The mathematical description of the interaction between a collisional plasma and an absorbing wall is a challenging issue. In this paper, we propose to model this interaction by considering a stationary bi-species Vlasov-Poisson-Boltzmann boundary value problem with boundary conditions that are consistent with the physics. In particular, we show that the wall potential can be uniquely determined from the ambipolarity of the particles flows as the unique solution of a nonlinear equation. We also prove that it is an increasing function of the electrons re-emission coefficient at the wall. Based on the Schauder fixed point theorem, our analysis establishes the existence of a solution provided, on the one hand that the incoming ions density satisfies a moment condition that generalizes the Historical Bohm criterion, and on the other hand that the collision frequency does not exceed a critical value whose definition is subordinated to the strict validity of our generalized Bohm criterion.

中文翻译：

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双物种Vlasov-Poisson-Boltzmann边值问题的碰撞鞘层解

碰撞等离子体与吸收壁之间相互作用的数学描述是一个具有挑战性的问题。在本文中，我们建议通过考虑具有与物理学一致的边界条件的平稳双物种Vlasov-Poisson-Boltzmann边值问题来对这种相互作用进行建模。尤其是，我们表明，壁势可以由颗粒流的双极性唯一确定，这是非线性方程的唯一解。我们还证明这是壁上电子再发射系数的增加函数。基于Schauder不动点定理，我们的分析建立了所提供解决方案的存在，一方面，入射离子密度满足概括历史Bohm准则的矩条件，