Cutoff Frequencies For Alfven Waves In The Solar Atmosphere

Abstract

Propagation of linear Alfven waves in the isothermal and non-isothermal solaratmosphere is investigated numerically and analytically. It is shown that thetwo wave variables, the velocity and magnetic field perturbations, behave differently and that there is a range of wave frequencies for which the wave behavior changes from propagating to non-propagating. The so-called transition and turning points corresponding to this change are determined analytically, and their locations in the atmosphere are calculated and verified against the numerical results. The transition and turning points are then used to introduce cutoff frequencies, which are different for different wave variables. The main result is that there isn't a unique cutoff frequency for Alfven waves. Instead, a number of cutoff frequencies can be introduced depending upon the method used to define them, as well as on the choice of the wave variable used to describe the waves. Relevance of the obtained results to recentobservations of Alfven waves in the solar atmosphere is also discussed.A concept of global cutoff frequencies is also introduced by using Leighton's,Hille's and Kneser's oscillation theorems, as well as the Sturm comparison theorems.The oscillation theorems have been applied to bounded and unbounded Alfven wave equations for both the velocity and magnetic field wave variables. The obtained results demonstrated that the global cutoff frequency and the local cutoff frequency are two different physical concepts. Furthermore, the latter exists if and only if the wave frequency is greater than the former. These analytical results have been verified using numerical solutions of the linear Alfven wave equations. The original ideal MHD equations were modified by taking into account the displacement current, and several oscillations theorems were applied to the resulting wave equations. As expected, onlyoscillatory solutions were found.The results presented in this PhD dissertation give strong theoretical evidencefor the existence of local and global cutoff frequencies for Alfven waves propagating in both isothermal and in more realistic non-isothermal solar atmospheres. The existence of these cutoffs has profound implications on the energy and momentum transport in the solar atmosphere and the role of Alfven waves in heating of the solar atmosphere, as well as in acceleration of the solar wind.