A theoretical relation between Dst and the solar wind merging electric field

Using a model in which magnetic merging near the nose of the magnetosphere results in energy transfer from the solar wind by means of a tangential force on the geomagnetic tail, we develop a linear relation between the time rate of change of Dst, representing energy transfer to the magnetosphere, and the merging electric field, with the proportionality factor an explicit function of magnetospheric parameters. The linear relation is in agreement with a recent empirical result; and using the empirical numerical coefficient, we find the distance from the earth to the neutral line in the tail during substorms to be in the range 10 R e to 30 R e .