Evidence of a new class of cnoidal electron holes exhibiting intrinsic substructures, its impact on linear (and nonlinear) Vlasov theories and role in anomalous transport

Novel types of solitary electron holes or in more general terms a novel class of cnoidal electron holes propagating in collisionless, driven plasmas is found numerically and described analytically. These structural modes are distinguished by substructures both in the electron density in real space and in the trapped electron distribution function in velocity space and are due to a two-fold trapping scenario; a regular one, called β -trapping, and a weakly singular one, called γ -trapping. Although the latter already appears early in O ( ϕ ) in the ϕ -expansion of the density, where ϕ is the electrostatic potential, it is the regular β -trapping effect, appearing in O ( ϕ 3/2 ), that remains the main cause of these new class of self-consistent structures. Through a proper participation of both trapping mechanisms the shortcomings (inconsistencies) of undamped linear wave theories (Landau, van Kampen) are nonlinearly rectified becoming true solutions of the Vlasov-Poisson system at this kinetic level of plasma description only. They hence provide the right key to the strictly nonlinear, kinetic world of undamped, coherent, small amplitude structures in driven, collisionless plasmas. A cusp-like slope singularity of the otherwise continuous electron distribution f e along the contour of a separatrix, on the other hand, exposes thereby a limit for the reliability of a kinetic nonlinear Vlasov-Poisson description and a simulation of structure formation in intermittent turbulent plasmas. It points to a new, deeper settled physics caused by a local enhancement of collisionality near separatrices through the generation of correlations. It is suggested that multiple trapping has the same origin than chaos in the particle trajectories near resonance, namely the non-integrability of discrete particle dynamics.