Planar Multipole Resonance Probe: A Functional Analytic Approach

Michael Friedrichs, Sebastian Wilczek, Junbo Gong, Ralf Peter Brinkmann, Jens Oberrath

WELT­PP-19, De­cem­ber 1-2, 2016 at Rol­duc, Kerk­ra­de, the Nether­lands


Abstract

Measuring plasma parameters, e.g. electron density and electron temperature, is an important procedure to verify the stability and behavior of a plasma process. For this purpose, the multipole resonance probe (MRP) represents a promising design. However, the influence of the probe on the plasma through its physical presence makes it unattractive for some processes in industrial application.

Combining a planar design and the benefits of the spherical MRP, a solution, fitting for industrial applications, is given by the planar version of the MRP (pMRP).

To analyze the resonance behavior of the pMRP the cold plasma model is coupled to Poisson’s equation. Based on this model an analytical expression for the admittance of the probe-plasma system can be derived by means of functional analytic methods [1,2]. It is adjusted to the design of the pMRP in cylindrical geometry and the corresponding spectra are presented and discussed.

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