11 - Thin Flux Tubes: The Kink Mode

Summary

The thin tube theory for a kink wave in a stratified flux tube is determined and explored in the case when the tube is unstratified. Perturbations are also considered for this case. Using a multiple scales approach, the wave equation is derived for the kink mode of a thin magnetic flux tube in an unstratified atmosphere, demonstrating the importance of the kink speed. The theory is illustrated for standing waves in a uniform loop and also extended to structured loops with non-uniform density along the structure. Two density profiles are considered in detail. Period ratios for standing waves under coronal conditions are explored. The role of a non-uniform magnetic field is explored, and leads to a wave equation with non-uniform kink speed. Dispersive corrections in a uniform tube are examined and compared with earlier results. Gravity effects are also examined.