Magnetohydrodynamic rotating shallow water system (MRSW) is a proposed model for a thin layer of electrically conducting fluid, which plays an important role in astrophysical plasma studies. For the spatial periodic domain, a mathematically rigorous framework is developed for deriving reduced systems for MRSW equations with general unbalanced initial data. It is shown that the reduced slow dynamics are the magnetohydrodynamic quasi-geostrophic equations.

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