The effect of compressive viscosity and thermal conduction on the longitudinal MHD waves

ABSTRACT Longitudinal magnetohydrodynamic (MHD) oscillations have been studied in a slowly cooling coronal loop, in the presence of thermal conduction and compressive viscosity, in the linear MHD approximation. The WKB method has been used to solve the governing equations. In the leading order approximation the dispersion relation has been obtained, and using the first-order approximation the time-dependent amplitude has been determined. Cooling causes the oscillations to amplify and damping mechanisms are more efficient in hot loops. In cool loops the oscillation amplitude increases with time but in hot loops the oscillation amplitude decreases with time. Our conclusion is that in hot loops the efficiency of the compressive viscosity in damping longitudinal waves is comparable to that of the thermal conduction.