Spectral approximation based on Hermite-Fourier expansion of the Vlasov-Poisson model for a collisionless plasma in the electro-static limit is provided, by including high-order artificial collision operators of Lenard-Bernstein type. These differential operators are suitably designed in order to preserve the physically-meaningful invariants (number of particles, momentum, energy). In view of time-discretization, stability results in appropriate norms are presented. In this study, necessary conditions link the magnitude of the artificial collision term, the number of spectral modes of the discretization, as well as the time-step. The analysis, carried out in full for the Hermite discretization of a simple linear problem in one-dimension, is then partly extended to cover the complete nonlinear Vlasov-Poisson model.

翻译：根据Vlasov-Poisson无碰撞等离子体在静电极限中扩展的Vlasov-Poisson模型的光谱-四倍近似值,通过纳入Lenard-Bernstein型高分级人造碰撞操作器提供,这些有区别操作器的设计适当,目的是保存具有物理意义的异质物(粒子数量、动力、能量),鉴于时间分解,提出了适当的规范。在本研究中,必要的条件将人造碰撞术语的大小、离散的光谱模式的数量以及时间步骤联系起来。为一分解中简单的线性问题的Hermite离散而进行的全面分析随后部分扩展,以涵盖完整的非线性Vlasov-Poisson模型。