Radio frequency (RF) and microwave (MW) plasma jets operated at medium to high pressures are important tools in many branches of plasma technology. Plasma jets have several advantages over other reactor designs. They are of moderate size, mechanically robust, economical, and offer good control of the plasma conditions. Their capability of generating high fluxes of reactive species at low temperature makes them attractive for applications from surface modification to plasma medicine. The mathematical modelling of such jets is of high interest, both from a fundamental (physical) and from an application-oriented (engineering) view. Attempts in this direction, however, encounter serious obstacles. Plasma jets are transient, highly inhomogeneous systems far from (even local) thermodynamic equilibrium. They involve physical phenomena on vastly different length and timescales and exhibit high chemical complexity arising from the many species and reactions present. So far only very simplified models of plasma jets have ben presented, such as volume-averaged global models which concentrate on the chemical complexity of the discharges but neglect their physical and geometrical complexity, or spatially resolved finite volume models which address the physical and geometrical complexity but include only an oversimplified view of the chemistry. All these approaches generate valuable insight, but are not able to deliver quantitative accuracy. This project will follow a new strategy to construct efficient and at the same time quantitatively accurate mathematical models of RF and MW driven plasma jets. The fundamental idea is to exploit the pronounced geometrical characteristics of the devices, namely their extreme aspect ratio: While the typical length L of the jets is several centimeters, the typical diameter scale H is only a few millimeters. Taking the ratio e = H/L to be a smallness parameter, a multi-length scale approach is applied. A family of two-dimensional local models (in the transversal dimensions y and z) results which communicate along the flow-oriented longitudinal axis x. These local models are solved by analytical means and averaged over y and z and over the RF or MW phase. The final description takes the form of a system of one-dimensional partial differential equations which resolve both macroscopic scales, namely the longitudinal axis x and the slow reaction timescale t.

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