The Effect of Plasma Flow on the Longitudinal Standing Waves in Magnetic Flux Tubes with a Perturbation Approach

In this paper, the standing magnetohydrodynamic slow waves in the magnetic flux tubes are investigated under coronal conditions. The temperature and equilibrium plasma density of the tube is assumed to be homogeneous and constant and the compressive viscosity is considered as the damping mechanism. Also, the plasma flow is considered in the flux tube. Assuming that the damping rate to be much smaller than the oscillation frequency of the waves, the perturbation method is used to solve the problem. The oscillation frequency and the eigenfunctions are found from the first-order perturbation while the damping rate is determined from the second-order perturbation. To increase the flow speed makes the oscillation frequency decreases and the damping rate increases. Also, increasing  each of the flow speed and background temperature of the tube, decreases the ratio of the damping time to the oscillation period. But this ratio increases due to the increasing the length of the tube The results found here are consistent with the theoretical results obtained earlier. Also, the obtained results can justify some observational cases.