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Phase mixing of Alfven waves is one of the most promising mechanisms forheating of the solar atmosphere. The damping of waves in this case requiressmall transversal scales, relative to the magnetic field direction. Here thisrequirement is achieved by considering a transversal inhomogeneity in theequilibrium plasma density profile. Using a single fluid approximation of apartially ionized chromospheric plasma we study the effectiveness of thedamping of phase mixed shear Alfven waves and investigate the effect of varyingthe ionization degree on the dissipation of waves. Our results show that thedissipation length of shear Alfven waves strongly depends on the ionizationdegree of the plasma, but more importantly, in a partially ionized plasma, thedamping length of shear Alfven waves is several orders of magnitude shorterthan in the case of a fully ionized plasma, providing evidence that phasemixing could be a large contributor to heating the solar chromosphere. Theeffectiveness of phase mixing is investigated for various ionization degrees,ranging from very weakly to very strongly ionized plasmas. Our results showthat phase mixed propagating Alfven waves in a partially ionized plasma withionization degrees in the range 0.518 to 0.657, corresponding to heights of1916 to 2150 km above the solar surface, can provide sufficient heating tobalance chromospheric radiative losses in the quiet Sun.

Phase mixing of propagating Alfv{\'e}n waves in a single-fluid partially ionized solar plasma