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A wave equation describing the generation of field-aligned current in the magnetosphere


A wave equation describing the generation of field-aligned current (FAC) in the magnetosphere is derived. The equation has four source terms. The first and second terms represent the effects of inhomogeneous Alfvén speed (VA) and curvilinear magnetic field line, respectively. The perpendicular perturbation inertial current produces the perturbation FAC via these effects. Around the magnetic equator in the region of dipolar magnetic field where VA is inversely proportional to the power of the radial distance from the Earth’s center, the first and second terms have magnitudes of the same order and their signs are identical. The first term dominates over the second one around the region where the gradient of VA is sharp and vice versa around the position where the stretched field line intersects the magnetic equator. The third and fourth terms are related to the diamagnetic current. When the unperturbed magnetic pressure has an inhomogeneous distribution, the perpendicular diamagnetic current due to the perturbation of the plasma pressure yields the perturbation FAC (third term). When the perpendicular diamagnetic current flows in the unperturbed state, the perturbations of the magnetic and plasma pressures also bring about the perturbation FAC (fourth term). In the case of β 1, the third and fourth terms have magnitudes of the same order. If the disturbance bears a diamagnetic property, this would be especially the case. However, if the disturbance propagates perpendicularly to the ambient magnetic field, the perturbation FAC would be little generated by the fourth term.


  1. Dungey, J. W., Hydromagnetic waves, in Physics of Geomagnetic Phenomena, edited by S. Matsushita and W. H. Campbell, pp. 913–934, Academic Press, New York, 1968.

  2. Hasegawa, A. and T. Sato, Generation of field aligned current during sub-storm, in Dynamics of the Magnetosphere, edited by S.-I. Akasofu, pp. 529–542, D. Reidel, Hingham, Mass., 1979.

  3. Itonaga, M. and A. Yoshikawa, The excitation of shear Alfvén wave and the associated modulation of compressional wave in the inner magnetosphere, J. Geomag. Geoelectr., 48, 1451–1459, 1996.

  4. Itonaga, M. and K. Yumoto, ULF waves and the ground magnetic field, J. Geophys. Res., 103, 9285–9291, 1998.

  5. Lester, M., W. J. Hughes, and H. Jinger, Polarization pattern of Pi 2 magnetic pulsations and the substorm current wedge, J. Geophys. Res., 88, 7958–7966, 1983.

  6. Ohtani, S., A. Miura, and T. Tamao, Coupling between Alfvén and slow magnetosonic waves in an inhomogeneous finite-β plasma—I. Coupled equations and physical mechanism, Planet. Space Sci., 37, 567–577, 1989.

  7. Sato, T., Auroral physics, in Magnetospheric Plasma Physics, edited by A. Nishida, pp. 197–243, D. Reidel, Hingham, Mass., 1982.

  8. Sato, T. and T. Iijima, Primary sources of large-scale Birkeland currents, Space Sci. Rev., 24, 347–366, 1979.

  9. Southwood, D. J. and M. G. Kivelson, An approximate description of field-aligned currents in a planetary magnetic field, J. Geophys. Res., 96, 67–75, 1991.

  10. Southwood, D. J. and M. A. Saunders, Curvature coupling of slow and Alfvén MHD waves in a magnetotail field configuration, Planet. Space Sci, 33, 127–134, 1985.

  11. Stern, D., Geomagnetic Euler potentials, J. Geophys. Res., 72, 3995–4005, 1967.

  12. Tanaka, T., Generation mechanisms for magnetosphere-ionosphere current systems deduced from a three-dimensional MHD simulation of the solar wind-magnetosphere-ionosphere coupling processes, J. Geophys. Res., 100, 12,057–12,074, 1995.

  13. Vasyliunas, V. M., Fundamentals of current description, in Magnetospheric Currents, edited by T. A. Potemra, pp. 63–66, AGU, Washington, D.C., 1984.

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Correspondence to Masahiro Itonaga.

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Itonaga, M., Yoshikawa, A. & Fujita, S. A wave equation describing the generation of field-aligned current in the magnetosphere. Earth Planet Sp 52, 503–507 (2000).

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  • Plasma Pressure
  • Fourth Term
  • Magnetic Equator
  • Magnetosonic Wave
  • Unperturbed State