A semi-analytical electrostatic dipole approach for systems of parallel metallic cylinders. (November 2020) - Islamov, Rafael Sh.
Highlights: The dipole simulation method is adapted to a system of parallel cylindrical conductors. The number of unknown charges remains unchanged during successive dipole imaging. Locations of the image dipoles are set strictly analytically. Maximum errors of the approximate solution decay exponentially with imaging stage. First few stages of dipole imaging give good accuracy for the maximum electric field. Abstract: A new semi-analytical approach is described for calculating the potential and electric field in a system of infinitely long parallel cylindrical conductors. The method is based on the dipole simulation technique and the method of successive dipole images. For a system of N conductors with predefined potential differences between them, this method leads to a linear system of n  =  N ( N –1)/2 equations for n unknown fictitious line dipole charges. The positions of these n pairs of dipole charges with equal and opposite sign and the images of these and successive dipoles inside the conductors are strictly predetermined using a well-known analytical solution for the cylinder-to-cylinder case of the charge problem. The electrostatic potential and electric field in each point of interest can be calculated by superposition the effects of all the introduced dipoles. The advantages of this formulation of the charge simulation method are a clear and fast algorithm, providing increased accuracy with the successive introduction of image dipoles, and self-validation capability. The results of sample calculations for various configurations and parameters are presented and the possibility of obtaining accurate results with exponential convergence is shown.