The effects of noise in particle-in-cell (PIC) and Vlasov simulations of the Buneman instability in unmagnetized plasmas are studied. It is found that, in the regime of low drift velocity, the linear stage of the instability in PIC simulations differs significantly from the theoretical predictions, whereas in the Vlasov simulations it does not. A series of highly resolved PIC simulations with increasingly large numbers of macroparticles per cell is performed using a number of different PIC codes. All the simulations predict highly similar growth rates that are several times larger than those calculated from the linear theory. As a result, we find that the true convergence of the PIC simulations in the linear regime is elusive to achieve in practice and can easily be misidentified. The discrepancy between the theoretical and observed growth rates is attributed to the initial noise inherently present in PIC simulations, but not in Vlasov simulations, that causes particle trapping even though the fraction of trapped particles is low. We show analytically that even weak distortions of the electron velocity distribution function (such as flattening due to particle trapping) result in significant modifications of the growth rates. It is also found that the common quiet-start method for PIC simulations leads to more accurate growth rates but only if the maximum growth rate mode is perturbed initially. We demonstrate that the quiet-start method does not completely remedy the noise problem because the simulations generally exhibit inconsistencies with the linear theory.
翻译:研究的是,在低漂移速度的制度中,石化模拟的不稳定线性阶段与理论预测大不相同,而在Vlasov的模拟中,情况并非如此。一系列高度解决的石化模拟,每个细胞的大型粒子数量越来越多,使用若干不同的石化代码进行。所有模拟都预测出非常相似的增长率比线性理论所计算的要高几倍。结果,我们发现线性系统中石化模拟的真正趋同在实践上难以实现,而且很容易被错误地确定。理论和观察到的增长率之间的差别,是由于石化模拟中固有的初始噪音,而不是Vlasov的模拟中,造成颗粒的陷阱,尽管被困颗粒的碎片很少。我们从分析上表明,电子速度分布功能(例如由于粒子捕捉而平坦缩)的扭曲程度甚至比线性要低几倍。我们发现,线性系统模拟中石化模拟的真正趋同性速度的趋同性速度,因为我们最初的理论导测算方法一般地表明,这种增长速度是平定的。我们发现,只有一种共同的模型推算方法才能使石化的增长率达到最接近的增长率。