Breakdown Characteristics in Capacitive Radio-Frequency Discharge with an External Magnetic Field

Breakdown characteristics in low-pressure capacitive radio-frequency (rf) discharges are of fundamental importance for the development of plasma source facilities and the optimization of their operating conditions. Although the fundamental mechanisms have been largely revealed by experiments and numerical simulations, the effects of an external magnetic field on the breakdown behaviors are not yet fully understood because of the wide parameter regimes. In this work, breakdown voltages in rf discharges in the presence of a transverse magnetic field are quantified according to the balance between electron production and losses via electrostatic particle-in-cell (PIC) simulations. Double-valued rf breakdown voltages corresponding to a given gas pressure are observed on the left branch of Paschen's curve. The left branch shifts toward the lower-pressure region as the magnetic field increase. More importantly, we observed the split of the left branch into lower and upper branches, which are analyzed by using a semi-analytic model. Furthermore, the effects of magnetic field with the variation of gap distance and driving frequency on the breakdown characteristics and the similarity laws of rf breakdown are discussed.