Nonlinear lumped circuit modeling of an atmospheric pressure rf discharge

The subject of our modeling approach is a specifically modified version of the atmospheric pressure plasma jet (APPJ, originally proposed by Selwyn and coworkers$^1$) with reduced discharge volume, the \emph{micro} atmospheric pressure plasma jet ($\mu$-APPJ). The $\mu$-APPJ is a homogeneous nonequilibrium discharge operated with Argon or Helium as the feedstock gas and a percentage volume admixture of a molecular gas (O$_2$, H$_2$, N$_2$). The efficiency of the discharge is mainly due to the dissociated and activated molecules in the effluent that can be selected depending on the application. A variety of applications in surface treatment have already been demonstrated, e.g., in semiconductor technology, restoration and bio-medicine. In this contribution we present and analyze a nonlinear lumped circuit model of the $\mu$-APPJ. We apply a two-scale formalism. The bulk is modeled by a generalized Ohm's law, whereas the sheath is described on a considerably higher level of mathematical sophistication. The main focus lies on the spectrum of the discharge current in order to support the characterization of the discharge via model-based diagnostics, i.e., the estimation of the spatially averaged electron density from the frequency of certain self-excitated collective resonance modes.\par \noindent J. Park et al., Appl. Phy. Lett. {\bf 76}, 288 (2000)