Effect of the radiative damping on magnetohydrodynamic waves in an isothermal medium

We investigate the effect of the heat radiation on the reflection and dissipation of upward propagating waves in an isothermal atmosphere. It is shown that the magnetic field produces a totally reflecting layer. Consequently, the atmosphere can be divided into two distinct regions. In the lower region, the solution can be written as a linear combination of an upward and a downward propagating wave, and in the upper region the solution, which satisfies the upper boundary condition, decays exponentially or behaves like a constant. These two regions are connected by a region in which the reflection and transmission of the waves takes place. Moreover, the heat radiation affects only the lower region and changes the sound speed from the adiabatic value to the isothermal one. The reflection coefficient and the attenuation factor of the amplitude of the waves are derived for all values of the heat radiation coefficient. Finally, the conclusions are presented in connection with the heating process of the solar atmosphere.