SOLUTION OF AN INVERSE PROBLEM OF FINDING SURFACE CHARGE DENSITY WITH A KNOWN ELECTRICAL POTENTIAL USING COMSOL MULTIPHYSICS
Relevance Polymer materials capable of electric charge accumulation on their surface and in volume have wide application in a great number of applied problems of electrophysics and high-voltage engineering due to their excellent dielectric property. This property can be both an advantage (in electret manufacture), and a disadvantage (when using polymers as an isolating medium). Fundamentally important here is the need to characterize and control the degree of charge using the value of surface charge density which, however, can be determined indirectly through the electric potential only. When measuring the potential using a capacitive probe, difficulties arise in solving an inverse problem of converting the potential into surface charge density, since the relationship between these values largely depends on the geometry of the charged body and the capacitive probe. An effective and universal conversion method will greatly simplify the measurement of the surface charge density that will be helpful in practical tasks of electrical technology and operation of high-voltage equipment with elements made of polymer materials. Aim of research Aim of the research is to develop a technique for restoring surface charge density distribution according to a given measured distribution of electric potential created by the surface charge; give recommendations on how to achieve an optimal balance between accuracy and labor intensity of numerical calculations. Methods The problem is solved using numerical modeling in finite element method based software Comsol Multiphysics. With the help of the created 3D model containing the reproduced design of the capacitive probe and the charged examined material, the principle of the weight coefficients matrix formation is explained, through which the relationship between a discrete set of measured potentials and the unknown distribution of the surface charge density is subsequently established. Results An effective method has been developed to recalculate the known distribution of the electric potential from a charged surface into its surface charge density. The principle of constructing and setting the boundary conditions in the 3D model required for recalculation is shown. On the example of one given distribution of electric potential, the high efficiency of the method for obtaining the distribution of the charge density was shown. It has been established that the accuracy of the method increases with a finer partition of the charged surface into elementary charged areas. Recommendations are given on the use of methods for solving the arising systems of linear algebraic equations. It was also shown how to simplify the technique used in the presence of an axisymmetric distribution of the charge density.