The Effect of Twisted Magnetic Field on the Period Ratio P₁/P₂ of Nonaxisymmetric MHD Waves

The nonaxisymmetric magnetohydrodynamic (MHD) modes in a zero-beta cylindrical compressible thin magnetic flux tube modelled as a twisted core surrounded by a magnetically twisted annulus, both embedded in a straight ambient external field is considered. The dispersion relation is derived and solved analytically and numerically to obtain the frequencies of the nonaxisymmetric MHD waves. The main result is that the twisted magnetic annulus does affect the period ratio P_1/P_2 of the kink modes. For the kink modes, the magnetic twist in the annulus region can achieve deviations from P_1/P_2 = 2 of the same order of magnitude as in the observations. Furthermore, the effect of the internal twist on the fluting modes is investigated.