Scale-invariant resonance characteristics in magnetized capacitive radio frequency plasmas

Resonance mechanisms have been found to be essential for the generation of high-density rf plasmas at low pressures, in which electrons can be continuously accelerated through multiple interactions with the oscillating rf sheaths. In this work, we report the scale-invariant resonance mechanisms, such as bounce resonance heating and plasma series resonance, in low-pressure capacitive rf plasmas in the presence of an external magnetic field. The generation conditions for the resonance mechanisms are determined via fully kinetic simulations. It is found that the resonance dynamical properties of single-frequency plasmas (e.g., a double-peak electron density vs magnetic field curve) can be exactly replicated at different scales when three combined control parameters, i.e., the reduced gap distance pd (pressure x distance), reduced driving frequency f/p (frequency divided by pressure), and reduced magnetic field B/p (magnetic field divided by pressure), are kept constant. The similarity relations for the electron density and electron power absorption in magnetized rf plasmas are numerically confirmed. Furthermore, the similarity and scale-invariant resonance characteristics are elucidated through the scaling of the Boltzmann equation with collisional terms for weakly ionized rf plasmas with a magnetic field, which is proven to be theoretically exact.