Similarity of Low-Pressure Radiofrequency Discharges

Similarity transformations are commonly used for correlating discharges at different scales, which were mostly applied to regimes when the local field or energy approximations hold [1], [2]. Similarity transformations are essential for correlating discharges at different scales, which have, however, never been applied to nonlocal regimes, where electron energy relaxation length is much larger than discharge dimensions. In this work, based on particle-in-cell simulations we studied the similarity of the radio-frequency (RF) discharges in geometrically similar gaps. The scaling relations of the electron density, electron heating, and electron impact ionization rate are confirmed with a dimension scaling factor varying from 1 to 10. The invariance of electron energy probability functions in similar discharges is confirmed in time and space. The results indicate that the similarity characteristics of RF discharges still exist in nonlocal discharge regimes, even though the traditional similarity relations based on the local kinetic approximations do not apply. This work promotes further applications of similarity laws in discharges from fluidic to kinetic regimes.