Micro atmospheric pressure gas discharges offer new applications in biomedical treatment and material processing . A global model is presented, which describes the bulk chemistry with wall looses and an electron temperature as a function of time. The chemical model is self-consistently coupled to an electrical model. The latter considers a capacitively coupled rf-discharge by means of a non-linear lumped circuit model which accounts for non-linear electron resonance heating . In this contribution a geometry, based on the micro atmospheric pressure plasma jet is considered. This device is investigated by {{V. Schulz-von der Gathen}} and co-workers at Ruhr-University Bochum. Various parameter studies are performed and results are shown for Helium as a working gas.\\[0.5 em] F. Iza, et al., Plasma Process. Polym.,\textbf {5}, 322 (2008)\\ D. Ziegler, et al., Physics of Plasmas,\textbf {16}, 023503 (2009)