Derivation of Equilibrium Magnetosphere

When a high beta ring current is set up, the earth dipole field is modified significantly and attains a new equilibrium satisfying p=J X B. If an axis symmetry is assumed, the equilibrium magnetic field is precisely obtained from the Gyad-Shafranov equation (Shafranov, 1966) given the pressure as a function of the flux function. This concept is used to derive a method to obtain the equilibrium magnetic field configurations using satellite data of plasma pressure at different L say in equatorial plane. Although the method is restricted to the axis symmetric case, it can be expanded to non axis-symmetric case by including the effect of the solar wind.