Time-dependent ionization in solar magnetic flux tubes

We explore the relevance of time-dependent ionization in solar magnetic flux tubes. We investigate detailed models of longitudinal tubes waves (LTW) also taking into account recent simulations of wave energy generation. In particular, we study tubes of different spreading as function of height representing tubes in environments of different magnetic filling factors. Time-dependent ionization is found to be relevant in all models studied. Effects of time-dependent ionization are most pronouced behind strong shocks and in low density regions, i.e., the middle and higher chromosphere. This work is a further step toward future research involving other types of magnetic waves, thus allowing a more thorough understanding of wave heating phenomena in solar and stellar atmospheres.