Magnetohydrodynamic Waves in Dynamic Plasmas with Solar Applications: Effect of Thermal Conduction

The highly magnetised coronal loops have been confirmed to support a variety of MHD waves and oscillations which are observed widely in the solar atmosphere and most of them are seen to be rapidly damped. One of these oscillations are interpreted as longitudinal slow (propagating or standing) MHD waves. In the last decade, the slow MHD waves have been subject to many observational and theoretical studies to investigate the dominant damping mechanisms. Thermal conduction is the main dissipation mechanism that is suggested to be the essential cause of the damping when compared to the other mechanisms. Therefore, we concentrate here on the damping of both propagating and standing slow magneto-acoustic waves due to thermal conduction.

In the present thesis we examine the effect of the cooling background coronal plasma on damping coronal oscillations. Most of the previous studies have assumed models with a time-independent equilibrium. Here we avoid this restriction and allow the equilibrium to develop as a function of time. The background plasma is assumed to be cooling because of thermal conduction. Moreover, the cooling of the background temperature is assumed to have an exponential profile with characteristic cooling times typical for solar coronal loops.

We have investigated the propagating slow magneto-acoustic waves in a homogeneous magnetised plasma embedded in a hot coronal loop. The background plasma is assumed to be cooling due to thermal conduction in a weakly stratified atmosphere. The influence of cooling of the background plasma on the properties of magneto-acoustic waves is examined. The background temperature is found to decrease exponentially with time by solving the background plasma equations.

On the other hand, we have considered the influence of a cooling background plasma on the longitudinal standing (slow) magneto-acoustic waves generated in a loop of hot corona. The cooling of the background plasma is dominated by a physically unspecified thermodynamic source. A dominance of the cooling in the absence of any dissipative mechanisms is found to amplify the oscillation amplitude. Thermal conduction, which is presumed to be a weak, is only present in the perturbations, causing a damping for the hot-loop oscillations.

The previous study is expanded on investigating the effect of strong thermal conduction on the hot coronal oscillations. The competition between the cooling of plasma and the damping of oscillations can be captured from the behaviour of MHD waves. The hot-loop oscillations undergo strong damping due to thermal conduction, although the cooling coronal plasma exerts resistive role on the damping method by decreasing the rate of decaying for cool coronal oscillations. Contrary to cool loops, the amplitude of very hot loops that undergoes a high amount of cooling experiences faster damping than others. However, the damping of the standing slow (acoustic) waves, because of strong thermal conduction, is brought to an end at a certain time instant and then the rate of damping decreases gradually beyond this limit.

In our analytic work for the models assumed above, we have applied the WKB theory to solve the governing equation which is derived and non-dimensionalised. The WKB estimates are used here since they provide good approximations to the properties of MHD waves. Further to this, we have exploited the method of characteristics and the properties of Sturm-Liouville problems to obtain the solution of the temporally evolving amplitude for the propagating and standing slow MHD waves. Numerical evaluations are employed to give clear view into the behaviour of slow acoustic waves, where the variable background plasma comprising the wave amplitude is measured using typical coronal values. In additions to this, the obtained results are compared to observations.