Ring current energy injection rate and solar wind-magnetosphere energy coupling

Assuming that the formation of the ring current belt is a direct consequence of an enhanced convection of plasma sheet protons, the expression for the energy injection rate U_R is formulated as a function of the cross-tail potential drop φ_CT for a simple electric field-magnetic field model. It is shown that an approximate expression for U_R thus formulated consists of two parts: (i) the first part U_R1, which is linearly proportional to φ_CT, is supplied by the corotation electric field and (ii) the second part U_R>2, which is proportional to φ²_CT, is supplied by the solar wind energy input to the magnetosphere. The second part U_R2 dominates the ring current energy input when the cross-tail potential drop φ_CT is greater than ～ 95 keV, namely during disturbed periods. An important finding is that the second part U_R2 of the ring current energy input is shown to be proportional to the solar wind-magnetosphere energy coupling function ?, recovering the observationally established relationship. Therefore, the present study verifies that an enhanced convection is the cause of the ring current formation.