A new reconstruction algorithm for Kerr electro-optic measurement of space charge in arbitrary geometries

Recently we used the onion peeling method to reconstruct the axisymmetric electric field distribution of point/plane electrodes from Kerr electro-optic measurements. The method accurately reconstructed the electric field from numerically generated data. However in the presence of experimental noise the performance was less satisfactory. The measurements were especially noisy and unstable near the needle tip which is also the most interesting region since most charge injection occurs here. In this paper we propose a new algorithm for Kerr electro-optic reconstruction of space charge in arbitrary geometries. The algorithm is built on the finite element method for Poisson´s equation and will be called the finite element based Kerr electro-optic reconstruction (FEBKER) hereafter. FEBKER is tested on a point/plane like simple artificial axisymmetric geometry. Research is underway for application of the method to actual axisymmetric point/plane experiments. The method is readily extendible to arbitrary three dimensional geometries