Multi-mode Striations in RF-driven He/2\%H2O Atmospheric Pressure Plasma (APP) Discharges

Previous 1D particle-in-cell (PIC) simulations of 1--4mm gap, He/2\%H2O atmospheric pressure plasmas (APP's) showed bulk striations. Assuming the ionization rate coefficient $K_{iz}\propto X^q$ with $X$ the reduced field, a striation model showed that $q<0$ is a necessary condition for the instability. A local calculation yielded $q>0$, implying that nonlocal electron kinetics are required for the instability. Wider gaps can fit a wider range of wavelengths $\lambda$, resulting in multi-mode striations. Previously, we assumed one mean $q$ value for each APP, and did not calculate $q$ for each mode separately. Here, we develop a wavelength resolved striation model and apply it to PIC simulations of 4 mm gap APP's with $J=0.04-0.30$ A/cm$^2$ at 27.12 MHz. We first examine the $J=0.23$ A/cm$^2$ case and observe a mixture of unstable modes within a window of $\lambda$. At shorter $\lambda$, the modes are suppressed by diffusion. At longer $\lambda$, a transition to locality occurs where $q$ becomes less negative with increasing $\lambda$, approaching its local positive value and stabilizing the modes. The unstable modes shift to shorter $\lambda$ at higher $J$ where they are suppressed by diffusion. At lower $J$, the decrease in density with decreasing $J$ suppresses the striations.