The plasma suppression effect can be ignored in realistic FRB models invoking bunched coherent radio emission

One widely discussed mechanism to produce highly coherent radio emission of fast radio bursts (FRBs) is coherent emission by bunches, either via curvature radiation or inverse Compton scattering (ICS). It has been suggested that the plasma oscillation effect can significantly suppress coherent emission power by bunches. We examine this criticism in this paper. The suppression factor formalism was derived within the context of radio pulsars in which radio waves are in the low-amplitude, linear regime and cannot directly be applied to the large-amplitude, non-linear regime relevant for FRBs. Even if one applies this linear treatment, plasma suppression is not important for two physical reasons. First, for an efficient radiation mechanism such as ICS, the required plasma density is not high so that a high-density plasma may not exist. Second, both bunched coherent mechanisms demand that a large global parallel electric field ($E_\parallel$) must exist in the emission region in order to continuously inject energy to the bunches to power an FRB. In order to produce typical FRB duration via coherent curvature or ICS radiation, a parallel electric field must be present to balance the acceleration and radiation back-reaction. The plasma suppression factor should be modified with the existence of $E_\parallel$. We show that the correction factor for curvature radiation, $f_{\rm cur}$, increases with $E_\parallel$ and becomes 1 when $E_\parallel$ reaches the radiation-reaction-limited regime. We conclude that the plasma suppression effect can be ignored for realistic FRB emission models invoking bunched coherent radio emission.