Diversity of solitary electron holes operating with non-perturbative trapping

Abstract

A non-perturbative update of Schamel's pseudo-potential method is employed to show the diversity in structure formation in collisionless plasmas, manifested already in the solitary wave limit. As an example, the Gaussian-shaped solitary electron hole, known from earlier Bernstein, Greene, and Kruskal (BGK) analyses, known to be a specific, albeit incomplete wave solution, is updated by subjecting it to a non-perturbative pseudo-potential analysis. Only by the latter can a speed be assigned to it. A perturbative trapping scenario is thereby defined by a Taylor expansion of the trapped electron distribution function fet with respect to −ϵ, where ϵ:=v22−ϕ(x) is the single particle energy. It stands for the class of privileged, solitary sech4-holes, and properly extends undamped linear waves into the nonlinear regime lifting them at a higher level of reliability. A non-perturbative trapping scenario, on the other hand, cannot be handled by a Taylor expansion as it refers to singular terms in the small ϵ-limit, affecting the collective dynamics in phase space especially near separatrices. Being not only suitable to update BGK solutions, it opens the door to a much richer world of structure formation than treated before. To face physical reality properly, however, one has to go one step further by locally and self-consistently incorporating a structure dependent collisionality in the kinetic description and in the numerical simulation, as well. By this removal of cusp-singularities, associated with reliable Vlasov–Poisson-solutions, a more realistic approach to intermittent plasma turbulence and anomalous resistivity may be achieved in forthcoming investigations.