Unique Solvability of the First Mixed Problem for the Vlasov–Poisson System in Infinite Cylinder

Belyaeva, Yu. O.; Скубачевский, А. Л.

doi:10.1007/s10958-020-04665-9

Cited by 3 publications

(5 citation statements)

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“…Concerning the confinement problem for a two-component plasma the articles [8,33,34,35,36] provide quantitative estimates for a bounded magnetic field guaranteeing the classical solution to the initial-boundary value problem of (1.1), (1.2), (1.3), (1.4) to exist and to be located at some distance from the boundary of a half-space and an infinite cylinder.…”

Section: Introductionmentioning

confidence: 99%

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A general way to confined stationary Vlasov-Poisson plasma configurations

Belyaeva,

Gebhard,

Skubachevskii

2020

Preprint

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We address the existence of stationary solutions of the Vlasov-Poisson system on a domain Ω ⊂ R 3 describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a subregion of Ω. In a first part we provide such an existence result for a generalized system of Vlasov-Poisson type and investigate the relation between the strength of the external magnetic field, the sharpness of the confinement and the amount of plasma that is confined measured in terms of the total charges. The key tools here are the method of sub-/supersolutions and the use of first integrals in combination with cutoff functions. In a second part we apply these general results to the usual Vlasov-Poisson equation in three different settings: the infinite and finite cylinder, as well as domains with toroidal symmetry. This way we prove the existence of stationary solutions corresponding to a two-component plasma confined in a Mirror trap, as well as a Tokamak.

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Section: Introductionmentioning

confidence: 99%

“…Unlike [8,33,34,35,36], the papers [10,11] deal with the confinement problem for a one-component plasma with an external magnetic field, which becomes infinite on a boundary. Equation (1.2) is studied in the whole space R 3 , and the influence of boundary conditions to a solution of equation (1.2) is not considered.…”

Section: Introductionmentioning

confidence: 99%

A general way to confined stationary Vlasov-Poisson plasma configurations

Belyaeva,

Gebhard,

Skubachevskii

2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Concerning the confinement problem for a two-component plasma the articles [8,33,34,35,36] provide quantitative estimates for a bounded magnetic field guaranteeing the classical solution to the initial-boundary value problem of (1), (2), (3), (4) to exist and to be located at some distance from the boundary of a half-space and an infinite cylinder.…”

mentioning

confidence: 99%

“…Unlike [8,33,34,35,36], the papers [10,11] deal with the confinement problem for a one-component plasma with an external magnetic field, which becomes infinite on a boundary. Equation 2is studied in the whole space R 3 , and the influence of boundary conditions to a solution of equation 2is not considered.…”

mentioning

confidence: 99%