- Open Access
Azimuthally small-scale Alfvén waves in magnetosphere excited by the source of finite duration
Earth, Planets and Space volume 59, pages 951–959 (2007)
In this paper the spatial structure of azimuthally small-scale Alfvén waves in magnetosphere excited by the impulse source is studied. The source is suddenly switched on at a definite moment and works as e−iω0t during the finite time interval. The influence of factors which lead to the difference of toroidal and poloidal eigenfrequencies (like curvature of field lines and finite plasma pressure) is taken into account. Due to these factors, a radial component of the group velocity of Alfvén wave appears. An important value is the time moment, t0, when a wave front moving with radial component of wave group velocity from the poloidal surface (a magnetic surface where the source frequency ω0 coincides with the poloidal frequency) passes the given magnetic shell with the radial coordinate x. The temporal evolution at all the points, where the front has not come yet, is determined by the phase mixing of the initial disturbance. At the points through which the wave front has already passed, the wave field structure almost coincides with the structure of monochromatic wave. The region where the front propagates is bounded by the interval between the poloidal surface and the toroidal one (that is, the Alfvén resonance surface). For this reason, outside this region the evolution is always determined by the phase mixing, which leads to much smaller amplitudes than between poloidal and toroidal surfaces. After the source turned off, a back wave front is formed, which comes through the given point in direction from the poloidal surface to the toroidal one. After the back front has come, the monochromatic wave structure disappears and there is only a weak disturbance, which steadily disappears because of the phase mixing and the final conductivity of ionosphere.
Anderson, B. J., Statistical studies of Pc 3–5 pulsations and their relevance forpossible source mechanisms of ULF waves, Ann. Geophys., 11, 128–143, 1993.
Antonova, A. E., Yu. I. Gubar’, and A. P. Kropotkin, Towards the model of relativistic electron fluxes: acceleration in the field of strong Alfvénic disturbances, Radiation Measure., 30, 515–521, 1999.
Denton, R. E. and G. Vetoulis, Global poloidal mode, J. Geophys. Res., 103, 6729–6739, 1998.
Denton, R. E., M. R. Lessard, and L. M. Kistler, Radial localization of magnetospheric guided poloidal Pc 4–5 waves, J. Geophys. Res., 108(A3), 1105, doi:10.1029/2002JA009679, 2003.
Dungey J. W., Hydromagnetic waves, in Physics of Geomagnetic Phenomena, Vol. II, 913–934, 1967.
Fenrich, F. R. and J. C. Samson, Growth and decay of field line resonances, J. Geophys. Res., 102, 20,031–20,039, 1997.
Glassmeier, K.-H., ULF pulsations, in Handbook of Atmospheric Electrodynamics, Vol. II, 463–502, 1995.
Hasegawa, A., K. N. Tsui, and A. S. Assis, A theory of long period magnetic pulsations. 3. Local field line oscillations, Geophys. Res. Lett., 10, 765–767, 1983.
Klimushkin, D. Yu., Method of description of the Alfvén and magne-tosonic branches of inhomogeneous plasma oscillations, Plasma Phys. Rep., 20, 280–286, 1994.
Klimushkin, D. Yu., Theory of azimuthally small-scale hydromagnetic waves in the axisymmetric magnetosphere with finite plasma pressure, Ann. Geophys., 16, 303–321, 1998a.
Klimushkin, D. Yu., Resonators for hydromagnetic waves in the magnetosphere, J. Geophys. Res., 103, 2369–2378, 1998b.
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., 105, 23,303–23,310, 2000.
Klimushkin, D. Yu., How energetic particles construct and destroy poloidal high-m Alfvén waves in the magnetosphere, Planet. Space Sci., 55, 722–730, 2007.
Klimushkin, D. Yu. and P. N. Mager, The spatio-temporal structure of impulse-generated azimuthally small-scale Alfvén waves interacting with high-energy charged particles in the magnetosphere, Ann. Geo-phys., 22, 1053–1060, 2004.
