Pattern formation in Vlasov-Poisson plasmas beyond Landau caused by the continuous spectra of electron and ion hole equilibria

This review presents an upgraded wave theory adapted to the high fluctuation level of driven realistic, i.e., non-idealized plasmas. Based on the author's early publication (H. Schamel, Plasma Phys. 14 (1972) 905) and supported by recent Vlasov-Poisson (VP) simulations, an extended theoretical framework is presented which not only covers the essential features of coherent hole structures, but which also enables to make the necessary corrections to the current wave theory. A linear stability analysis for single harmonic waves that successfully incorporates trapped particle effects (in contrast to previous analyses) shows an unconditional marginal stability independent of the drift between electrons and ions, which irrevocably contradicts Landau's theory. Moreover, holes of negative energy are of particular interest because they act as attractors in the dynamic system. They are the source for the release of further modes and thus increase the level of intermittent turbulence. In summary, pattern formation in collision-free plasmas is inherently nonlinear, kinetic, and extremely diverse. However, to have a satisfactory, if not yet complete understanding of its processes, a twofold paradigm shift is imperative: one from the conventional linear, discrete wave models to the nonlinear wave models dealing with continuous spectra due to trapping and a second from the BGK to the present method for the correct handling of equilibria.