static green's functions for a bisected coaxial cavity

This paper deals with the three-dimensional potential equation in cylindrical coordinates and its Green's function for geometry close to a rather uncommon Time Projection Chamber field-cage, namely a bisected coaxial cavity. The methods used to derive the Green's function for a coaxial cavity (see [CERN-OPEN-2009-003]) were adapted to deduce novel representations for a bisected geometry, where the additional Dirichlet conditions in phi have to be fulfilled. The necessary modifications are described in detail. In combination, these three novel representations allow fast converging calculations of the electric field components and therefore for any desired space charge configuration within this cavity.