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This review presents an upgraded wave theory adapted to the high fluctuationlevel of driven realistic i.e. non-idealized plasmas. Above all, this meansgiving up the well-known concept of a linear wave theory in favor of athoroughly nonlinear theory.  Based on the author's early publication (H. Schamel, Plasma Phys. 14 (1972)905) and supported by recent Vlasov-Poisson simulations of realistic noisyplasmas, an extended framework is presented which not only covers the essentialfeatures of coherent hole structures, but which also enables to make thenecessary corrections to the current wave theory. These corrections are longoverdue and can be briefly summarized under the heading: loss of linear Vlasovdynamics when adequately addressing equilibrium states (i.e. failure of linearLandau theory and of continuous van Kampen spectra, respectively). A linearstability analysis for single harmonic waves that successfully incorporatestrapped particle effects (in contrast to previous analyses) shows anunconditional marginal stability independent of the drift between electrons andions, which irrevocably contradicts Landau's theory. Moreover, holes ofnegative energy are of particular interest because they act as attractors inthe dynamical system. They are the source for the release of further modes andthus increase the level of intermittent turbulence. In summary, patternformation in collisionless plasmas is inherently nonlinear and kinetic.However, to have a satisfactory, if not yet complete, understanding of itsprocesses a twofold paradigm shift is imperative: one from the conventionallinear, discrete wave models to the nonlinear wave models dealing withcontinuous spectra due to trapping and a second from the BGK to the presentmethod for the correct handling of equilibria.

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