The stability and uniformity of a radio-frequency (RF) discharge is limited by a critical power density. Beyond this critical power density, instability occurs in the form of physical changes in the plasma (such as contraction due to arcing). The RF discharge used in this study is the non-equilibrium Atmospheric Pressure Plasma Jet (APPJ ® ) developed by Apjet, Inc. This discharge is known to operate uniformly in helium gas. However, for some proposed applications such as surface modification, there is a need to operate with reactive gases such as O 2 . Our experimental studies show that addition of molecular gas to a discharge operating in helium increases its power density (W cm −2 ), until it reaches the critical unstable arcing limit. Moreover, an increase in the frequency of operation (from 13 to 27 MHz) allows the plasma to sustain higher molecular gas concentrations and power densities before instability occurs. Further, it is observed that this critical power density is dependent on the type of molecular gas added. These results provide a motivation for the development of a mathematical model that can provide insight into the causes of instability and potential methods of suppression. The two commonly studied modes of instability are (1) thermal instability (TI) and (2) α-γ -arc mode transition. For the APPJ ® discharge conditions, the development time scales of TI are much longer (∼1 ms) as compared with discharge oscillation period (∼100 ns). Hence, if the instability was indeed thermal, discharge frequency increase would have no consequence, contrary to experimental findings. A 1D fluid model based on the local field approximation is developed to study instability in APPJ ® discharge. The analysis of modeling results confirmed our hypothesis that the instability development actually takes place via breakdown of sheath i.e. α-γ -arc mode transition and not by TI.

The stability and uniformity of a Radio-Frequency (RF) discharge is limited by a critical power density. Beyond this critical power density, instability occurs in the form of with physical changes in the plasma (such as contraction due to arcing). Levitsky' identified and studied the two glow modes, cx and y, of operation of an RF discharge. A detailed description of each mode can be found in the literature2.The RF discharge under consideration in the current study is the non-equilibrium Atmospheric Pressure Plasma Jet (APPJ®) developed by Apjet, Inc. This plasma operates uniformly in helium gas. However, for some proposed applications, such as surface modification, there is a need to operate with reactive gases such as 02. Experimentally, an increase in molecular gas concentration in helium increases the power density (W.cm-3) until it reaches the unstable arcing limit. Moreover, an increase in the frequency of operation (from 13 to 27 MHz) allows the plasma to sustain higher molecular gas concentrations and power densities before instability occurs. The critical power density is dependent on the type of molecular gas added. Addition of 02 makes the discharge more stable, while the addition of CO2 decreases stability.These results provide a motivation for the development of a model that can provide insight into the causes of instability and potential methods of suppression. The two commonly studied modes of instability are 1. thermal instability (TI), and 2. oc-y -arc, mode transition (AGAT). For our discharge conditions, the development time scales of TI are much longer (-1 ms) as compared to discharge oscillation period ( 100 ns). Hence, if the instability was indeed thermal, discharge frequency increase would have no consequence, contrary to experimental findings. A 1-D fluid model was developed with a local field approximation (LFA) assumption. The analysis of modeling results confirmed our hypothesis that the instability development actually takes place via breakdown of sheath i.e. AGAT and not the TI mode.