Active plasma resonance spectroscopy (APRS) is a process-compatible plasma diagnostic method, which utilizes the natural ability of plasmas to resonate on or near the electron plasma frequency. The multipole resonance probe (MRP) is a particular design of APRS that has a high degree of geometric and electric symmetry. The principle of the MRP can be described on the basis of an idealized geometry that is particularly suited for theoretical investigations. In a pressure regime of a few Pa or lower, kinetic effects become important, which cannot be predicted by the Drude model. Therefore, in this paper, a dynamic model of the interaction of the idealized MRP with a plasma is established. The proposed scheme reveals the kinetic behavior of the plasma that is able to explain the influence of kinetic effects on the resonance structure. Similar to particle-in-cell, the spectral kinetic method iteratively determines the electric field at each particle position, however, without employing any numerical grids. The optimized analytical model ensures the high efficiency of the simulation. Eventually, the presented work is expected to cover the limitation of the Drude model, especially for the determination of the pure collisionless damping caused by kinetic effects. A formula to determine the electron temperature from the half-width [Formula: see text] is proposed.

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The Multipole Resonance Probe (MRP) is an innovative sensor suitable for monitoring and control of industrial plasma processes. It is a realization of “active plasma resonance spectroscopy”, a class of electromagnetic diagnostic methods which employ the ability of plasmas to resonate on or near the plasma frequency. A signal in the GHz range is fed to the plasma via an electrical probe; the spectral response S(ω) is recorded, and then evaluated with a mathematical model to obtain information on the internal plasma parameters. In this study, a spectral kinetic model of the MRP is discussed. It is superior to previous analyses based on the Drude model, as it allows to determine not only the electron density ne but also the electron temperature Te from S(ω). Good agreement with independent measurements shows the suitability of the model.