  Fast radio bursts (FRBs) are extragalactic radio transients with extremely
high brightness temperature, which strongly suggests the presence of coherent
emission mechanisms. In this study, we introduce a novel radiation mechanism
for FRBs involving coherent Cherenkov radiation (ChR) emitted by bunched
particles that may originate within the magnetosphere of a magnetar. We assume
that some relativistic particles are emitted from the polar cap of a magnetar
and move along magnetic field lines through a charge-separated magnetic plasma,
emitting coherent ChR along their trajectory. The crucial condition for ChR to
occur is that the refractive index of the plasma medium, denoted as $n_r$, must
satisfy the condition $n_r^2 > 1$. We conduct comprehensive calculations to
determine various characteristics of ChR, including its characteristic
frequency, emission power, required parallel electric field, and coherence
factor. Notably, our proposed bunched coherent ChR mechanism has the remarkable
advantage of generating a narrower-band spectrum. Furthermore, a frequency
downward drifting pattern, and $\sim100\%$ linearly polarized emission can be
predicted within the framework of this emission mechanism.
