  We solve the full quasilinear kinetic equation governing nonresonant
interactions of Alfv\'en waves with relativistic plasmas. This work was
motivated by the need to determine the energy available for the synchrotron
maser in the context of Fast Radio Bursts (FRBs). This interaction can result
in plasma heating and the formation of population inversions necessary for the
maser. We find that population inversions containing $\sim 1-10\%$ of the
distribution's energy form in the relativistic regime, providing an explanation
for the formation of the inversion in the environment expected near FRBs.
