Kinetic theory of periodic hole and double layer equilibria in pair plasmas

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 v 0 , are uniquely characterized by two parameters, the periodicity parameter k 0 and the spectral parameter B . Whereas k 0 = 0 describes double layers, with a phase velocity in the thermal range, k 0 ≠ 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.