A new finite-element analysis of an ionized field in coaxial cylindrical geometry

This communication aims at the analysis of a unipolar ionized field. An efficient iterative method that uses the finite element technique (FET) as a numerical tool is proposed. The method seeks a solution to only one second-order partial differential equation (PDE) rather than a solution to a nonlinear third-order PDE or a solution to two simultaneous second-order PDES. The effectiveness of the proposed method has been tested through application to the coaxial cylindrical geometry where the ionized field has been evaluated analytically. The voltage value at the stressed conductor as well as the constancy of the field at the onset value around the conductor represent the boundary conditions of the proposed method, which is characterized by quick convergence to achieve the accuracy and simplicity required for computer programming.