Abstract
The existence of manifestly nonlinear electrostatic modes in pair plasmas is shown analytically by means of the quasi-potential method applied to the Vlasov–Poisson system. These modes owe their existence to the trapping of particles in the potential trough(s) and are typically characterized by a notch in the particle distribution functions at resonant velocity, forming vortices in phase space. Both entities, wave structure Φ(x) and phase velocity v0, are uniquely characterized by two parameters, the periodicity parameter k0 and the spectral parameter B. Whereas k0 = 0 describes double layers, with a phase velocity in the thermal range, k0 ≠ 0 represents a periodic wave train which can propagate with two rather distinct phase velocities. One is related to the fast plasma wave, the other one to the slow acoustic mode.
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