  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.

Plasma Physics