  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 predict a maximum isotropic equivalent
luminosity of (~2x10^{47} erg/s) min({\rho}^2, B{\rho}^{4/3}{\nu}^{-2/3}),
where {\rho} is the curvature radius of the magnetic field lines near the
source region in units of 10 km, B is the local magnetic field strength in
units of 10^{16} G, and {\nu} is the FRB wave frequency in units of GHz. This
is because the electric field responsible for accelerating the radiating
particles becomes close to the quantum critical field strength and is then
quickly shielded by Schwinger pairs within a nano-second. Future observations
should be able to confirm this cut-off luminosity and hence provide a unique
probe of the source location and magnetic field strength. We discuss how the
maximum luminosity affects the observed flux distributions for repeating bursts
from the same object and for the entire FRB population.
