Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations

Silantyev, Denis A.; Lushnikov, Pavel M.; Rose, Harvey A.

doi:10.1063/1.4979289

Cited by 11 publications

(3 citation statements)

References 44 publications

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“…(2) There is a small damping (and frequency shift) acting on DNS, an effect that we attribute to the numerical dissipation well known in Vlasov simulations [36,37]. We confirm this hypothesis in Sec.…”

Section: B Comparison Between Direct Numerical Simulations and The Rsupporting

confidence: 78%

Towards a classification of bifurcations in Vlasov equations

2020

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Section: B Comparison Between Direct Numerical Simulations and The Rsupporting

confidence: 78%

Towards a classification of bifurcations in Vlasov equations

2020

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“…i) The agreement is good, both in terms of frequency and amplitude, over fairly long time scales. ii) There is a small damping (and frequency shift) acting on the direct numerical simulation (DNS), an effect that we attribute to the numerical dissipation well known in Vlasov simulations [29,30]. We confirmed that hypothesis by varying grid sizes (see SM [24]).…”

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confidence: 78%

Towards a classification of bifurcations in Vlasov equations

Barré,

Métivier,

Yamaguchi

2019

Preprint

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We propose a classification of bifurcations of Vlasov equations, based on the strength of the resonance between the unstable mode and the continuous spectrum on the imaginary axis. We then identify and characterize a new type of generic bifurcation where this resonance is weak, but the unstable mode couples with the Casimirs of the system to form a size 3 Jordan block. We derive a three-dimensional reduced noncanonical Hamiltonian system describing this bifurcation. Comparison of the reduced dynamics with direct numerical simulations on a test case gives excellent agreement. We finally discuss the relevance of this bifurcation to specific physical situations.

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“…For σ > 2 one can interpret the term −νΛ σ ω in (1) as a hyperviscosity which is widely used in many applications, see e.g. [38], where hyperviscosity is employed in high temperature plasmas.…”

Section: Introductionmentioning

confidence: 99%

Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains

Ambrose,

Lushnikov,

Siegel

et al. 2023

Nonlinearity

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The question of global existence versus finite-time singularity formation is considered for the generalized Constantin–Lax–Majda equation with dissipation − Λ σ , where Λ σ ˆ = | k | σ , both for the problem on the circle x ∈ [ − π , π ] and the real line. In the periodic geometry, two complementary approaches are used to prove global-in-time existence of solutions for σ ⩾ 1 and all real values of an advection parameter a when the data is small. We also derive new analytical solutions in both geometries when a = 0, and on the real line when a = 1 / 2 , for various values of σ. These solutions exhibit self-similar finite-time singularity formation, and the similarity exponents and conditions for singularity formation are fully characterized. We revisit an analytical solution on the real line due to Schochet for a = 0 and σ = 2, and reinterpret it terms of self-similar finite-time collapse. The analytical solutions on the real line allow finite-time singularity formation for arbitrarily small data, even for values of σ that are greater than or equal to one, thereby illustrating a critical difference between the problems on the real line and the circle. The analysis is complemented by accurate numerical simulations, which are able to track the formation and motion of singularities in the complex plane. The computations validate and build upon the analytical theory.

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Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations

Cited by 11 publications

References 44 publications

Towards a classification of bifurcations in Vlasov equations

Towards a classification of bifurcations in Vlasov equations

Towards a classification of bifurcations in Vlasov equations

Global existence and singularity formation for the generalized Constantin–Lax–Majda equation with dissipation: the real line vs. periodic domains

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