Considerations of the application of Ramoʹs theorem for segmented HPGe detector pulse-shape calculations

The application of Ramoʹs theorem for waveform simulations of segmented HPGe detector electrodes neglects the force between charge clouds as well as the influence of induced surface charges on the electrodes. For a planar detector geometry we show that this is indeed justified, where we calculate the electric field caused by the surface charge density based on the methods of mirror charges. With the same approach and in the same geometry we investigate an induced surface current on the electrodes, which mathematically disregards the detectorʹs segmentation. It is identified as a virtual surface current resulting from the way charge is transported to the outer circuit in the model of a perfect conductor. Since a mirror charge solution does not allow to include the boundary condition of electronic segmentation, we show for a simple segmented electrode that Ramoʹs theorem and the method of mirror charges are consistent.