Magnetostatic-field solution for Tesla transformer’s coupling coefficient

Based on the Laplace equation in cylindrical coordinates, coefficient matrix equations of the magnetic field series expression were derived with magnetostatic method for the Tesla transformer. Thus, we obtained the axial magnetic field distributions of the magnetic cores, and the axial and radial magnetic field distributions between the cores. The average coupling coefficient was put forward, which is the average of every single secondary coil’s coefficient. Then we studied the influences of aspect ratio, radius ratio of outer to inner magnetic cores, length ratio of primary winding to magnetic core and relative permeability on the average coefficient. It is found that increasing aspect ratio and decreasing radius ratio are two effective ways to enhance the average coupling coefficient, i