Solitary wave propagation in solar flux tubes

The aim of the present work is to investigate the excitation, time-dependent dynamic evolution, and interaction of nonlinear propagating (i.e., solitary) waves on vertical cylindrical magnetic flux tubes in compressible solar atmospheric plasma. The axisymmetric flux tube has a field strength of 1000 G at its footpoint, which is typical for photospheric regions. Nonlinear waves that develop into solitary waves are excited by a footpoint driver. The propagation of the nonlinear signal is investigated by solving numerically a set of fully nonlinear 2.0D magnetohydrodynamic (MHD) equations in cylindrical coordinates. For the initial conditions, axisymmetric solutions of the linear dispersion relation for wave modes in a magnetic flux tube are applied. In the present case, we focus on the sausage mode only. The dispersion relation is solved numerically for a range of plasma parameters. The equilibrium state is perturbed by a Gaussian at the flux tube footpoint. Two solitary solutions are found by solving the full nonlinear MHD equations. First, the nonlinear wave propagation with external sound speed is investigated. Next, the solitary wave propagating close to the tube speed, also found in the numerical solution, is studied. In contrast to previous analytical and numerical works, here no approximations were made to find the solitary solutions. A natural application of the present study may be spicule formation in the low chromosphere. Future possible improvements in modeling and the relevance of the photospheric chromospheric transition region coupling by spicules is suggested.