Modelling the Excitation and Decay of Solar Coronal Loop Oscillations by using Laplace Transforms and Numerical Inversions

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Recent research within Coronal Helioseismology has had some focus on the rapid decay of coronal magnetic loops observed by TRACE. The cause of this rapid decay is not clear yet. In this M.Sc. Thesis in Space Engineering at Luleå University of Technology, the theory energy wave leakage via kink modes is supported. A stationary magnetic flux tube embedded in a typical coronal environment is considered. The flux tube is perturbed by a local disturbance representing a solar flare. The time dependent solution is studied, so a Laplace transform of the time component is applied to the set of the equations describing the displacement of the magnetic flux tube and the total pressure perturbation. Hence it is possible to introduce an initial value function for the system. The external region is excited by an impulse function placed at a certain distance from the edge of the flux tube, and then matched to the internal region with appropriate matching conditions. Transient solutions arise, and are associated with branch cuts in the complex frequency plane. Branch cuts decay algebraically in time, which is initially more rapid than the exponential decay (associated with poles). A recently developed numerical Laplace inversion algorithm by Abate and Valkó (2004) is applied. It is found that the magnetic flux tube has an initial algebraic decay. The decay rate depends on the flux tube's thickness, length and strength. After the initial transient decay, the flux tube ends up oscillating with a frequency corresponding to the the non-le...