Formation of population inversions in relativistic plasmas through nonresonant interactions with Alfv\'en waves

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.