MHD Pulsations of Cylindrical Coronal Loops with Tangential Magnetic Discontinuity

Abstract

We study the dispersive properties of the fast-sausage MHD mode in a cylindrical coronal loop with tangential magnetic discontinuity at its interface. To model this effect, we consider a straight axial magnetic field inside a coronal tube and a force-free twisted field in the external medium. The obtained dispersion relation was solved numerically and a number of limiting cases were explored analytically. The results indicate that the principal fast-sausage mode is trapped for all axial wavenumbers. Even a tiny magnetic discontinuity (or external twist) has a crucial effect on the global sausage mode. This mode is almost nondispersive in the long wavelength limit for small external twist, whereas it is strongly dispersive for large magnetic twist. In all cases the phase speed of the fundamental mode tends to the lower vicinity of the external Alfvén speed for small axial wavenumbers. The cutoffs of higher radial order modes were found reduced with respect to the reference model with a straight external field. The damping rate of the leaky modes grows as the external magnetic twist increases. Some applications of the developed theory to explain the observed quasi-periodic pulsations in flaring loops were given.