3-D Numerical Model For The Magnetopause

Shue et al.[1997] model proposed a new function form: where (r,θ) is the spatial parameters of the magnetopause, to represent the place of the magnetopause. r is the radial distance from the center of the Earth to a point on the magnetopause under specially designatedθ,θis the angle between the sun-earth line and the direction of r. (r0,α) is the configuration parameters of the magnetopause, to represent the size and shape of the magnetopause. r0 is the standoff distance, to represent the distance from earth's core to subsolar namely the size of the magnetopause; a is the level of tail flaring, to represent the open and closed character of the tail namely the shape of the magnetopause. Both the values of subsolar distance r0 and the level of tail flaring a vary with the solar wind conditions (the Z component of the interplanetary magnetic field BZ and the dynamic pressure of the upstream solar wind DP).This paper studies the relationship between the configuration parameters of the magnetopause and the solar wind conditions in 3-D with global MHD data based on Shue97 model, and we also present a predictive model for the magnetopause. As Shue97 model is constructed in 2-D, so we extend the model to 3-D with an additional variable azimuthal angle cp based on the spatial parameters (r,θ). the configuration parameters of the magnetopause is not only function with the variables of the solar wind conditions (BZ, DP), but also function with the varialbles of the azimuthal angleφ. the function form of (r0,α) is: the coefficient (a0,a2;b0,b2) is irrelevant toφand just the function with the variables of the solar wind conditions, we can know the function form of (a0, a2; b0, b2) based on the function form of (r0,α) in the Shue97 model:Now we have gotten a 3-D model of the magnetopause, with the model we can calculate the 3-D shape of the magnetopause under any solar wind conditions. We can obtain the relationship between the configuration parameters (r0,α) of the magnetopause in the equatorial plane and the solar wind conditions (BZ, DP) according to this model. We find when BZ is northward increasing, r0 increases a little and a decreases; when BZ is southward increasing, r0 decreases a little and a decreases. When DP is increasing, r0 decreases sharply, r0 and DP are related by a power functional relation, a remain virtually unchanged. Magnetic field chiefly affect the shape of the magnetopause, dynamic pressure chiefly affect the size of the magnetopause. The shape of the magnetopause in the equatorial plane changes very little with the solar wind conditions in aggregate, which means the magnetopause in the equatorial plane is strong self-similar.We can obtain the relationship between the configuration parameter (r0,α) of the magnetopause in the meridian plane and the solar wind conditions (BZ, DP) according to this model. We find when BZ is northward increasing, r0 increases a little and a decreases; when BZ is southward increasing, r0 decreases a little and a increases. When DP is increasing, r0 decreases sharply, r0 and DP are related by a power functional relation, a remain virtually unchanged. Magnetic field chiefly affect the shape of the magnetopause, dynamic pressure chiefly affect the size of the magnetopause. When solar wind conditions are changing, the shape of the magnetopause in the meridian plane changes larger than the shape of the magnetopause in the equatorial plane. The magnetopause in the meridian plane is divided into two stages because of the existence of the cusp, but in this model we still fit with just one curve, so the error is larger.Under every solar wind condition this model fit global MHD data well. When BZ is northward this model fit empirical models well, when BZ is southward this model do not fit empirical models well. The reason of this problem is not clear and needs further research in our work from now on.