The solar corona extends outward from the Sun into interplanetary space as the solar wind. Important aspects of heliospheric structure, such as the position and shape of the heliospheric current sheet and the regions of fast and slow wind, are defined by coronal structures. The structure of the solar corona is determined by the outward extension of the Sun's magnetic field. While there are few measurements of the magnetic fields in the corona, the Sun's magnetic field has been measured in the photosphere for many years. To understand the large-scale structure of the solar corona and inner heliosphere, it is necessary to accurately map the photospheric magnetic field into the corona and beyond. We are interested in the large-scale and long-wavelength interaction of the plasma and magnetic fields, so the phenomena of interest are well described by the magnetohydrodynamic (MHD) equations. Until recently, self-consistent MHD solutions of the corona have typically been confined to idealized situations, suitable for many theoretical purposes but incapable of direct comparisons with actual data. The goal of our research is to bring MHD computations to a new level, where they can not only be used in theoretical studies but as a tool for the analysis of solar and heliospheric data.

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