The effect of random Alfvén waves on the propagation of hydromagnetic waves in a finite-beta plasma

Using first-order smoothing theory, Fourier analysis and perturbation methods, we obtain the evolution equation of the wave spectrum as well as the nonlinear forces generated by random Alfvén waves in a finite-β plasma with phenomenological Landau-damping effects. The effect of microscale random Alfvén waves on the propagation of large-scale hydromagnetic waves is also investigated by solving the mean-field equations. It is shown that parallel-propagating random Alfvén waves are modulationally stable and that obliquely propagating random Alfvén waves can be modulationally unstable when the energy of random waves is converted to slow magneto-acoustic waves that can be Landau-damped, providing a dissipation mechanism for the Alfvén waves.