Relation between Magnetic Fields and Kink Oscillations with Flows

In this paper, we discuss a method by which Magnetic Fields which are prevalent in the Sun's Atmosphere, namely, the Corona, can be calculated with the Kink Oscillations, which is basically an MHD (Magneto Hydro Dynamic) wave. Kink Oscillations are found in structured media, in particular in cylindrical geometries, which are modeled in the Coronal Loops. The MHD equations are linearized and the solution of the resulting wave equation, is written in terms of Bessel Functions. The boundary conditions (continuity of velocity and total pressure ) at the interface of the cylinder are applied. The resulting dispersion relation is a complicated transcendental function. Analytical solutions of this relation are hard to find. However, in the limit of large wave numbers, ka → ·, the dispersion relation can be simplified and an analytical solution of this relation can be found. Using the phase velocity of the Kink Oscillations, and a few parameters such as the loop length, the density ratio and the frequency (or period), one can determine the magnetic field. The dispersion relation with the effect of uniform flows has also been derived. Limiting cases of incompressible flows, curvature effects and no flows are presented briefly.