The synchrotron maser emission from relativistic shocks in Fast Radio Bursts: 1D PIC simulations of cold pair plasmas

The emission process of Fast Radio Bursts (FRBs) remains unknown. We investigate whether the synchrotron maser emission from relativistic shocks in a magnetar wind can explain the observed FRB properties. We perform particle-in-cell (PIC) simulations of perpendicular shocks in cold pair plasmas, checking our results for consistency among three PIC codes. We confirm that a linearly polarized X-mode wave is self-consistently generated by the shock and propagates back upstream as a precursor wave. We find that at magnetizations $\sigma\gtrsim 1$ (i.e., ratio of Poynting flux to particle energy flux of the pre-shock flow) the shock converts a fraction $f_\xi' \approx 7 \times 10^{-4}/\sigma^2$ of the total incoming energy into the precursor wave, as measured in the shock frame. The wave spectrum is narrow-band (fractional width $\lesssim 1-3$), with apparent but not dominant line-like features as many resonances concurrently contribute. The peak frequency in the pre-shock (observer) frame is $\omega^{\prime \prime}_{\rm peak} \approx 3 \gamma_{\rm s | u} \omega_{\rm p}$, where $\gamma_{\rm s|u}$ is the shock Lorentz factor in the upstream frame and $\omega_{\rm p}$ the plasma frequency. At $\sigma\gtrsim1$, where our estimated $\omega''_{\rm peak}$ differs from previous works, the shock structure presents two solitons separated by a cavity, and the peak frequency corresponds to an eigenmode of the cavity. Our results provide physically-grounded inputs for FRB emission models within the magnetar scenario.