Comment on “Symmetry in electron and ion dispersion in 1D Vlasov-Poisson plasma” [Phys. Plasmas 25, 112102 (2018)

Abstract

It is shown that the dispersion relation of “Thumb - Teardrop” type, investigated by Trivedi and Ganesh [P. Trivedi and R. Ganesh, Phys. Plasmas 25, 112102 (2018)], is, generally speaking, justified only as a nonlinear one. The reason is that under regular conditions, both linear derivations (van Kampen, Landau) face either internal inconsistencies or unphysical assumptions violating causality or generality, respectively, which can be surmounted only by an incorporation of particle trapping. The four associated discrete modes are hence nothing else but the four harmonic modes of the continuous wave spectrum consisting of the privileged class of cnoidal electron and ion hole equilibria. They have been termed a long time ago as Langmuir, slow electron acoustic, ion acoustic, and slow ion acoustic. As a consequence, Landau's theory of plasma instability is rendered inadequate since at the threshold, the nonlinearly updated wave solution has to be taken into account rather than Landau's linear one. Landau's linear wave theory hence loses its role as a universally valid tool to describe the onset scenarios of instability of coherent waves in favor of a multifaceted onset that, however, relies on the complex manifestations of hole equilibria.