Reflection of vertically propagating waves in a thermally conducting isothermal atmosphere with a horizontal magnetic field

We examine the reflection of vertically propagating waves in an isothermal atmosphere of small thermal conductivity with a weak horizontal magnetic field. Two limiting cases are considered: (1) Dominant thermal conduction; (2) Dominant magnetic field. Reflections take place in transition layers that separate regions of large and small thermal diffusivity, and of large and small Alfven speed. Reflection coefficients are derived for both cases and it is shown that resonances will occur. The solution for Case 1 is derived from the results for the analogous problem of a viscous and thermally conducting isothermal atmosphere. The singular perturbation problem for Case 2 is solved by matching inner and outer approximations.