Generalizing Similarity Laws for Radio-Frequency Discharge Plasmas across Nonlinear Transition Regimes

We generalize similarity theory based on the scaling and solution invariance of the Boltzmann equation, coupled with the Poisson equation, and demonstrate similarity laws for radio-frequency (rf) discharge plasmas across three nonlinear transitional regimes, namely, the alpha-gamma mode transition, the stochastic-Ohmic-heating mode transition, and the bounce-resonance-heating mode transition. Fundamental plasma parameters, e.g., the electron power absorption, under similar discharge conditions are examined via fully kinetic particle-in-cell simulations, and electron-kinetic invariance is exemplified in similar rf discharge plasmas. The results unambiguously confirm the applicability of similarity laws for rf plasmas in extended operating regimes, and strengthen the foundations and framework of similarity physics with universality.