High-frequency dissipative MHD waves in straight magnetic cylindrical plasma: Coronal loops heating application

The theoretical model for analyzing the waves and oscillatory behavior in the structured solar corona using straight magnetic cylindrical geometry filled with uniform low-beta plasma has been recognized as the most preferable classical model for the last few decades. A number of observations, since the first observation of the transition region and coronal explorer to the latest ones, have been adequately explained by adopting this model. In order to analytically formulate the oscillatory characteristics of magnetohydrodynamic (MHD) waves, most of the studies have considered the nature of plasma as an ideal fluid, particularly in the context of solar physics. However, a departure from ideal plasma consideration to non-ideal may lead to a number of modifications in the characteristics of the MHD waves, including its damping too. In what follows, we derive a more general analytical dispersion relation by extending the classical dispersion relation of [Edwin and Roberts, "Wave propagation in a magnetic cylinder," Sol. Phys. 88, 179-191 (1983)] taking into account the effect of plasma viscosity as a non-ideal term in the existing formulations of the classical model. Consequently, the effects of viscosity on the damping of sausage and kink modes are examined in detail. Multiple trapped body waves of different frequencies exist for both kink and sausage modes in which trapped sausage body wave of comparatively high frequency is damped potentially to generate enough energy to balance the radiative losses of the coronal loop regions. For the coronal loop's plasma parameters, it is found that trapped first radial overtone body wave of sausage type is able to balance the radiative losses of coronal loop structure provided magnetic field strength does not exceed its value of more than 20G.