Kinetic damping in the spectra of the spherical impedance probe

TL;DR

This paper derives an explicit response function for the spherical impedance probe using functional analytic methods, revealing kinetic damping effects in plasma spectra that align with previous kinetic analyses.

Contribution

It introduces a novel explicit response function for the spherical impedance probe derived through algebraic expansion, highlighting kinetic damping effects in plasma spectra.

Findings

Kinetic effects cause additional damping in the spectra.

The derived spectra agree with previous kinetic analyses.

The response function is obtained via an algebraic basis expansion.

Abstract

The impedance probe is a measurement device to measure plasma parameter like electron density. It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with an alternating potential is applied to the electrode and the response of the plasma is measured. Its dynamical interaction with the plasma in electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods. These methods provide the opportunity to derive a general solution, which is given as the response function of the probe-plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamical operator. Based on the general solution a residual damping for vanishing pressure can be predicted and can only be explained by kinetic effects. Within this manuscript an explicit response function of the spherical impedance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows to compute an approximated response function and its corresponding spectra. These spectra show additional damping due to kinetic effects and are in good agreement with former kinetically determined spectra.