Linear Theory of Alfvén Wave Reflections at a Density Discontinuity
One of the most important outstanding problems in solar physics is explaining why the corona is much hotter than the surrounding solar atmosphere, called the Coronal Heating Problem (CHP). There has been much work in trying to understand the origin of this issue, as it contradicts what one may think when it comes to basic thermodynamics. One such theory is Alfv´en wave turbulence. These waves are a form of low frequency electromagnetic waves that have been proposed as a suitable heating mechanism behind the CHP. There is a thin layer that separates the chromosphere and the corona, known as the transition region. This region is where the temperature soars from ∼ 104 K to well above 106 K. The goal of this thesis is to use the framework of Reduced-Magnetohydrodynamic (RMHD) model, to determine the basic physics of how Alfv´en waves propagate in a simulated transition region modeled by a step function, which will be used to model the steep density drop in the transition region. This will be examined by following an incident wave propagating in the direction of a homogeneous background magnetic field B0, then calculating reflection (R) and transmission (T) coefficients of the Alfv´en waves after interacting with the transition region.