Kink oscillation of a system of two braided magnetic flux tubes

ABSTRACT

For the first time we study kink oscillations of braided coronal magnetic loops. We use the simplest model of a braided loop that consists just of two identical curved magnetic tubes. It is assumed that the plasma density is constant inside the tubes, and also in the surrounding plasma. To describe the kink oscillations we use the linear ideal magnetohydrodynamic equations in the cold plasma approximation. We introduce the geometrical parameter q characterizing the value of braiding, the greater q the stronger the braiding is. When $q = 0$ there is no braiding. In this case there are two modes of kink oscillations, fast and slow. We use the regular perturbation method to calculate the first corrections to the frequencies of these oscillations for small q. We found that these corrections are proportional to $q^2$. The dependence of the coefficients of proportionality on the ratio of densities inside and outside the tubes, and on the ratio of distance between the tubes to their cross-section radius is calculated numerically. We found that braiding reduces the frequency of fast oscillations and enhances the frequency of slow oscillations. The implication of obtained results for coronal seismology is discussed.