We verify the similarity law (SL) and show a violation of frequency scaling (f-scaling) in low-pressure capacitive radio frequency (rf) plasmas via fully kinetic particle-in-cell simulations. The SL scaling relations for electron density and electron power absorption are first confirmed in similar rf discharges. Based on these results, with only the driving frequency varied, the f-scaling for electron density is also validated, showing almost the same trend as the SL scaling, across most of the frequency regime. However, violations of the f-scaling are observed at lower frequencies, which are found to be relevant to the electron heating mode transition from stochastic to Ohmic heating. Electron kinetic invariance is illustrated for the SL and f-scaling being valid, respectively, whereas the electron kinetic variation is observed when the f-scaling is violated.

中文翻译：

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低压电容射频等离子体中的相似律和频率缩放

我们验证了相似定律 (SL) 并通过全动力学粒子在细胞模拟中显示了低压电容射频 (rf) 等离子体中频率缩放 (f-scaling) 的违反。电子密度和电子功率吸收的 SL 比例关系首先在类似的射频放电中得到证实。基于这些结果，只有驱动频率发生变化，电子密度的 f 缩放也得到验证，在大多数频率范围内显示出与 SL 缩放几乎相同的趋势。然而，在较低频率下观察到 f 标度的违反，这被发现与从随机加热到欧姆加热的电子加热模式转变有关。对于 SL 和 f 标度分别有效，说明了电子动力学不变性，