Analytical Study of Damped Standing Longitudinal MHD Waves in Flowing Coronal Loops: The Effect of Thermal Conduction

Abstract

The longitudinal magnetohydrodynamic (MHD) oscillations of coronal loops have been investigated in dissipative flowing loops. Thermal conduction has been considered as the damping mechanism of the wave. We aim to construct the damped longitudinal waves by superposing two propagating waves that propagate in opposite directions. The two propagating components must have the same oscillation frequencies and damping rates, which has been described impossible by some authors, but we have used a technique to overcome this difficulty. The equations of motion are combined to obtain a differential equation for the velocity perturbation. Using the weak damping condition, the perturbation method is used to solve the dispersion relation. In the leading order approximation, the oscillation frequency of the standing waves is determined. In the first-order approximation, we let both the oscillation frequency and wavelength of the propagating waves be perturbed due to the presence of thermal conduction, which enables us to determine the damping rate of the standing waves. Our results show that the plasma flow is an essential parameter in determining the effectiveness of the damping mechanism. Also, the exact solutions of the dispersion relation have been determined without using weak damping assumption. Interestingly the two solutions are the same. Introducing plasma flow to the coronal loop causes the period ratio of the fundamental mode to the first overtone to decrease more.