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When the magnetosphere of a magnetar is perturbed by crustal deformation, anelectric field $E_\parallel$ parallel to the magnetic field line would appearvia Alvf\'en waves in the charge starvation region. The electron-positron pairbunches will be generated via two-stream instability in the magnetosphere, andthese pairs will undergo charge separation in the $E_\parallel$ and in themeantime emit coherent curvature radiation. Following the approach of Yang &Zhang (2018), we find that the superposed curvature radiation becomes narrowerdue to charge separation, with the width of spectrum depending on theseparation between the electron and positron clumps. This mechanism caninterpret the narrow spectra of FRBs, in particular, the spectrum of GalacticFRB 200428 recently detected in association with a hard X-ray burst from theGalactic magnetar SGR J1935+2154.

Pair separation in parallel electric field in magnetar magnetosphere and narrow spectra of fast radio bursts