Klimushkin, D. Yu., A. S. Leonovich, and V. A. Mazur, On the propagation of transversally-small-scale standing Alfvén waves in a three-dimensionally inhomogeneous magnetosphere, J. Geophys. Res., 100, 9527–9534, 1995.
Klimushkin, D. Yu., P. N. Mager, and K.-H. Glassmeier, Toroidal and poloidal Alfvén waves with arbitrary azimuthal wave numbers in a finite pressure plasma in the Earth’s magnetosphere, Ann. Geophys., 22, 267–288, 2004.
Leonovich, A. S., Magnetospheric MHD response to a localized disturbance in the magnetosphere, J. Geophys. Res., 105, 2507–2520, 2000.
Leonovich, A. S. and V. A. Mazur, A theory of transverse small-scale standing Alfvén waves in an axially symmetric magnetosphere, Planet. Space Sci., 41, 697–717, 1993.
Leonovich, A. S. and V. A. Mazur, Linear transformation of the standing Alfvén waves in an axisymmetric magnetosphere, Planet. Space Sci., 43, 885–893, 1995a.
Leonovich, A. S. and V. A. Mazur, Magnetospheric resonator for transverse-small-scale standing Alfvén waves, Planet. Space Sci., 43, 881–883, 1995b.
Leonovich, A. S. and V. A. Mazur, A model equation for monochromatic standing Alfvén waves in the axially-symmetric magnetosphere, J. Geophys. Res., 102, 11,443–11,456, 1997.
Leonovich, A. S. and V. A. Mazur, Standing Alfvén waves in an axisymmetric magnetosphere excited by a non-stationary source, Ann. Geophys., 16, 914–920, 1998.
Leonovich, A. S. and V. A. Mazur, Standing Alfvén waves in the magnetosphere from a localized monochromatic source, J. Geophys. Res., 104, 2411–2420, 1999.
Mager, P. N. and D. Yu. Klimushkin, Theory of azimuthally small-scale Alfvén waves in an axisymmetric magnetosphere with small but finite plasma pressure, J. Geophys. Res., 107, 1356, doi:1029/2001JA009137, 2002.
Mager, P. N. and D. Yu. Klimushkin, On impulse excitation of the global poloidal modes in the magnetosphere, Ann. Geophys., 24, 2429–2433, 2006.
Mann, I. R. and A. N. Wright, Finite lifetimes of ideal poloidal Alfvén waves, J. Geophys. Res., 100, 23,677–23,686, 1995.
Mann, I. R., A. W. Wright, and A. W. Hood, Multiple-timescales analysis of ideal poloidal Alfvén waves, J. Geophys. Res., 102, 2381–2390, 1997.
Radoski, H. R., Highly asymmetric MHD resonances. The guided poloidal mode, J. Geophys. Res., 72, 4026–4033, 1967.
Radoski, H. R., A theory of latitude dependent geomagnetic micropulsations: the asymptotic fields, J. Geophys. Res., 79, 595–613, 1974.
Southwood, D. J. and W. J. Hughes, Theory of hydromagnetic waves in the magnetosphere, Space Sci. Rev., 35, 301–366, 1983.
Takahashi, K., Multisatellite studies of ULF waves, Adv. Space Res., 8(9–10), (9)427–(9)436, 1988.
Vetoulis, G. and L. Chen, Kinetic theory of geomagnetic pulsations, 3, global analysis of drift Alfvén-ballooning modes, J. Geophys. Res., 101, 15,441–15,456, 1996.
Wright, A. N., Asymptotic and time-dependent solutions of magnetic pulsations in realistic magnetic field geometries, J. Geophys. Res., 97, 6429–6450, 1992.
Yumoto, K., External and internal sources of low-frequency MHD waves in the magnetosphere—a review, J. Geomag. Geoelectr., 40(3), 293–311, 1988.
About this article
Cite this article
Klimushkin, D.Y., Podshibyakin, I.Y. & Cao, J.B. Azimuthally small-scale Alfvén waves in magnetosphere excited by the source of finite duration. Earth Planet Sp 59, 951–959 (2007). https://doi.org/10.1186/BF03352034
- Alfvén wave
- poloidal mode
- impulse excitation