Revisiting damping of Alfv'en waves in partially ionized plasmas

We investigate the damping rate of Alfvén waves by means of the linear analysis of the two-fluid ten-moments system. To treat effects of viscosity in a wide frequency range, we take account of the time evolution of the traceless part of the pressure tensor. In addition, to treat effects of viscosity in a wide range of the ionization degree, we consider interactions between hydrogen atoms and between protons and hydrogen atoms in the equation of the traceless part of the pressure tensor. We find approximate analytical solutions to the dispersion relation for some limits. Our analysis in the low-frequency limit shows that the viscous damping dominates over the frictional damping in the high-beta plasma, which is independent of the ionization degree. Therefore, the viscosity of hydrogen gas significantly affects cosmic-ray propagation in a partially ionized high-beta plasma.