圆柱形Langmuir探针双物种动力学模型解的存在性
Existence of solutions for a bi-species kinetic model of a cylindrical Langmuir probe
摘要：
本文研究了圆柱形金属朗缪尔探针附近等离子体的无碰撞动力学模型。该模型由一个双种群Vlasov-泊松方程组成，该方程位于两个圆柱体之间的区域中，具有预定的边界条件。内部圆柱体模拟探针，而外部圆柱体模拟与等离子体核心的相互作用。我们证明了该模型的弱-强解的存在性，即我们得到了2个Vlasov方程的弱解和泊松方程的强解。文章的第一部分致力于解释模型，并进行详细的研究弗拉索夫方程。本文将泊松方程转化为一维非线性非局部方程，并利用迭代不动点方法证明了该方程存在强解.
英文摘要：
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 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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