Analytical and Numerical Study on the Characteristics at the $\alpha {-}\gamma$ Transition Point in Radio-Frequency Helium Discharges at Atmospheric Pressure

It is well accepted that increasing the frequency and reducing the electrode gap are effective ways to enhance the discharge stability in atmospheric radio-frequency (rf) discharges. In this paper, we explore a 1-D fluid model to investigate the discharge characteristics when the α-γ mode transition occurs. The differential equation satisfied at the α-γ mode transition point is given based on the governing equations. From the theoretical analysis and computational data, with an increase in the electrode gap, the power density coupled to the plasmas decreases, and the critical electron density modestly increases at the transition point; the electron temperature both in the sheath and bulk plasma decreases as the sheath shrinks. On the other side, as the frequency is raised, just at the mode transition point, the applied voltage reduces, and the plasma density increases almost exponentially with a higher electron temperature in the sheath. From the view point of application, the discharge driven by a high frequency at a narrow gap is desirable to produce a stable and high-density atmospheric plasma with a large power density coupled.