Wave function properties of a single and a system of magnetic flux tube(s) oscillations

In this study, the properties of wave functions of the MHD oscillations for a single and a system of straight flux tubes are investigated. Magnetic flux tubes with a straight magnetic field and longitudinal density stratification were considered in zero-β approximation. A single three-dimensional wave equation (eigenvalue problem) is solved for longitudinal component of the perturbed magnetic field using the finite element method. Wave functions (eigenfunction of wave equation) of the MHD oscillations are categorized into sausage, kink, helical kink, and fluting modes. Exact recognition of the wave functions and the frequencies of oscillations can be used in coronal seismology and also helps to the future high-resolution instruments that would be designed for studying the properties of the solar loop oscillations in details. The properties of collective oscillations of nonidentical and identical system of flux tubes and their interactions are studied. The ratios of frequencies, the oscillation frequencies of a system of flux tubes to their equivalent monolithic tube ( ω~sys/ω~mono), are obtained between 0.748 and 0.841 for a system of nonidentical tubes, whereas the related ratios of frequencies for a system of identical flux tubes are fluctuated around 0.761.