A formulation of non-ideal localized (or ballooning) modes in the solar corona

The stability equations for localized (or ballooning) modes in the solar atmosphere are formulated. Dissipation due to viscosity, resistivity, and thermal conduction are included using the general forms due to Braginskii (1965). In addition, the effect of gravity, plasma radiation, and coronal heating are included. The resulting equations are nondimensional and only involve derivatives along the equilibrium magnetic field. Thus, the stabilizing influence of photospheric line-tying, which is normally neglected in most numerical simulations, can be studied in a simple manner. Two applications to sound wave propagation and thermal instabilities in a low-beta plasma are considered with a view to determining realistic coronal boundary conditions that model the lower, denser levels of the solar atmosphere in a simple manner.