Propagation of nonlinear, radiatively damped longitudinal waves along magnetic flux tubes in the solar atmosphere

For solar magnetic flux tubes the authors compare three types of waves: longitudinal MHD tube waves, acoustic tube waves propagating in the same tube geometry but with rigid walls and ordinary acoustic waves in plane geometry. They find that the effect of distensibility of the tube is small and that longitudinal waves are essentially acoustic tube waves. Due to the tube geometry there is considerable difference between longitudinal waves or acoustic tube waves and ordinary acoustic waves. Longitudinal waves as well as acoustic tube waves show a smaller amplitude growth, larger shock formation heights, smaller mean chromospheric temperature but a steeper dependence of the temperature gradient on wave period.