Particle-in-Cell Simulations of the Alpha and Gamma Modes in Collisional Nitrogen Capacitive Discharges

We perform 1D particle-in-cell (PIC) simulations to study the $\alpha$ and $\gamma$ modes in an intermediate pressure (0.6 and 6 Torr), 2.5 cm gap capacitive nitrogen discharge driven at 13.56 MHz with current density amplitudes $J_0$=10 to 75 A/m$^2$. As in a previous study of a comparable argon discharge,[Kawamura et al, JVST A {\bf 38}, 023003 (2020)], the nitrogen discharge can be described by a ``passive bulk'' model in which the ionization is negligible in the central bulk region and is due solely to electron sheath heating. However, unlike the argon discharge, the nitrogen discharge undergoes an $\alpha$-$\gamma$ transition in the applied $J_0$ range due to secondary electron emission, characterized by an increase in density and a decrease in sheath widths. We introduce a theoretical $J_0$-$V_1$ transition curve, where $V_1$ is the sheath voltage amplitude at 13.56 MHz, giving the $\alpha$-$\gamma$ transition. We compare the PIC results in the $\alpha$-mode to the passive bulk model, and, in the $\gamma$-mode with the expected $J_0$-$V_1$ curve. We find reasonable agreement with the simulations in both the $\alpha$~and~$\gamma$ regimes, and the $\alpha$-$\gamma$ transition is reasonably well predicted by the model.