Stability of relativistic transverse cold plasma waves. Part 2. Linearly polarized waves

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Abstract
This is part 2 of a paper concerned with the stability against small perturbations of a certain class of nonlinear wave solutions of the equations that describe a cold unmagnetized plasma. It refers to transverse linearly polarized waves in an electron-positron plasma. A numerical method, based on Floquet's theory of linear differential equations with periodic coefficients, is used to solve the perturbation equations and obtain the instability growth rates. All the three possible types of perturbations are discussed for a typical value of the (large) amplitude of the nonlinear wave: electrically longitudinal slightly unstable modes (with maximum growth rate γ approximately equal to 0·07ω0, where ω0is the frequency of the nonlinear wave); purely transverse moderately unstable modes (with γ ≃ 0·26ω0); and highly unstable electrically transverse modes (with γ ≃ l·5ω0).