analytical study of gravitational magnetoacoustic waves in the solar corona

Coronal loops are one of the important waveguides in the solar atmosphere. waveguides can be considered as the magnetic flux tubes for the generation and propagation of magnetohydrodynamic waves. in this paper, we have used a cylindrical geometry model to study the behavior of magnetohydrodynamic waves in coronal loops analytically. we considered a plasma structure with gravity acceleration and a uniform magnetic field. wave equations were derived under specific assumptions and initial conditions. after linearization, perturbations were applied to obtain the dispersion relation. using the dispersion equation, we obtained the frequency graph in terms of wave number. we investigated the effect of some parameters such as density, alfvén velocity and gravitational acceleration on the behavior of waves. our analysis of wave's behavior across different kl regimes, and the observed convergence of phase speeds toward specific limits, provided valuable information regarding mode stability. the results showed that the sausage and kink modes approach each other at particular values of kl, where their phase speeds act as asymptotes. this convergence behavior demonstrates a fundamental relationship between these two types of wave modes under varying waveguide thickness conditions.