Department of Earth and Space Sciences, University of California, Los Angeles, CA 90024

A new formula for the solar wind-magnetosphere energy input parameter, P_i, is sought by applying the constraints imposed by dimensional analysis. Applying these constraints yields a general equations for P_i which is equal to r V³l²_CF(M_A,q ) where, r V³ is the solar wind kinetic energy density and l²_CF is the scale size of the magnetosphere's effective energy "collection" region. The function F which depends on M_A, the Alfvén Mach number, and on q , the interplanetary magnetic field clock angle is included in the general equation for P_i in order to model the magnetohydrodynamic processes which are responsible for solar wind-magnetosphere energy transfer. By assuming the form of the function F, it is possible to further constrain the formula for P_i. This is accomplished by using solar wind data, geomagnetic activity indices, and simple statistical methods. It is found that P_i is proportional to (r V²)^1/6VBG(q ) where, r V² is the solar wind dynamic pressure and VBG(q ) is a rectified version of the solar wind motional electric field. Furthermore, it is found that G(q ), the gating function which modulates the energy input to the magnetosphere, is well represented by a "leaky" rectifier functions such as sin⁴(q / 2). This function allows for enhanced energy input when the interplanetary magnetic field is oriented southward. This function also allows for some energy input when the interplanetary magnetic field is oriented northward.

in Solar Wind-Magnetosphere Coupling, edited by Y. Kamide and J. A. Slavin, pp. 101-110, Terra Scient. Publ. Co., Tokyo, 1986