Viscous heating and instabilities in the partially ionized solar atmosphere

In weak magnetic fields (≲ 50 G), parallel and perpendicular viscosities, mainly from neutrals, may exceed magnetic diffusivities (Ohm, Hall, and ambipolar) in the middle and upper chromospheres. Ion-driven gyroviscosity may dominate in the upper chromosphere and transition region. In strong fields (≳ 100 G), viscosities primarily exceed diffusivities in the upper chromosphere and transition region. Parallel and perpendicular viscosities, being similar in magnitude, dampen waves and potentially compete with ambipolar diffusion in plasma heating, potentially inhibiting Hall and ambipolar instabilities when equal. The perpendicular viscosity tensor has two components, ν₁ and ν₂, which differ slightly and show weak dependence on ion magnetization. Their differences, combined with shear, may destabilize waves, though magnetic diffusion introduces a cut-off for this instability. In configurations with a magnetic field B having vertical (b_z = B_z/|B|) and azimuthal (b_y = B_y /|B|) components, and a wavevector k with radial (k_x= k_x /|k|) and vertical (k_z = k_z/|k|) components, parallel viscosity, and Hall diffusion can generate the viscous-Hall instability. Gyroviscosity further destabilizes waves in the upper regions.