Skip to main content

On the validity of Akasofu’s ε parameter and of the Vasyliunas et al. general formula for the rate of solar wind-magnetosphere energy input


The ε parameter of Akasofu and the general formula of Vasyliunas et al. (1982) have been widely used as functions representing the rate of the solar wind energy input into the Earth’s magnetosphere. These two functions have a feature that dependence on the interplanetary magnetic field (IMF) is assumed to be expressed by the combination of B, the magnitude of the IMF, and sin (θ/2), where θ is the clock angle, or by the combination of B T = (By2 + Bz2)1/2, the magnetic field perpendicular to the Sun-Earth line, and sin(θ/2), not by the Bz component. We check the validity of this assumption by presuming that the AL index has good correlation with the solar wind energy input rate and by applying the regression analysis in a power law form to hourly values of the AL index and of solar wind parameters during the period 1966–1987. We show that Bz generally gives high correlation coefficients and shows higher consistency in exponents than the combination of B (or B T ) and sin (θ/2). Thus we conclude that the IMF dependence of the rate of the solar wind energy input is described better by Bz than by the combination of B (or B T ) and sin(θ/2).


  • Akasofu, S.-I., Interplanetary energy flux associated with magnetospheric substorms, Planet. Space Sci., 27, 425–431, 1979.

    Article  Google Scholar 

  • Allen, J. H. and H. W. Kroehl, Spatial and temporal distributions of magnetic effects of auroral electrojets as derived from AE indices, J. Geophys. Res., 80, 3667–3677, 1975.

    Article  Google Scholar 

  • Aoki, T., Influence of the dipole tilt angle on the development of auroral electrojets, J. Geomag. Geoelectr., 29, 441–453, 1977.

    Article  Google Scholar 

  • Baker, D. N., Statistical analyses in the study of solar wind-magnetosphere coupling, in Solar Wind-Magnetosphere Coupling, edited by Y. Kamide and J. A. Slavin, pp. 17–38, Terrapub/Reidel, Tokyo, 1986.

    Chapter  Google Scholar 

  • Hakamada, K., T. Aoki, and T. Murayama, Influence of the east-west component of the interplanetary magnetic field on the intensity of the auroral electrojet, Planet. Space Sci., 28, 29–39, 1980.

    Article  Google Scholar 

  • Kamide, Y. and S.-I. Akasofu, Notes on the auroral electrojet indices, Rev. Geophys. Space Phys., 21, 1647–1656, 1983.

    Article  Google Scholar 

  • Koskinen, H. E. J. and E. I. Tanskanen, Magnetospheric energy budget and the epsilon parameter, J. Geophys. Res., 107(A11), 1415, doi:10.1029/2002JA009283, 2002.

    Article  Google Scholar 

  • Maezawa, K., Statistical study of the dependence of geomagnetic activity on solar wind parameters, in Quantitative Modeling of Magnetospheric Processes, Geophys. Monogr. Ser., vol. 21, edited by W. P. Olson, pp. 436–447, AGU, Washington, D.C., 1979.

    Chapter  Google Scholar 

  • Murayama, T. and K. Hakamada, Effects of solar wind parameters on the development of magnetospheric substorms, Planet. Space Sci., 23, 75–91, 1975.

    Article  Google Scholar 

  • Murayama, T., T. Aoki, H. Nakai, and K. Hakamada, Empirical formula to relate the auroral electrojet intensity with interplanetary parameters, Planet. Space Sci., 28, 803–813, 1980.

    Article  Google Scholar 

  • Perreault, P. and S.-I. Akasofu, A study of geomagnetic storms, Geophys. J. R. Astron. Soc., 54, 547–573, 1978.

    Article  Google Scholar 

  • Rostoker, G., H. L. Lam, and W. D. Hume, Response time of the magnetosphere to the interplanetary electric field, Can. J. Phys., 50, 544–547, 1972.

    Article  Google Scholar 

  • Vasyliunas, V. M., J. R. Kan, G. L. Siscoe, and S.-I. Akasofu, Scaling relations governing magnetospheric energy transfer, Planet. Space Sci., 30, 359–365, 1982.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Takao Aoki.

Rights and permissions

Open Access  This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.

The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

To view a copy of this licence, visit

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Aoki, T. On the validity of Akasofu’s ε parameter and of the Vasyliunas et al. general formula for the rate of solar wind-magnetosphere energy input. Earth Planet Sp 57, 131–137 (2005).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

Key words