Investigation of the viscous potential using an MHD simulation

The viscous interaction between the solar wind and Earth's magnetosphere is extremely difficult to study through direct observations. The viscous contribution to the polar cap potential, the viscous potential, is typically swamped by the much larger reconnection potential or obscured by rapidly changing solar wind conditions. We used the Lyon-Fedder-Mobarry (LFM) magnetohydrodynamic simulation to study the response of the viscous potential to a variety of ideal conditions both in the solar wind and the ionosphere. We found that the viscous potential in LFM increases with either increasing solar wind density or velocity, with a relation that is similar to some previous empirical results in form but different in detail. The density dependence scales as n^0.439 (in cm^-3) and velocity scales as V _x^1.33 (in km s^-1). Combining these results with a reference value, the viscous potential in LFM can be predicted using the formula _V = (0.00431)n^0.439V_x^1.33 kV. We also found that the viscous potential changes inversely in relation to constant Pedersen conductivity in an idealized ionosphere, a result that was previously predicted for LFM but not explored until now.