PIC Simulations of Atmospheric Pressure Capacitive RF He/N$_2$ Discharges

Atmospheric pressure rf micro-discharges have been extensively studied, due to emerging applications, particularly in medical and related areas. Because of their small size, diagnostics are difficult. A previous work studied discharges with a helium feed gas and small admixture of N$_2$ by using a 1D hybrid analytical-numerical model [1]. But this model did not consider sheath breakdown phenomena, thus limiting its applicability to the lower power range. To overcome this, we perform 1D particle-in-cell (PIC) simulations of atmospheric pressure capacitve RF He/N$_2$ discharges and use the results to guide the development of a model for the $\gamma$ mode of the discharge. We noted from [1] that the dominant species in He/N$_2$ discharges with 0.1\% N$_2$ were N${_2}^+$ ions, electrons, and metastable helium atoms He$^*$. This enabled us to develop a simplified cross-section set only involving those three species.\\[4pt] [1] C. Lazzaroni, P. Chabert, M.A. Lieberman, A.J. Lichtenberg and A. Leblanc, Plasma Sources Sci. Technol. {\bf 21}, 035012 (2012).