Scale-invariant breathing oscillations and transition of the electron energization mechanism in magnetized discharges

Scale-invariant breathing oscillations are observed in similar magnetized discharges at different spatiotemporal scales via fully kinetic particle-in-cell simulations. With an increase in the similarity invariant B/p, i.e., the ratio of magnetic field to pressure, breathing oscillations are triggered, leading to an appreciable time-averaged potential fall outside the sheath. With the onset and development of breathing oscillations, the electron energization mechanism shifts from sheath energization to direct Ohmic heating in the ionization region due to the change in the potential fall inside and outside the cathode sheath. Based on the scale invariance of the Boltzmann equation and its collision term, the characteristics of breathing oscillations and the transition of the electron energization mechanism are confirmed to be scale-invariant under similar discharge conditions.