Free energy and spatial periodicity of generalized cnoidal ion holes

Das, Nilakshi; Borah, Pranjal; Schamel, H.

doi:10.1016/j.physleta.2018.06.042

Cited by 6 publications

(5 citation statements)

References 20 publications

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“…Other extensions may involve distributions that are discontinuous at the separatrix, as analysed by [24,25,28]. This corresponds to a line discontinuity in the terminology of [29] being defined as a discontinuity along a 1D manifold (separatrix) embedded in a 2D surface (phase space).…”

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confidence: 99%

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

2020

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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.

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Section: ˜≔mentioning

confidence: 99%

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

2020

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“…No matter whether the plasma is treated as a dielectricum [51,52] or refined by treating resonant particles more carefully linearly [53] the result is O(ψ 2 ). This is in strong contrast to a proper nonlinear treatment [7,26,36,[48][49][50] since the result is O(ψ) (for more details see Sect.IX). This not only implies that the effect appears one order earlier in an expansion procedure and is hence stronger but also that negative energy states occur more frequently.…”

Section: A3 the Thumb-tear Drop Relation Is A Linear Dispersion Relat...mentioning

confidence: 88%

“…The present status report was limited to continuous distributions, to a Maxwellian background plasma, to nonrelativistic electrons and to non-magnetized plasmas. Various extensions were carried out with regard to discontinuous distributions by [36,67,68], to κ or Fermi-Dirac distributions by [35,69] and [70], respectively, to relativistic electrons by [71,72] and to magnetized plasmas by [73].…”

Section: Discussionmentioning

confidence: 99%

“…It is, however, not necessarily the actual wave number k which is defined by k = π L where 2L is the actual wavelength. The correct relation between k and k 0 is found by the overall charge neutrality condition and becomes to lowest order ( [36,37]):…”

Section: Theory Of Electron Hole Equilibriamentioning

confidence: 99%

“…This topic was developed in a series of papers [26,36,[48][49][50], to which we refer for a more intensive examination. The total energy density w of a plasma that is structurally excited by an equilibrium hole is given in the laboratory system by…”

Section: Negative Energy Statesmentioning

confidence: 99%

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

Schamel¹

2021

Preprint

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The data that supports the findings of this study are available from the corresponding author upon reasonable request. CONTENT I. INTRODUCTION p.2 II. THEORY OF ELECTRON HOLE EQUILIBRIA p.4 III. THE GALLERY OF ELEMENTARY MODES p.7 III.1 The harmonic mode (single wave) III.2 The privileged sech 4 (x) -solitary mode III.3 The Gaussian e −x 2 -solitary mode III.4 The Second Order Gaussian e − sinh 2 (x) -solitary mode III.5 The sech 2 (x) -soliton IV. HOLES CAUSED BY TWO TRAPPING SCENARIOS p.12 IV.1 The cnoidal electron hole (CEH) IV.2 The Schamel-Korteweg-de Vries solitary electron hole (SKdV-SEH) IV.3 The modified second order Gaussian SEH IV.4 The undisclosed logarithmic Schamel SEH V. THE CLASS OF NEGATIVELY POLARIZED SOLITARY ELECTRON HOLES (npSEHs) p.15

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

Schamel

2023

Rev. Mod. Plasma Phys.

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This review presents an upgraded wave theory adapted to the high fluctuation level of driven realistic, i.e., non-idealized plasmas. Based on the author’s early publication (H. Schamel, Plasma Phys. 14 (1972) 905) and supported by recent Vlasov–Poisson (VP) simulations, an extended theoretical framework is presented which not only covers the essential features of coherent hole structures, but which also enables to make the necessary corrections to the current wave theory. A linear stability analysis for single harmonic waves that successfully incorporates trapped particle effects (in contrast to previous analyses) shows an unconditional marginal stability independent of the drift between electrons and ions, which irrevocably contradicts Landau’s theory. Moreover, holes of negative energy are of particular interest because they act as attractors in the dynamic system. They are the source for the release of further modes and thus increase the level of intermittent turbulence. In summary, pattern formation in collision-free plasmas is inherently nonlinear, kinetic, and extremely diverse. However, to have a satisfactory, if not yet complete understanding of its processes, a twofold paradigm shift is imperative: one from the conventional linear, discrete wave models to the nonlinear wave models dealing with continuous spectra due to trapping and a second from the BGK to the present method for the correct handling of equilibria.

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Free energy and spatial periodicity of generalized cnoidal ion holes

Cited by 6 publications

References 20 publications

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

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

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

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

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