Ion acoustic damping effects on parametric decays of Alfvén waves: Right-hand polarization

We study ion acoustic damping effects on parametric decays of right‐hand‐polarized electromagnetic waves. We do this because ion beams have been observed in a variety of space environments, and consequently, these waves can exist in those places. Damping effects are incorporated into the model by adding to the longitudinal component of the equation of motion a collision‐like term. Like for left‐hand‐polarized waves, the effect of damping is twofold. On the one hand, damping decreases the maximum growth rate of the existing instabilities while increasing the instability range, and on the other hand, it destabilizes regions that are stable in the absence of damping. Thus, for low‐frequency pump waves, ω0 ≪ ωci, and for low β = vt/vA (ωci is the ion gyrofrequency, and vt and vA are the thermal and the Alfvén velocities, respectively), where the only parametric instability is a decay instability, damping destabilizes the frequency range between ω = 0 and the threshold of the decay instability. As β increases, two new parametric instabilities develop: One of them is a modulational instability, and above some threshold value of the pump wave amplitude, there is also a beat wave instability. The decay instability is also possible for pump wave amplitude above some threshold. For even larger β the decay instability is no longer possible. In all cases, damping effects reduce the growth rate of the existing instabilities and destabilize regions which are stable in the absence of damping. These results are in agreement with those obtained by Vasquez [1995]. It is also shown that for large‐frequency pump waves, electron/ion whistler waves, the decay instability reappears even for large β and has very large growth rates.