ALFVÉN WAVE AND FAST WAVE COUPLING RESONANCE IN CORONAL LOOPS

Complete Orthogonal Function Series Expansion （OFSE） method is generalized and applied to make research about the time evolution coupling process of fast and Alfvén waves in coronal loops. With the OFSE method, intrinsic angular frequencies of coronal loop quasi-modes could be described mathematically and the intrinsic angular frequency of torsional Alfvén waves in every magnetic field line of coronal loops is investigated theoretically and numerically. With the method, the relationship between a coupling driven term and torsional Alfvén wave resonance is analyzed. Numerical result presents wave amplitude features at the coupling resonant place. It is found that: when the footpoint driven angular frequency is not equal to one of quasi-mode intrinsic angular frequencies, at the resonant position with a δ profile of Alfvén wave amplitude, absolute value of radial gradient of fast wave amplitude is very large and approximates a discontinuity, which is necessary to dissipate fast waves. On the other hand, if the footpoint driven angular frequency is equal to one of quasi-mode intrinsic angular frequencies, widespread small scale structure of Alfvén wave amplitude and an approximate discontinuity at resonant plece, which are necessary to dissipate Alfvén waves, appear.