The maximum luminosity of fast radio bursts

Under the assumption that fast radio bursts ( FRBs) are from coherent curvature emission powered by the dissipation of magnetic energy in the magnetosphere of neutron stars, we show that there is a maximum isotropic equivalent luminosity L-max similar to (2 x 10(47) erg s(-1)) min(rho(2)(6), B-16 rho(4/3)(6) nu(2/3)(9)), where rho(6) = rho/10 km is the curvature radius of the magnetic field lines near the source region, B-16 = B/10(16) G is the local magnetic field strength, and nu(9) = nu/GHz is the FRB wave frequency. This is because the electric field responsible for accelerating the emitting particles becomes close to the quantum critical strength and is then quickly shielded by Schwinger pairs within a nano-second. Future observations should be able to measure this cut-off luminosity and hence provide a unique probe of the source location and magnetic field strength. We discuss the effects of L-max on the observed flux distributions for repeating bursts from the same object and for the entire FRB population.