Dependence of the power consumed by the magnetosphere on the solar wind parameters

The results of the previous studies, where the expressions were obtained for the electric current, which is generated at the bow shock front and is closed through the magnetosphere, and for the magneto-pause potential as a function of such solar wind parameters as the plasma density and velocity and the IMF intensity, are used. The power (W) consumed by the magnetosphere is equal to the Poynting vector flux S through the magnetopause. According to the special case of the Poynting theorem applied by Heikkila to the-magnetosphere, the energy flux can be expressed in terms of the electric potential (the integration is carried out over the entire surface of the magnetosphere). As a result, the required dependence, which is quadratic with respect to the IMF B _z component, has been obtained for W. It is discussed why the magnetosphere is energy-isolated at the northward IMF B _z component despite this.