The coupling resonance of torsional alfven wave and fast wave in coronal loops

The method of Orthogonal Function Series Expansion (OFSE) is generalized and applied to the study of the evolution of the coupling of nondissipative torsional Alfven wave and fast wave in coronal loops. Using this method, the intrinsic angular frequency of the overall wave mode can be described mathematically and that of the Alfven waves along the magnetic lines in the coronal loop during the coupling of the Alfven and fast waves can be analyzed both theoretically and numerically. Also with this method, the relation between the coupling driven term and the Alfven wave resonance may be analyzed. Results of computation reveal the place of appearance of coupling resonance as well as the characteristics of the amplitudes of the Alfven and fast waves. As found by the calculations, if the footpoint driven angular frequency is not equal to the intrinsic angular frequency of the overall wave mode of the coronal loop and when a δ section appears at the place of coupled resonance, the radial gradient of the fast waveʹs amplitude is quite large. Sometimes it approximates to a discontinuity, and this is extremely favorable for the dissipation of the fast wave. If the footpoint driven angular frequency is equal to the intrinsic angular frequency of the overall wave mode and when a δ section occurs in the Alfven wave amplitude, abundant small-scale structures appear in the radial direction. Then the location of resonance approximately becomes a discontinuity, very favorable to the dissipation of the Alfven wave.