3D numerical simulations of propagating two-fluid, torsional Alfvén waves and heating of a partially ionized solar chromosphere

We present a new insight into the propagation, attenuation and dissipation of two-fluid, torsional Alfv\'en waves in context heating lower solar atmosphere. By means numerical simulations partially-ionized plasma, we solve set two-fluid equations for ion plus electron neutral fluids three-dimensional (3D) Cartesian geometry. implement initially current-free magnetic field configuration, corresponding to flux-tube that is rooted photosphere expands chromosphere corona. put boundary our simulation region low chromosphere, where ions neutrals begin decouple, there monochromatic driver directly generates with wave period 30 s. As ion-neutral drift increases height, effects become more significant energy carried by both magneto-acoustic can be thermalized process collisions there. In fact, observe increase plasma temperature along flux-tube. conclusion, potentially play role chromosphere.