Large amplitude, low-frequency Alfv́n waves constitute one of the most essential elements of magnetohydrodynamic (MHD) turbulence in the fast solar wind. Due to small collisionless dissipation rates, the waves can propagate long distances and efficiently convey such macroscopic quantities as momentum, energy, and helicity. Since loading of such quantities is completed when the waves damp away, it is important to examine how the waves can dissipate in the solar wind. Among various possible dissipation processes of the Alfv́n waves, parametric instabilities have been believed to be important. In this paper, we numerically discuss the parametric instabilities of coherent/incoherent Alfv́n waves in a finite ion beta plasma using a one-dimensional hybrid (superparticle ions plus an electron massless fluid) simulation, in order to explain local production of sunward propagating Alfv́n waves, as suggested by Helios/Ulysses observation results. Parameter studies clarify the dependence of parametric instabilities of coherent/incoherent Alfv́n waves on the ion and electron beta ratio. Parametric instabilities of coherent Alfv́n waves in a finite ion beta plasma are vastly different from those in the cold ions (i.e., MHD and/or Hall-MHD systems), even if the collisionless damping of the Alfv́n waves are neglected. Further, "nonlinearly driven" modulational instability is important for the dissipation of incoherent Alfv́n waves in a finite ion beta plasma regardless of their polarization, since the ion kinetic effects let both the right-hand and left-hand polarized waves become unstable to the modulational instability. The present results suggest that, although the antisunward propagating dispersive Alfv́n waves are efficiently dissipated through the parametric instabilities in a finite ion beta plasma, these instabilities hardly produce the sunward propagating waves.
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