On the scaling laws for low-temperature plasmas at macro and micro scales

The theoretical background and historical development of the similarity theory during the past decades are reviewed. We demonstrate similar discharges in local and nonlocal kinetic regimes, taking the low-pressure capacitive radio frequency (rf) discharges and microdischarges as examples. By using fully kinetic particle-in-cell simulations, we verify the similarity law (SL) and show a violation of frequency scaling (f-scaling) in the low-pressure capacitive rf plasmas. The similarity relations for electron density and electron power absorption are confirmed in similar rf discharges. With only the driving frequency varied, the f-scaling for electron density is also validated, showing almost the same trend as the similarity 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. The scaling characteristics have also been comprehensively studied for microdischarges with dimensions from hundreds to several microns, with transition from secondary electron dominated regime to field emission regime. Finally, practical applications of the similarity and scaling laws are summarized.