A general way to confined stationary Vlasov-Poisson plasma configurations
A general way to confined stationary Vlasov-Poisson plasma configurations
复制标题
约束静态弗拉索夫-泊松等离子体配置的通用方法
DOI：
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发表时间：
2020
影响因子：
1
通讯作者：
A. Skubachevskii
中科院分区：
文献类型：
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作者：
Yu. O. Belyaeva;Bjorn Gebhard;A. Skubachevskii
我们讨论了描述高温等离子体的Vlasov-Poisson方程组在区域$Omegasubsetmathbb{R}^[3]$上定态解的存在性，由于外磁场的影响，该等离子体在空间上被限制在$Omegasubsetmathbb {R}^[3]$的一个子区域内。在第一部分中，我们提供了这样一个存在的结果为一个广义系统的Vlasov-Poisson型和调查之间的关系的外部磁场的强度，限制的锐度和量的等离子体被限制在总电荷方面的测量。这里的关键工具是子/上解的方法和使用第一积分结合截止函数。在第二部分中，我们将这些一般的结果通常Vlasov泊松方程在三个不同的设置：无限和有限的圆柱，以及域与环形对称。这样，我们证明了存在的固定的解决方案相对应的两个组件的等离子体限制在镜陷阱，以及托卡马克。
We address the existence of stationary solutions of the Vlasov-Poisson system on a domain $Omegasubsetmathbb{R}^3$ describing a high-temperature plasma which due to the influence of an external magnetic field is spatially confined to a subregion of $Omega$. 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.