论文标题
限制固定固定的Vlasov-Poisson等离子体配置的一般方法
A general way to confined stationary Vlasov-Poisson plasma configurations
论文作者
论文摘要
我们解决了vlasov-Poisson系统在域上的固定解决方案的存在，描述了高温等离子体的$ω\ subset \ mathbb {r}^3 $，由于外部磁场的影响，该溶液在空间上仅限于$ω$的子区域。在第一部分中，我们为Vlasov-Poisson类型的广义系统提供了这种存在的结果，并研究了外部磁场强度，限制的清晰度和根据总电荷测量的限制的等离子体量之间的关系。这里的关键工具是子/超溶液的方法，以及将第一积分与截止功能结合使用。在第二部分中，我们将这些一般结果应用于通常的三种不同设置的通常的vlasov-Poisson方程：无限和有限的圆柱体以及带有环形对称性的域。这样，我们证明存在与隔离镜陷阱中的两个组件血浆以及托卡马克相对应的固定溶液的存在。
We address the existence of stationary solutions of the Vlasov-Poisson system on a domain $Ω\subset\mathbb{R}^3$ 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.
