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In order to check the validity of Akasofu’s ε parameter and of the Vasyliunas et al. (1982) general formula, we examine the dependence of the ring current injection rate, calculated from the Dst index for the period of 1965–1990, on the interplanetary magnetic field (IMF). We compare the influence of the Bz component with the influence of the combination of sin(θ/2), where θ is the IMF clock angle, and the IMF magnitude, B, (or the transverse component of the IMF, BT = (By2 + Bz2)1/2) by using the regression analysis in a power law form. The main results are as follows: (1) the exponent for Bz shows higher consistency than that for sin(θ/2); (2) we never obtain B2 sin4(θ/2) or BT2 sin4(θ/2), which is the IMF dependence expected from the ε parameter; and (3) the ring current injection rate has a very low correlation with the Alfven Mach number, from which the IMF dependence of the Vasyliunas et al. general formula is assumed to arise. On the basis of the above results we conclude that the ε parameter and the Vasyliunas et al. general formula are less appropriate than a function of Bz, and that the energy coupling function between the solar wind and the Earth’s magnetosphere is described better by Bz than by the combination of B (or BT) and sin(θ/2). The above results and conclusions are the same as those obtained by Aoki (2005) through the analysis of the AL index.

Influence of the interplanetary magnetic field on the ring current injection rate