Partially ionized plasmas constitute an essential ingredient of the solar atmosphere, and ground- and space-based observations have pointed outthe presence of oscillations in partially ionizedsolar plasmas such as chromosphere, photosphere, prominences or spicules, which have been interpreted in terms of magnetohydrodynamic waves. Our aim is to study the spatial behaviour of propagating weakly and fully nonlinear Alfvén waves, and the subsequent excitation of field-aligned motions and perturbations, when dissipative mechanisms, such as ambipolar diffusion and radiative losses, together with parametrized heating mechanisms, are taken into account. When only ambipolar diffusion is taken into account, first-order Alfvén waves as well as ponderomotive-driven perturbations are spatially damped, while field-aligned motions and perturbations representing propagating slow waves are undamped. These perturbations are damped when thermal effects are also considered and their damping lengths can be longer or shorter than those of ponderomotive-driven perturbations. Therefore, after the initialexcitation, Alfvén waves and ponderomotive-driven perturbations could be quickly damped while slow waves still remain in the plasma, and vice versa. This article is part of the theme issue 'Partially ionized plasma of the solar atmosphere: recent advances and future pathways'.
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