Propagation of strong electromagnetic waves in tenuous plasmas

We study the propagation of electromagnetic waves in tenuous plasmas, where the wave frequency ω0 is much larger than the plasma frequency ωP. We show that in pair plasmas, nonlinear effects are weak for a0≪ω0/ωP, where a0 is the wave strength parameter. In electron-proton plasmas, a more restrictive condition must be satisfied, namely, either a0≪1/ωPτ0, where τ0 is the duration of the radiation pulse, or a0≪1. We derive the equations that govern the evolution of the pulse in the weakly nonlinear regime. Our results have important implications for the modeling of fast radio bursts. We argue that (i) millisecond duration bursts with a smooth profile must be produced in a proton-free environment, where nonlinear effects are weaker, and (ii) propagation through an electron-proton plasma near the source can imprint a submicrosecond variability on the burst profile.