A general way to confined stationary Vlasov-Poisson plasma configurations

Belyaeva, Yulia O.; Gebhard, Björn; Скубачевский, А. Л.

doi:10.3934/krm.2021004

Cited by 10 publications

(2 citation statements)

References 38 publications

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“…We also mention the work of Bernis [6] which is concerned with the existence of stationary solution with cylindrical symmetry for the Vlasov-Poisson equations in the whole space. Others works on stationary Vlasov-Poisson equations can be found in the non exhaustive list [10,14,16,5,3].…”

Section: Introductionmentioning

confidence: 99%

Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe

Badsi¹,

Godard-Cadillac²

2022

Preprint

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In this article, we study a collisionless kinetic model for plasmas in the neighborhood of a cylindrical metallic Langmuir probe. This model consists in a bi-species Vlasov-Poisson equation in a domain contained between two cylinders with prescribed boundary conditions. The interior cylinder models the probe while the exterior cylinder models the interaction with the plasma core. We prove the existence of a weak-strong solution for this model in the sense that we get a weak solution for the 2 Vlasov equations and a strong solution for the Poisson equation. The first parts of the article are devoted to explain the model and proceed to a detailed study of the Vlasov equations. This study then leads to a reformulation of the Poisson equation as a 1D non-linear and non-local equation and we prove it admits a strong solution using an iterative fixed-point procedure.

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Section: Introductionmentioning

confidence: 99%

Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe

Badsi¹,

Godard-Cadillac²

2022

Preprint

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“…In order to investigate steady states of plasmas described by Vlasov type models, the system has to be equipped with a suitable external field. Besides the aforementioned papers [22] and [39], confined steady states in various settings under the influence of an external magnetic field were constructed in [3,4,37]. In the non-stationary case, an external magnetic field becoming infinite at the boundary of the confinement device was used in [7][8][9][10] to confine a Vlasov-Poisson plasma.…”

Section: Introductionmentioning

confidence: 99%

On the two and one-half dimensional Vlasov-Poisson system with an external magnetic field: global well-posedness and stability of confined steady states

Knopf,

Weber

2021

Preprint

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The time evolution of a two-component collisionless plasma is modeled by the Vlasov-Poisson system. In this work, the setting is two and one-half dimensional, that is, the distribution functions of the particles species are independent of the third space dimension. We consider the case that an external magnetic field is present in order to confine the plasma in a given infinitely long cylinder. After discussing global well-posedness of the corresponding Cauchy problem, we construct stationary solutions which indeed have support away from their confinement device. Then, in the main part of this work we investigate the stability of such steady states, both with respect to perturbations in the initial data, where we employ the energy-Casimir method, and also with respect to perturbations in the external magnetic field.

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On the two and one-half dimensional Vlasov–Poisson system with an external magnetic field: Global well-posedness and stability of confined steady states

Knopf

Weber

2022

Nonlinear Analysis: Real World Applications

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A general way to confined stationary Vlasov-Poisson plasma configurations

Cited by 10 publications

References 38 publications

Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe

Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe

On the two and one-half dimensional Vlasov-Poisson system with an external magnetic field: global well-posedness and stability of confined steady states

On the two and one-half dimensional Vlasov–Poisson system with an external magnetic field: Global well-posedness and stability of confined steady states

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