Propagation of strong electromagnetic waves in tenuous plasmas

We study the propagation of electromagnetic waves in tenuous plasmas, where the wave frequency <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msub><a:mi>ω</a:mi><a:mn>0</a:mn></a:msub></a:math> is much larger than the plasma frequency <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:msub><b:mi>ω</b:mi><b:mi mathvariant="normal">P</b:mi></b:msub></b:math>. We show that in pair plasmas, nonlinear effects are weak for <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:msub><d:mi>a</d:mi><d:mn>0</d:mn></d:msub><d:mo>≪</d:mo><d:msub><d:mi>ω</d:mi><d:mn>0</d:mn></d:msub><d:mo>/</d:mo><d:msub><d:mi>ω</d:mi><d:mi mathvariant="normal">P</d:mi></d:msub></d:mrow></d:math>, where <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:msub><f:mi>a</f:mi><f:mn>0</f:mn></f:msub></f:math> is the wave strength parameter. In electron-proton plasmas, a more restrictive condition must be satisfied, namely, either <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mrow><g:msub><g:mi>a</g:mi><g:mn>0</g:mn></g:msub><g:mo>≪</g:mo><g:mn>1</g:mn><g:mo>/</g:mo><g:msub><g:mi>ω</g:mi><g:mi mathvariant="normal">P</g:mi></g:msub><g:msub><g:mi>τ</g:mi><g:mn>0</g:mn></g:msub></g:mrow></g:math>, where <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:msub><i:mi>τ</i:mi><i:mn>0</i:mn></i:msub></i:math> is the duration of the radiation pulse, or <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:msub><j:mi>a</j:mi><j:mn>0</j:mn></j:msub><j:mo>≪</j:mo><j:mn>1</j:mn></j:mrow></j:math>. 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. Published by the American Physical Society 2024