MHD eigenmodes in a semi-infinite structured solar atmosphere

Linear eigenmodes are determined for the solar atmosphere in the presence of a gravitational field and a magnetic field. The atmosphere consists of a horizontal nonuniform chromosphere and a semi-infinite nonuniform corona. It is bounded from below by a heavy and immovable photosphere. Inhomogeneity is confined to the vertical direction. The gravitational acceleration is constant and the equilibrium magnetic field is horizontal. The equilibrium temperature increases linearly with height in the chromosphere and is constant in the corona. The equilibrium magnetic field is constant in the chromosphere and it decreases with height in the corona in such a way that the Alfvén speed is constant there. The results show that there are two sets of eigenmodes which can be viewed as p- and g-modes modified by the immobile lower boundary of the atmosphere and by the magnetic field. The modes can become damped quasimodes with complex frequencies arising from the resonant coupling of eigenmodes to the local MHD continua in the nonuniform chromospheric layer.