Similarity-based scaling networks and energy transport analysis for breathing oscillations in magnetized discharges

In our previous work [Appl. Phys. Lett. 124, 194101 (2024)], we demonstrated the scale invariance of breathing oscillations and electron energization mechanisms in magnetized discharges at the kinetic level. This study further extends the concept of similarity-based scaling networks to magnetized plasmas through fully kinetic particle-in-cell simulations. A similarity-based scaling network is a tool for analyzing plasma characteristics under varying discharge conditions, enabling effective cross-comparisons, predictions, and control of breathing oscillation dynamics. By correlating plasma characteristics from the base state to similarity states, this approach systematically analyzes the impact of different discharge parameters on breathing oscillations. Using the second-order velocity moment of the Boltzmann equation, i.e., the energy transport equation, the impact of breathing oscillations on the energy transport behavior of charged particles is analyzed with kinetic precision. The findings reveal that increasing the reduced magnetic field B / p or the reduced length p d triggers breathing oscillations and reconstructs the spatial distribution of the potential, preventing electrons from effectively gaining energy in the sheath and requiring them to travel longer distances in the pre-sheath to accumulate sufficient energy for ionization. The onset and development of breathing oscillations significantly affect the processes of electron energy absorption, loss, and transport, resulting in reduced energy utilization efficiency due to inadequate thermalization and increased energy loss at the boundaries.