Escape of fast radio bursts from magnetars

Fast radio bursts (FRBs) are bright extragalactic transients likely produced by magnetars. We study the propagation of FRBs in magnetar winds, assuming that the wind is strongly magnetized and composed of electron-positron pairs. We focus on the regime where the strength parameter of the radio wave, $a_0$, is larger than unity, and the wave frequency, $\omega_0$, is larger than the Larmor frequency in the background magnetic field, $\omega_{\rm L}$. We show that strong radio waves with $a_0>1$ are able to propagate when $\omega_0 > a_0\omega_{\rm L}$, as the plasma current is a linear function of the wave electric field. The dispersion relation is independent of the wave strength parameter when $\omega_0 > a_0\omega_{\rm L}$. Instead, radio waves could be damped when $\omega_0 < a_0\omega_{\rm L}$, as a significant fraction of the wave energy is used to compress the plasma and amplify the background magnetic field. Our results suggest that FRBs should be produced at large distances from the magnetar (i.e., $R>10^{12}{\rm\; cm}$, where the condition $\omega_0 > a_0\omega_{\rm L}$ is satisfied). Alternatively, the structure of the magnetar wind should be strongly modified during a flare to allow the escape of FRBs produced at radii $R<10^{12}{\rm\; cm}$.