%0 Journal Article %T Numerical simulations of the lower solar atmosphere heating by two-fluid nonlinear Alfv¨¦n waves %A B. Ku£¿ma %A D. W¨®jcik %A D. Yuan %A K. Murawski %A S. Poedts %J - %D 2020 %R 10.1051/0004-6361/201937260 %X Context. We present new insight into the long-standing problem of plasma heating in the lower solar atmosphere in terms of collisional dissipation caused by two-fluid Alfv¨¦n waves.Aims. Using numerical simulations, we study Alfv¨¦n wave propagation and dissipation in a magnetic flux tube and their heating effect.Methods. We set up 2.5-dimensional numerical simulations with a semi-empirical model of a stratified solar atmosphere and a force-free magnetic field mimicking a magnetic flux tube. We consider a partially ionized plasma consisting of ion + electron and neutral fluids, which are coupled by ion-neutral collisions.Results. We find that Alfv¨¦n waves, which are directly generated by a monochromatic driver at the bottom of the photosphere, experience strong damping. Low-amplitude waves do not thermalize sufficient wave energy to heat the solar atmospheric plasma. However, Alfv¨¦n waves with amplitudes greater than 0.1£¿km s£¿1 drive through ponderomotive force magneto-acoustic waves in higher atmospheric layers. These waves are damped by ion-neutral collisions, and the thermal energy released in this process leads to heating of the upper photosphere and the chromosphere.Conclusions. We infer that, as a result of ion-neutral collisions, the energy carried initially by Alfv¨¦n waves is thermalized in the upper photosphere and the chromosphere, and the corresponding heating rate is large enough to compensate radiative and thermal-conduction energy losses therein %U https://www.aanda.org/articles/aa/full_html/2020/07/aa37260-19/aa37260-19.html