Propagation of strong electromagnetic waves in tenuous plasmas

We study the propagation of electromagnetic waves in tenuous plasmas, where the wave frequency omega(0) is much larger than the plasma frequency omega(P). We show that in pair plasmas, nonlinear effects are weak for a(0) << omega(0)/omega(P), where a(0) is the wave strength parameter. In electron-proton plasmas, a more restrictive condition must be satisfied, namely, either a(0) << 1/omega(P)tau(0), where tau( 0) is the duration of the radiation pulse, or a(0) << 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.