Comment on “Undamped electrostatic plasma waves” [Phys. Plasmas 19, 092103 (2012)]

Abstract

The relevance of linear “corner modes” for the description of coherent electrostatic structures, as proposed by Valentini et al. [Phys. Plasmas 19, 092103 (2012)], is questioned. Coherency in their on-dispersion simulation is instead found to be caused by particle trapping in agreement with Schamel's nonlinear wave model [Phys. Plasmas 19, 020501 (2012)]. The revealed small amplitude structures are hence of cnoidal electron hole type exhibiting vortices in phase space. They are ruled by trapping nonlinearity rather than by linearity or quasi-linear effects, as commonly assumed. Arguments are presented, which give preference to these cnoidal hole modes over Bernstein-Greene-Kruskal modes. To fully account for a realistic theoretical scenario, however, at least four ingredients are mandatory. Several corrections of the conventional body of thought about the proper kinetic wave description are proposed. They may prove useful for the general acceptance of this “new” nonlinear wave concept concerning structure formation, updating several prevailing concepts such as the general validity of a linear wave Ansatz for small amplitudes, as assumed in their paper. It is conjectured that this nonlinear trapping model can be generalized to the vortex structures of similar type found in the more general setting of driven turbulence of magnetized plasmas. They appear as eddies in both, the phase and the position spaces, embedded intermittently on the Debye length scale.

Response to “Comment on ‘Undamped electrostatic plasma waves’” [Phys. Plasmas 20, 034701 (2013)]

“…2 In his Comment, 3 Schamel has written a broad spectrum diatribe touching on many points; we agree with some of these points, in fact, some of them were originally advocated by some of us. In particular, we are in agreement that off-dispersion excitations, made possible by particle trapping, are important.…”

“…3 in an attempt to use our numerical and experimental results to substantiate his case. We are not convinced by his arguments and stand by our original conclusion of Ref.…”

Electron Holes in a Regularized Kappa Background

“…The exact quadrature of Eq. ( 30) with all terms has been fully discussed in (Schamel , 2012(Schamel , , 2000, where the pseudopotential is formally the same as in Eq. ( 31) after rescaling.…”

Electrostatic Ion Cyclotron and Ion Plasma Waves in a Symmetric Pair-Ion Plasma Cylinder

“…(20): In the frequency range 3Ω < ω < 5Ω, Eq. (13) reads 19) and the solution is approximately given by…”

“…Thus, in order to explain experiments, a kinetic theory is needed together with cyclotron and cylindrical effects. However, the story may still be one sided and incomplete, because the same may hold for trapping which cannot be ruled out [18,19], and a complete picture can only be delivered by treating all these aspects simultaneously.…”