  In the present work we expand the study of time-dependent ionization
previously identified to be of pivotal importance for acoustic waves in solar
magnetic flux tube simulations. We focus on longitudinal tube waves (LTW) known
to be an important heating agent of solar magnetic regions. Our models also
consider new results of wave energy generation as well as an updated
determination of the mixing length of convection now identified as 1.8 scale
heights in the upper solar convective layers. We present 1-D wave simulations
for the solar chromosphere by studying tubes of different spreading as function
of height aimed at representing tubes in environments of different magnetic
filling factors. Multi-level radiative transfer has been applied to correctly
represent the total chromospheric emission function. The effects of
time-dependent ionization are significant in all models studied. They are most
pronounced behind strong shocks and in low density regions, i.e., the middle
and high chromosphere. Concerning our models of different tube spreading, we
attained pronounced differences between the various types of models, which were
largely initiated by different degrees of dilution of the wave energy flux as
well as the density structure partially shaped by strong shocks, if existing.
Models showing a quasi-steady rise of temperature with height are obtained via
monochromatic waves akin to previous acoustic simulations. However,
longitudinal flux tube waves are identified as insufficient to heat the solar
transition region and corona in agreement with previous studies.
