Fast and Alfvén waves driven by azimuthal footpoint motions

Abstract

The excitation of Alfv en and fast magneto-acoustic waves in coronal loops driven by footpoint motions is studied in linear, ideal MHD. The analysis is restricted to azimuthally polarized footpoint motions so that only Alfv en waves are directly excited which couple to fast magneto-acoustic waves at later times. In the present study a periodic driver is applied at one end of the loop. The eects of a more realistic random driver are studied in the companion paper De Groof & Goossens (2002) (hereafter referred to as Paper II). The rst part of the paper is devoted to the study of resonant absorption and phase-mixing in the absence of coupling (azimuthal wavenumber ky = 0). Since the density varies across the loop, resonances occur at the magnetic surfaces where the driving frequency equals the local Alfv en frequency. In a second part where Alfv en waves with ky 6 0 coupling to fast waves are taken into account, we nd that the behaviour of the MHD waves is strongly dependent on the driving frequency !d. Especially driving frequencies equal to a quasi-mode frequency seem to make the dierence. The fast waves excited in these cases are global oscillations of the system and form quasi-modes as they are damped through the resonant coupling with Alfv en modes. Since these resonances occur at the same location where the original Alfv en wave peaks, the resonant peak is further amplied. While in most cases coupling has a negative eect on the growth of the directly excited Alfv en waves, driving with a quasi-mode frequency leads to a faster growth of the resonant peaks and a more ecient decrease in length scales than in the uncoupled case.