Convergence analysis of an approximated response function of the impedance probe — •Jan Hendrik Röhl and Jens Oberrath — Institute of Product and Process Innovation, Modelling within Local Engineering, Leuphana University Lüneburg, 21339 Lüneburg, Germany

Active plasma resonance spectroscopy (APRS) is a widely used method to measure plasma parameters like electron density and electron temperature. In Plasmas of a few Pa measurements with APRS probes typically show a broadening of the spectrum due to kinetic effects. A general kinetic model in electrostatic approximation based on functional analytic methods has been presented to analyze the broadening in the spectra of these probes [1]. One of the main results is, that the system response function Y is given in terms of the matrix elements of the resolvent of the dynamic operator evaluated for values on the imaginary axis.

The dynamic operator is approximated by a huge matrix, which is given by a banded block structure. This structure allows to apply a block-based LU decomposition to determine the response function of the impedance probe with a minimum of computation time. However, a convergence analysis dependent on the dimension of the approximated matrix is necessary to analyze the final broadening of the spectra, especially in the collisionless case.