A mechanism for fast radio bursts and their narrow spectra

We find an emission mechanism for fast radio bursts (FRBs) capable of producing broad and narrow spectra. It operates in magnetar explosions, which launch an electromagnetic pulse from the inner magnetosphere at radii r 0 about 10 7 cm. Plasma inside the pulse accelerates outward with Lorentz factor Γ(r) about r/r 0. Before exiting the magnetosphere at radius r about 10 10 cm, the pulse passes through ambient kHz waves that populate the magnetospheres of active magnetars. We show that the waves experience stimulated scattering inside the pulse, with the boost factor Γ squared converting them into radial GHz radiation. This process exponentially amplifies tiny GHz seeds to extreme luminosities consistent with observed FRBs. The produced GHz burst rides inside the explosion pulse, which helps it escape to distant observers. The FRB duration and energy are controlled by the pulse duration and energy. In a saturated emission regime, the predicted burst contains an ultrastrong microsecond component.