The global computer simulation based on the magnetohydrodynamic (MHD) theory describes the evolution of physical conditions in the simulation domain based on measurements for each point in the solar wind. Considering the size of magnetosphere and strong spatial variation of the energy transfer process, the amount of transferred energy cannot be directly measured on the surface of magnetosphere, called the magnetopause. Therefore, simulation can provide a unique opportunity to calculate quantitatively the amount of solar wind energy transfer to the magnetosphere and to determine where the energy transfer process mainly takes place. Only a small amount of the transferred energy is consumed in the earth’s polar ionosphere and in its two sinks: part of the energy is converted to Joule heat , which is caused by the ionospheric closure of the electric currents flowing between the magnetosphere and the ionosphere and the remainder of the energy is left in the ionosphere as charged particles originating from the magnetosphere precipitate (these particles collide with atmospheric particles and produce auroral light).
In this paper, the energy related to the ionospheric processes was quantified by the magnetosphere`s structure of using a computer code based on MHD equations. Also, the amount and time variation of the total energy consumed by the ionosphere was correlated with solar wind parameters to predict the total ionospheric energy from a point measurement in the solar wind. The developed relationship can have practical significance in situations where the total ionospheric energy needs to be estimated quickly, for example, for space weather prediction purposes.
In this paper, the global MHD simulation is done in the GSE coordinates system.The origin is on the earth`s center and the direction of X-axis always pointing sunward. The Z-axis is normal to elliptic plane and its direction is northward, and the Y-axis completed the right-handed coordinate system and its direction is duskward. The location of the sunward simulation boundary is about from the earth`s center and is covered until on the midnight sector of the earth by cubic cells. The dimensions of the cells are selected about .