Symmetry in electron and ion dispersion in 1D Vlasov-Poisson plasma

Abstract

Using a Vlasov-Poisson model which treats both electrons and ions on the same physics footing or symmetrically in terms of kinetics, we demonstrate perhaps for the first time that the hitherto separate normal mode branches of electrons (or “Thumb curve”) and ions (or the “Teardrop curve”) are “continuously” connected branches of a general symmetric dispersion. Our findings are obtained using a dispersion relation analysis and verified using a driven nonlinear Vlasov Poisson solver. A simple explanation is suggested in terms of the real part of the plasma dispersion function obtained for arbitrary ratios of ion to electron masses and temperatures. It is demonstrated that the “Thumb” and “Teardrop” curves are recovered from the general symmetric dispersion at appropriate limits.

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

“…(We note in parenthesis that the correctness of this set obtained in a linear fashion does not imply that the linear route chosen for its derivation must be correct as well. Linearization is a prohibited procedure violating intrinsic consistency [15,36].…”

“…Similarly, we can upgrade Landau's zero-damped harmonic wave solution too, satisfying the dispersion part of the dispersion relation, the thumb curve, by setting B e =0, k 0 =k and γ=0 [15,36] . In this case it is the β-trapping effect alone that accounts for this upgraded, trustworthy solution of the full VP system.…”

On the Evolution Equations of Nonlinearly Permissible, Coherent Hole Structures Propagating Persistently in Collisionless Plasmas

“…The fact that Landau and van Kampen/Case equilibria actually obey the same equation and thus could be equally well used oversees that they only obey the linear Vlasov but not the full Vlasov equation. [13,14] To say that this mode is the ordinary ion acoustic wave structure and therefore well-known and not new misjudges the nonlinear background. A monochromatic wave structure is subject to the nonlinear particle-wave interaction as well, which leads to ergodic particle trajectories (see also [15]) in the resonance region of phase space, i.e., near the separatrix, which is manifest in the various trapping scenarios.…”

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

“…Our mode is therefore the correctly upgraded, nonlinear counterpart to Landau (Γ = 0) and to van Kampen (−Γ = λ). It is moreover for Γ = 0 the well-known "Thumb-Teardrop" DR which has been studied for v D = 0 in detail by [9] mistakenly believing that it is a linear DR. As explained by the author in a comment in [10], however, it makes sense only in the nonlinear regime, although formally it exists linearly, too. On the other hand, a Γ = 0 provides a new parameter resulting in a continuous spectrum of possible solutions, analogous but of course different to the continuous linear spectrum of van Kampen.…”

“…In addition, the second dispersion branch, which was later termed "slow ion acoustic wave" (SIAW) branch and which is e.g. part of the thumb-teardrop dispersion relation [9,10], was advertised for the first time in this article (see the Figs. 2.3 and eqs.…”