The effect of collisions on driven electrostatic phase space vortices is analyzed by means of Eulerian simulation for two different collision models. It was demonstrated recently [P. Trivedi and R. Ganesh, Phys. Plasmas 23, 062112 (2016)] that in the absence of collisions, at late times, steady state phase space vortices manifest to form a plateau in the resonant region of the particle velocity distribution function, due to trapping of particles supporting multiextrema giant phase space vortices (PSVs). In the presence of collisions, over long time, this multiextrema plateau are found to smooth out, since collisions drive the velocity distribution toward Maxwellian, irrespective of how weak the collisions are as long as they are non-zero. In these conditions, kinetic processes and collisionality are found to be in competition, and the evolution of the plasma is found, therefore, to be a result of nontrivial combination of these two effects. An attempt has been made by means of numerical simulations to study the effect of weak collisionality on the electrostatic driven phase space vortices with two types of collision operators: (1) Bhatnagar–Gross–Krook (Krook) collision operator, where the colliding particles can be treated as isolated pairs and, (2) Fokker–Planck (FP) type collision operator (Zakharov–Karpman) in one dimension, where many weak collisions lead to particle diffusion in velocity space. It is shown that depending on the collision model used, the nature of smoothing in velocity space of giant PSVs results in qualitatively very different phase space structures. However, irrespective of the collision model used, excess density fractions over 10% are retained.

中文翻译：

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一维弱耗散 Vlasov-Poisson 系统中的驱动静电相空间涡旋

通过两种不同碰撞模型的欧拉模拟，分析了碰撞对驱动静电相空间涡旋的影响。它最近得到了证明 [P. Trivedi 和 R. Ganesh，物理学。Plasmas 23, 062112 (2016)]，在没有碰撞的情况下，在后期，稳态相空间涡流显现，在粒子速度分布函数的共振区域形成平台，这是由于粒子的捕获支持多极值巨相空间涡流 (PSV)。在存在碰撞的情况下，随着时间的推移，发现这种多极值平台变得平滑，因为碰撞将速度分布推向麦克斯韦分布，无论碰撞有多弱，只要它们不为零。在这些条件下，发现动力学过程和碰撞在竞争，因此，发现等离子体的演化是这两种效应的非平凡组合的结果。已经尝试通过数值模拟来研究弱碰撞对静电驱动相空间涡旋的影响，具有两种类型的碰撞算子：（1）Bhatnagar-Gross-Krook（Krook）碰撞算子，其中碰撞粒子可以被视为孤立对和， (2) 一维 Fokker-Planck (FP) 型碰撞算子 (Zakharov-Karpman)，其中许多弱碰撞导致粒子在速度空间中扩散。结果表明，根据所使用的碰撞模型，巨型 PSV 速度空间中的平滑性质导致质量上非常不同的相空间结构。但是，无论使用哪种碰撞模型，都会保留超过 10% 的过量密度分数。