plasma system with dipole magnetic field configuration,” Adv. Astron. Space Phys. 2, 103–106 (2012).

24.P. M. Edwin and B. Roberts, “Wave propagation in a magnetic cylinder,” Sol. Phys. 88, 179–191 (1983).

25.R. Erdélyi and V. Fedun, “Linear MHD sausage waves in compressible magnetically twisted flux tubes,” Sol. Phys. 246, 101–118 (2007).

26.E. Hameiri and M. G. Kivelson, “Magnetospheric waves and the atmosphere–ionosphere layer,” J. Geophys. Res.: Space Phys. 96, 21125–21134 (1991).

27.F. Hameiri, P. Laurence, and M. Mond, “The ballooning instability in space plasmas,” J. Geophys. Res.: Space Phys. 96, 1513–1526 (1991).

28.A. S. Leonovich, D. A. Kozlov, and V. A. Pilipenko, “Magnetosonic resonance in a dipole-like magnetosphere,” Ann. Geophys. 24, 2277–2289 (2006).

29.P. N. Mager, D. Yu. Klimushkin, V. A. Pilipenko, and S. Schäfer, “Field-aligned structure of poloidal Alfvén waves in a finite pressure plasma,” Ann. Geophys. 27, 3875–3882 (2009).

30.S. M. Mahajan, D. W. Ross, and G. L. Chen, “Discrete Alfvén eigenmode spectrum in magnetohydrodynamics,” Phys. Fluids 26, 2195–2199 (1983).