Calculation of the electric field distribution under the point-plane gap configurations using the FEM

In our previous work on the prebreakdown density change steamers in cyclohexane, we found that the structures of streamers differ by the tip radius of needle electrode and the applied voltage. We had considered that this might be caused by the difference of the field distribution between gap, and were eager to calculate it to make considerations on the phenomena. In this paper, we employed the finite element method (FEM) to calculate the field under point-plane gaps. The gap length and the plane diameter were set to 5 mm and 30 mm respectively, and the field distributions for the needles with tip radii ranging from 0.1 μm to 30 μm were calculated. Although employing the classical method, we had difficulties in the calculation caused by severe non-uniformity of the field. By employing an optimization method based on the potential lines, a mesh, which is a combination of approximately 5,000 triangular elements of different sizes differing from 10^-8 m to 10^-2 m, was obtained and we could calculate the field satisfactorily well. Using this calculation method, the field distribution at the streamer, inception voltage in cyclohexane obtained in our previous work was calculated and the mechanism of the steamer initiation is considered