The planar Multipole Resonance Probe (pMRP) is a measurement device for plasma processes, especially suited for industrial applications. Due to its planar design, the probe can be mounted directly into a chamber wall of a reactor and offers the ability to monitor the plasma during the process. The calculation of plasma parameters requires an appropriate mathematical model to obtain a proportional relation between the resonance and the plasma parameters. A fluid model of the probe-plasma interaction offers the ability to calculate the electron density by measuring the resonance frequency. The information of the electron temperature can be obtained by analyzing another resonance parameter like e.g. the half width of the resonance peak. However, it requires a kinetic description of the resonance phenomenon. In this work a kinetic model, adapted to the pMRP, is analyzed using functional analytic methods. An approximated solution for the admittance of the probe-plasma interaction will be investigated and a study of the influence of the truncation on the resonance spectrum will be shown.

The authors gratefully acknowledge funding by the German Research Foundation (DFG) within the project OB 469/1-1.