A parametric study of population inversions in relativistic plasmas through non-resonant interactions with Alfvén waves and their applications to fast radio bursts

ABSTRACT Synchrotron maser emission is a leading candidate to explain the coherent emission from fast radio bursts (FRBs). This mechanism requires a population inversion in order to operate. We show that non-resonant interactions between Alfvén waves and a relativistic plasma result in the formation of population inversions across a wide range of magnetizations, $\sigma \gtrsim 10^{-4}$, and temperatures, $10^{-2} \le k_bT/mc^2 \le 3$, spanning the parameters expected in FRB environments. We calculate the fraction of energy contained in the inversion across the whole of this parameter space for the first time and we show that energy fractions of $f_{\rm{ inv}}\gtrsim 10^{-2}$ are achieved for high magnetizations $\sigma >1$. The population inversion forms on time-scales compatible with the typical dynamical time-scales of magnetars for all magnetizations. Furthermore, we provide physical explanations for the behaviour of the interaction in different magnetization regimes, and identify the important characteristic values at which this behaviour changes. We also show that the mechanism is capable of producing an FRB signal at GHz frequencies in a relativistic magnetar wind close to the light cylinder and that this signal can escape the magnetar environment without significant damping.